Method for predicting coating state, prediction device, prediction program, and recording medium

Abstract

By considering the movement and rotation of particulate components during the drying process, the accuracy of predicting the position and orientation of particulate components in the dry coating is improved. [Solution] In a drying model for obtaining a dry coating by drying a wet coating containing non-spherical particulate components, the model takes shape information of the particulate components and orientation information including the angle and proportion of the particulate components in the wet coating as input information, and includes the steps of dividing the calculation area of ​​the wet coating into a plurality of calculation grids, performing a calculation of the movement of the particulate components in the coating, performing a calculation of the diffusion state and volatilization amount of the solvent, assuming the particulate components as spheres circumscribed therein, and detecting at least one of the overlap between the spheres and the upper surface of the calculation grid, the overlap between the spheres and the bottom surface of the calculation grid, and the overlap between one sphere and another sphere, and if an overlap is detected, translating and rotating the particulate components to eliminate the overlap by the shortest distance.

Description

[Technical Field]

[0001] This disclosure relates to a method for predicting the state of a coating film, a prediction apparatus, a prediction program, and a recording medium. [Background technology]

[0002] One painting technique involves a coating process in which a solvent-containing paint is applied to a substrate, followed by a drying process in which the solvent is evaporated by heat, thereby forming a paint film on the substrate. In such painting techniques, the state of the paint film after drying can affect the performance of the painted parts. Therefore, conventionally, computer simulations have been performed on models of the coating process and drying process to predict the state of the paint film, with the aim of obtaining the conditions necessary to obtain an appropriate paint film in a short time.

[0003] For example, Patent Document 1 discloses a method for determining the solvent drying rate of a coating solution containing a solvent and a polymer as an actual measured value, deriving the solvent diffusion coefficient from that solvent drying rate using the Regular Regime theory and the flux comparison method, and simulating the residual solvent ratio in the coating solution.

[0004] Patent Document 2 describes a method for obtaining a porous coating film (porous body) by applying a paste containing particles, a solvent, and a binder to a substrate, and then drying the solvent to form voids between the particles. Furthermore, in this method, it is disclosed that the drying state of the coating film is predicted by considering solvent movement driven by capillary pressure within the porous body, phase change from liquid to gas phase of the solvent, and solvent movement by diffusion in the gas phase during the decay drying period in which the evaporation rate of the solvent decreases.

[0005] Furthermore, Patent Document 3 discloses a method for estimating the orientation state of pigments, which involves setting the orientation state of pigments at the time of paint application and calculating the orientation state of pigments at a predetermined time after application based on the shrinkage rate gradient during the drying process of the paint. [Prior art documents] [Patent Documents]

[0006]

Patent Document 1

Patent Document 2

Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0007] By the way, in ADAS (Advanced Driving Assistance System) and autonomous driving technology in automobiles, sensor units that sense distance, speed, and obstacles using electromagnetic waves are provided on bumpers and the like of vehicles. A plurality of coating films are stacked on the surface of the vehicle body to form a surface coating, which is intended to protect the vehicle body and improve its design. However, since the coating film contains particulate components that impede the transmission of electromagnetic waves, it is difficult to install the sensor unit behind the coating film. Therefore, the sensor unit is generally covered with a coating film different from that of the vehicle body surface in view of electromagnetic wave permeability and installed separately. If the coating film on the vehicle body surface can achieve both design and electromagnetic wave permeability, the sensor unit can be installed behind it, and the design of the vehicle body can be improved.

[0008] Therefore, in the present disclosure, in a coating film state prediction method, prediction device, prediction program, and recording medium, for a coating film containing non-spherical particulate components, the problem is to improve the prediction accuracy of the position and orientation of the particulate components in the dry coating film by considering the movement and rotation of the particulate components in the drying process. Further, by enabling the control of the particles in the coating film using this technology, the problem is to obtain a coating film that can achieve both high design and electromagnetic wave permeability.

Means for Solving the Problems

[0009] To solve the above problems, one aspect of the coating film state prediction method disclosed herein is A method for predicting the state of a dry coating film after drying using computer simulation, In a drying model in which a wet coating film formed by applying a paint containing non-spherical particulate components and a solvent to a substrate surface is dried to obtain a dry coating film, The input information includes the shape information of the particulate component, orientation information including the angle and proportion of the particulate component in the wet coating, and physical property information of paint components other than the particulate component. The steps include dividing the computational domain of the wet coating into multiple computational grids, The steps include: performing a calculation of the movement of the particulate components in the paint; The steps include: performing calculations of the diffusion state and volatilization amount of the solvent; Assuming the particulate component is a sphere circumscribing it, the calculation of the movement of the particulate component includes the step of detecting at least one of the following: the overlap between the sphere and the upper surface of the computational grid, the overlap between the sphere and the bottom surface of the computational grid, and the overlap between one sphere and another sphere. The method is characterized by comprising the step of, if an overlap is detected, translating and rotating the particulate components to eliminate the overlap over the shortest distance.

[0010] As a result of diligent research, the inventors of this application have found that when simulating the drying process of a wet coating film formed by applying a paint containing non-spherical particulate components and a solvent to a substrate surface, it is useful to calculate the diffusion and volatilization behavior of the solvent, and to consider not only the parallel movement but also the rotational movement of the particulate components in order to improve the accuracy of predicting the position and orientation angle of the particulate components in the dry coating film after drying.

[0011] In wet coatings, non-spherical particulate components initially consist mostly of particles with a large angle to the substrate immediately after application. However, as the solvent evaporates, particles with a smaller angle become more prevalent. This change in the orientation of non-spherical particulate components during the drying process is influenced by solvent parameters such as the evaporation rate. Therefore, it is important to calculate the behavior of non-spherical particulate components in conjunction with the diffusion and evaporation behavior of the solvent.

[0012] Furthermore, in the actual wet coating, particulate components may collide with the top or bottom surface of the coating or with each other during the drying process, and it is thought that these collisions can change the direction of movement. Therefore, in this prediction method, if any overlap between the top or bottom surface of the computational grid and particulate components, or overlap between particulate components, is detected, the overlap is resolved by translating and rotating the particulate components. This makes the movement of the particulate components closer to actual movement, thereby improving the accuracy of predicting the position and orientation angle of particulate components in the dry coating. For overlap detection, the calculation can be simplified and computation time and cost can be reduced by assuming that the particulate components are circumscribing spheres.

[0013] Preferably, the shape information includes the average major axis and average minor axis of the particulate component.

[0014] Preferably, the translation and rotational translation are calculated using the horizontal vector component and the rotational vector component obtained from the center of gravity of the particulate component and the center of gravity of the overlapping region.

[0015] In a coating model in which a coating containing particulate components and a solvent is applied to a substrate surface to form a wet coating, The process preferably includes a step of setting coating conditions and calculating the coating state of the paint applied to the substrate surface from the coating device, and the thickness of the wet coating and the solid content of the coating obtained in this step are used as input information for performing the computer simulation in the drying model described above.

[0016] According to this embodiment, by setting appropriate computational models for the coating model and the drying model, and analyzing them in a coupled manner, it is possible to improve the accuracy of the entire calculation process from coating to drying. Furthermore, by inputting the information obtained from the coating model simulation into the drying model simulation and performing the two types of simulations sequentially, computational efficiency can be improved.

[0017] The movement of the particulate components is preferably derived using Stokes' equation, which derives the terminal velocity of the particles.

[0018] The position of particulate matter as it moves affects the amount of solvent evaporated and the overlap of the particulate matter. By considering the buoyancy and sinking of the particulate matter and calculating its detailed behavior, the coordinates of the particulate matter can be calculated with high accuracy. By considering these coordinates, it becomes possible to determine the amount of solvent evaporated that is closer to the actual value.

[0019] In this embodiment, it is preferable to output the coordinates and orientation angles of each particulate component in the dry coating film.

[0020] From this output information, it is possible to predict whether or not a dry coating can transmit electromagnetic waves, and whether or not its appearance is good. Furthermore, by coupling this output information with further calculation methods, it is thought that it will be easier to calculate, for example, the dispersion state of a filler that can transmit electromagnetic waves, and the dispersion state and orientation angle of a filler that can achieve high aesthetic appeal.

[0021] One embodiment of the coating state prediction device disclosed herein is: A device for predicting the state of a dry coating film after drying using computer simulation, In a drying model in which a wet coating film formed by applying a paint containing non-spherical particulate components and a solvent to a substrate surface is dried to obtain a dry coating film, The input information includes the shape information of the particulate component, orientation information including the angle and proportion of the particulate component in the wet coating, and physical property information of paint components other than the particulate component. A computational grid forming unit that divides the computational area of ​​the wet coating into a plurality of computational grids, A particle coordinate calculation unit that performs calculations for the movement of the particulate components in the paint, A volatilization amount calculation unit that performs calculations of the diffusion state and volatilization amount of the solvent, Assuming the particulate component is a sphere circumscribing it, the system includes an overlap detection unit that detects at least one of the following in the movement calculation of the particulate component: the overlap between the sphere and the upper surface of the computational grid, the overlap between the sphere and the bottom surface of the computational grid, and the overlap between one sphere and another sphere. The device is characterized by comprising an overlap resolution unit that, when an overlap is detected, moves the particulate components in parallel and rotation to resolve the overlap over the shortest distance.

[0022] According to this embodiment, when the drying process of a wet coating film formed by applying a paint containing non-spherical particulate components and a solvent to a substrate surface is the subject of simulation, the accuracy of predicting the state of the dry coating film after drying can be improved by considering not only the parallel movement of the particulate components but also the rotational movement of the particulate components in the computational grid.

[0023] One aspect of the coating state prediction program disclosed herein is: A program for predicting the state of a dry coating film after drying using computer simulation, On the computer, Using a drying model in which a wet coating film formed by applying a paint containing non-spherical particulate components and a solvent to a substrate surface is dried to obtain a dry coating film, The input information includes the shape information of the particulate component, orientation information including the angle and proportion of the particulate component in the wet coating, and physical property information of paint components other than the particulate component. The computational domain of the wet coating is divided into multiple computational grids, Perform a calculation of the movement of the particulate component in the paint. The system is instructed to perform calculations on the diffusion state and volatilization amount of the aforementioned solvent. Assuming the particulate component is a sphere circumscribing it, in the calculation of the movement of the particulate component, at least one of the following is detected: the overlap between the sphere and the upper surface of the computational grid, the overlap between the sphere and the bottom surface of the computational grid, and the overlap between one sphere and another sphere. When an overlap is detected, the particulate components are moved in parallel and rotation to eliminate the overlap over the shortest distance.

[0024] According to this embodiment, when the drying process of a wet coating film formed by applying a paint containing non-spherical particulate components and a solvent to a substrate surface is the subject of simulation, the accuracy of predicting the state of the dry coating film after drying can be improved by considering not only the parallel movement of the particulate components but also the rotational movement of the particulate components in the computational grid.

[0025] One aspect of the recording medium disclosed herein is: This is a computer-readable recording medium on which the above-mentioned program for predicting the state of the coating film is stored. [Effects of the Invention]

[0026] As described above, according to this disclosure, when simulating the drying process of a wet coating formed by applying a paint containing non-spherical particulate components and a solvent to a substrate surface, the accuracy of predicting the state of the dry coating after drying can be improved by considering not only the parallel movement but also the rotational movement of the particulate components in the calculation of the movement of the particulate components in the computational grid. [Brief explanation of the drawing]

[0027] [Figure 1] This is a diagram illustrating the coating process, the drying process, and their models. [Figure 2] This figure shows an example of the configuration of a coating state prediction device related to this disclosure. [Figure 3]This is an example of a flowchart for the coating process of the coating film state prediction method described herein. [Figure 4] This is an example of a flowchart for the drying process of the coating film state prediction method related to this disclosure. [Figure 5] This figure shows an example of a computational grid. [Figure 6] This diagram illustrates the particle duplication correction process. [Figure 7] This diagram illustrates the particle duplication correction process. [Figure 8] This diagram illustrates the particle duplication correction process. [Figure 9] This diagram illustrates the particle duplication correction process. [Figure 10] This diagram illustrates the particle duplication correction process. [Figure 11] This diagram illustrates the particle duplication correction process. [Figure 12] This diagram illustrates the particle duplication correction process. [Figure 13] This diagram illustrates the particle duplication correction process. [Figure 14] This diagram illustrates the particle duplication correction process. [Figure 15] This graph shows the volatilization rates of mixed solvents prepared at various mixing ratios. [Figure 16A] This is a schematic front view of the computational grid and the particulate components protruding from its top surface. [Figure 16B] This is a schematic top view of the computational grid and the particulate components protruding from its top surface. [Modes for carrying out the invention]

[0028] Embodiments of the present disclosure will be described in detail below with reference to the drawings. The following description of preferred embodiments is illustrative in nature and is not intended to limit the present disclosure, its applications, or its uses in any way.

[0029] The technology disclosed herein comprises a coating step of applying a paint containing a solvent onto a substrate, and a drying step of drying and curing the paint while volatilizing the solvent by heat, and can be applied to all methods of forming a coating film on a substrate.

[0030] <coating film> The coating film used as the target of the prediction method of this disclosure is formed by drying a paint containing non-spherical particulate components, a solvent, and a resin binder. The paint is not particularly limited as long as it can form a coating film by volatilizing the solvent, but examples include paints used to impart heat shielding, heat resistance, design properties, etc., to a substrate. In the following description, the coating film containing the solvent before drying is referred to as a wet coating film, and the coating film after drying, when the solvent has been volatilized, is referred to as a dry coating film.

[0031] The type, shape, and particle size of non-spherical particulate components can be appropriately selected depending on the application of the coating film. Non-spherical refers to a shape with an aspect ratio greater than 1, for example. The aspect ratio is the ratio of the length of the major axis to the length of the minor axis of a particle (length of major axis / length of minor axis). The major axis is the longest diameter of the particulate component, and the minor axis is the shortest diameter of the particulate component. Examples of non-spherical particulate components include disc-shaped, elliptical, flake-shaped, rod-shaped, columnar, plate-shaped, needle-shaped, and fibrous shapes. In the case of disc-shaped particulate components, the diameter (particle size) may be considered the major axis and the thickness the minor axis.

[0032] When considering automotive surface coatings and other applications as a base material, and a metallic sheen is desired, it is preferable to use a glossy material such as aluminum flakes as a non-spherical particulate component. When using aluminum flakes, the aspect ratio (average particle size / average thickness) is preferably between 30 and 300. The average particle size can be obtained, for example, by determining D50, which is the 50th percentile value of the particle size distribution measured by a laser diffraction particle size distribution analyzer. The average particle size is preferably the number-average particle size. The average thickness can be obtained, for example, by observing with a scanning electron microscope, measuring the thickness of multiple (e.g., 50) particulate components, and calculating the average value.

[0033] As the solvent, various organic solvents capable of dissolving the resin binder can be used. One solvent may be used alone, or two or more may be mixed. Examples of solvents include hydrocarbon solvents such as xylene, toluene, hexane, and heptane; ester solvents such as ethyl acetate, butyl acetate, and ethylene glycol monomethyl ether acetate; ether solvents such as ethylene glycol monomethyl ether and ethylene glycol diethyl ether; alcohol solvents such as butanol, propanol, octanol, cyclohexanol, and diethylene glycol; and ketone solvents such as methyl ethyl ketone and methyl isobutyl ketone. While not intended to limit the solvents, hydrocarbon solvents and alcohol solvents are preferred.

[0034] The resin binder is not particularly limited as long as it can form a coating film, but for example, when considering the surface coating of an automobile as the substrate, an acrylic resin can be preferably used.

[0035] The base material is not particularly limited and can be of various shapes and uses.

[0036] <Coating film formation method> Figure 1 shows a series of steps in which a coating step S1 is performed in which a paint 20 containing a solvent 21 and non-spherical particulate components 22 is applied to a substrate 10, followed by a drying step S2 in which the paint is dried and cured while the solvent is evaporated at room temperature and by heating, thereby forming a dry coating film on the substrate.

[0037] [Coating process] In coating step S1, a wet coating film 40 is formed by applying paint 20 to the substrate 10 using a coating device 30. The coating method is not particularly limited, and coating may be done using a brush or spatula, but here we give an example in which a spray gun is used as the coating device 30 to spray and coat the substrate 10 from above. In the prediction method of this disclosure, a simulation is performed in the coating model of coating step S1 to calculate the coating state of the paint applied from the coating device to the substrate surface. Details of the calculation will be described later, but the coating model analyzed in coating step S1 includes a paint atomization model that calculates the spray gun 30 and the sprayed paint, a mist paint volatilization model that calculates the paint after it has been sprayed from the spray gun 30, and a coating bounce model of paint particles on the substrate surface.

[0038] [Drying process] The drying step S2 includes a step of drying the wet coating 40 at room temperature and a step of accelerating the hardening of the wet coating 40 by volatilizing the solvent with heat. Heat drying is generally carried out by placing the substrate in a heating oven, for example, but it may also be carried out by placing heat sources on both sides of the substrate. In the prediction method of this disclosure, following the calculation of the coating step S1, calculations regarding the behavior of particulate components in the wet coating, solvent diffusion and volatilization are performed in the drying step S2. Details of the calculations will be described later, but the drying model analyzed in this drying step S2 includes a particle motion model and a solvent diffusion model that use the wet coating as the calculation target.

[0039] <Coating film state prediction device> Figure 2 shows an example of the configuration of the coating state prediction device 100 (hereinafter also referred to as "prediction device 100") according to this disclosure. The prediction device 100 is a CAE (Computer Aided Engineering) system with a computer 110 as its basic configuration. The prediction device 100 is a device that predicts the state of a dry coating after drying by analyzing the particulate components and solvent in the coating using the finite element method through computer simulation.

[0040] This prediction device 100 sprays paint using a spray gun and predicts the coordinates and orientation angles of non-spherical particles in the dry coating film formed by the evaporation of the solvent through computer simulation. Note that the prediction device 100 shown in Figure 2 is merely an example of a coating film state prediction device according to this disclosure, and the device configuration is not limited to this example.

[0041] The prediction device 100 includes a storage unit 120 consisting of, for example, ROM, RAM, or a hard disk, and a processor 130 (arithmetic unit) consisting of, for example, a CPU. The prediction device 100 also includes a display unit 140 consisting of, for example, a display, an input unit 150 consisting of, for example, a keyboard, and a reading unit 160 for acquiring information stored in various recording media 170. The storage unit 120 and / or recording media 170 store information such as programs for arithmetic processing and various analysis data. The processor 130 can function as a wet coating information calculation unit 131 for executing a coating model, a calculation grid formation unit 132 for executing a drying model, a particle coordinate calculation unit 133, a volatility calculation unit 134, a dry coating information calculation unit 135, a duplicate detection unit 136, and a duplicate resolution unit 137. The processor 130 performs various arithmetic processing based on the above information stored in the storage unit 120, information input via the input unit 150, and information acquired from the recording media 170 via the reading unit 160. Furthermore, this prediction device 100 is configured to communicate with external devices via an interface (not shown).

[0042] The memory unit 120 stores various programs. It also stores model information, including coating models and drying models. This model information includes, for example, information showing a model of the substrate to be coated. The memory unit 120 also stores information regarding coating and drying conditions. The data stored in the memory unit 120 can be modified and added by the user. Furthermore, the memory unit 120 also stores various calculation results generated by the execution of various programs.

[0043] <Method for predicting the state of the coating film> The method for predicting the state of a coating film according to this disclosure (hereinafter also referred to as "this prediction method") is a method for analyzing a coating film using the finite element method through computer simulation, and is performed, for example, using the prediction device 100 described above.

[0044] [Coating Model] The wet coating film formation process in the coating process is calculated using a coating model. Figure 3 is an example of a flowchart for the coating film state prediction method in the coating process according to this disclosure. In the coating process S1, this prediction method performs three-dimensional fluid analysis (3D-CFD) using the coating model. The Navier-Stokes equations are used as the governing equations for the fluid analysis. In this embodiment, the thermal fluid analysis program CONVERGE from Convergent Science Inc. was used as the calculation software for this simulation, but other software such as icon-CFD from IDAJ Corporation, and Star-CD or Star-CCM+ from Siemens can also be used. As shown in Figure 3, in the coating process, this prediction method comprises a coating condition setting process S11, a numerical analysis process S12, a wet coating film information calculation process S13, and a wet coating film information output process S14.

[0045] Specifically, first, various physical properties of the paint are input, along with the spray particle size and spray speed obtained from actual measurements using a spray gun. Then, in the coating condition setting step S11, coating conditions such as the spray angle of the spray gun, the distance from the tip of the spray gun to the substrate surface (gun distance), the viscosity coefficient of the paint, surface tension, heat of vaporization, vapor pressure, thermal conductivity, density, specific heat, and viscosity after coating are set.

[0046] Next, in numerical analysis step S12, the coating state of the paint applied from the spray gun to the substrate surface is calculated by three-dimensional fluid analysis using a coating model. The coating model includes a paint atomization model that calculates the spray gun and the sprayed paint, a mist paint volatilization model that calculates the paint after it has been sprayed, and a coating bounce model of paint particles on the substrate surface.

[0047] The paint atomization model is a model that simulates the further atomization of paint particles atomized at the tip of a spray gun due to instability caused by the density difference between the gas phase. Specifically, the RT (Rayleigh-Taylor) model was used. The calculation formulas used in the paint atomization model are shown in the following formulas (1) and (2).

[0048]

Number

[0049] In Formulas (1) and (2), r c is the particle diameter of the paint particle, C RT is a constant, g t is the acceleration, ρ f is the paint density, ρ g is the gas phase density, and σ is the surface tension of the paint.

[0050] The atomized paint volatilization model is a model that simulates how paint particles volatilize from the tip of a spray gun until they adhere to the substrate surface. Specifically, the Frossling model was used. Considering the mass transfer between droplet vapors, Formulas (3) to (6) below were used for the atomized paint volatilization model.

[0051]

Number

[0052] In Formulas (3) to (6), D is the mass diffusion coefficient between droplet vapors, Y k * is the mass fraction of vapor at the droplet surface, Y k is the mass fraction of vapor in the mainstream, Sh d is the Sherwood number, M is the molecular weight, p is the vapor pressure, X is the mole fraction, and T is the temperature of the droplet. B is a coefficient used in the mathematical formula for evaporation. When the mass fraction of vapor in the mainstream Y k is smaller than the mass fraction of vapor at the droplet surface Y k * the droplet radius decreases. The evaporation amount is related to the mass fraction Y k *It depends on Y. k * The vapor pressure p is entered from the literature values ​​for each solvent. vap And determined by the molecular weight M.

[0053] The model of paint particle adhesion and rebound on the substrate surface is calculated using the Weber number (We number), a dimensionless number that describes the adhesion behavior of droplets, as shown in equation (7) below.

[0054]

number

[0055] In equation (7), L is the particle size of the paint particles, V is the velocity of the paint particles, ρ is the paint density, and σ is the surface tension of the paint.

[0056] Once the numerical analysis process S12 is completed, the wet coating information calculation process S13 calculates wet coating information such as the thickness of the wet coating and the amount of coated solids (NV) based on the analysis results of the numerical analysis process S12.

[0057] The wet coating information calculated in the wet coating information calculation step S13 is output in the wet coating information output step S14. Of the wet coating information, the film thickness and the amount of coated solids (NV) are used as input information for performing simulations in the drying model. In Figure 3, the flowchart ends in the wet coating information output step S14, but the coating model and the drying model may be coupled.

[0058] [Dry Model] The dry film formation process during drying is calculated using a drying model. In the embodiments described below, the wet film contains aluminum flakes, which are a glossing agent, as non-spherical particulate components. The wet film may also contain pigments and additives, but these are treated as solid components, similar to the resin binder.

[0059] Figure 4 is an example of a flowchart in the drying process of the coating state prediction method according to the present disclosure. As shown in Figure 4, the prediction method uses a drying model and comprises a drying condition setting step S21, a computational grid creation step S22, a particle overlap correction step S23, a porosity calculation step S24, a Brownian motion calculation step S25, a particle terminal velocity calculation step S26, a particle overlap correction step S27, a porosity calculation step for each layer S28, a solvent volatilization amount calculation step S29, a solvent transfer calculation step S30, a film thickness update step S31, a drying process completion determination step S32, and a dry coating information output step S33.

[0060] Specifically, the inputs include, first, the film thickness and coated solids content (NV) of the wet coating obtained from the analysis of the coating model, and as shape information of particulate components, for example, the average major diameter (maximum diameter) and average minor diameter (minimum diameter) of the glossy material, the minimum and maximum thickness of the glossy material, orientation information including the angle and proportion of the glossy material in the wet coating, particle size distribution of particulate components, viscosity of components other than the glossy material (solvent, resin binder, pigment, etc.), density of each component, volatilization rate and diffusion coefficient of the solvent, and interaction coefficient of each solvent in the mixed solvent. For the shape information of particulate components, the average diameter and average thickness may be input depending on the shape of the particles. The orientation information including the angle and proportion of particulate components in the wet coating is, for example, an angle distribution where the horizontal axis is the angle and the vertical axis is the proportion or frequency of particles at that angle. The angle distribution can be derived by measuring the surface of the wet coating frozen with liquid nitrogen immediately after coating the substrate using a laser microscope, and then performing image analysis. The viscosity of components other than the luminescent material (solvent, resin binder, pigment, etc.) is the viscosity corresponding to the change in solvent volume and is an experimentally obtained value. The diffusion coefficient of the solvent is the diffusion coefficient corresponding to the change in solvent volume and is an experimentally obtained value. As an example of input information, Table 1 shows the input information used in this embodiment. Table 1 includes the setting conditions set in the drying condition setting step S21.

[0061] [Table 1]

[0062] When the coating model and drying model are coupled, the information obtained from the analysis of the coating model can be applied to the drying model, and input information other than that obtained from the coating model may be input at the start of the coating model. When the coating model and drying model are not coupled, the inputs required for the drying model may be values ​​obtained from separate calculations or experiments.

[0063] Then, in the drying condition setting step S21, drying conditions are set such as the initial cell (computational grid) size reflecting the information on the film thickness of the wet coating, the number of time steps and step intervals, temperature setting, pressure setting, the volume fraction of each component reflecting the information on the amount of solids coated (NV), and the contribution of particulate components that protrude from the surface of the coating to the solvent evaporation rate.

[0064] Next, in the calculation grid creation step S22, a calculation grid with the cell size set in the drying condition setting step S21 is created as the calculation domain for the wet coating film. An example of a calculation grid is shown in Figure 5. The calculation grid is created with width x, depth y, and height z as the film thickness, and is divided into multiple calculation grids in the xy and z directions. It is assumed that a mixed solvent of multiple types of solvents is diffused and present at the set concentration. Furthermore, it is assumed that there are a number of non-spherical particulate components within these multiple calculation grids calculated by the volume ratio and particle size, and these are placed at positions determined using the random number generation command XSRAND and the random number seed Xorshift, with the angle distribution and particle size distribution specified by the input information. Since the random number seed is a constant value, the position of each particle is reproduced each time even if the same program is run.

[0065] Next, in the particle overlap correction step S23, for particulate components placed in the computational grid in the computational grid creation step S22, at least one of the following is detected: overlap between particulate components and the top surface of the computational grid, overlap between particulate components and the bottom surface of the computational grid, and overlap between one particulate component and another particulate component, and the overlap is eliminated. By eliminating the overlap in this step, it is possible to approximate the actual arrangement of particulate components, and especially when coupling the coating model and the drying model, it becomes possible to ensure consistency between the end of the coating model and the start of the drying model.

[0066] Specifically, as shown in Figure 6, first, the particulate component is assumed to be a sphere circumscribing it, or a sphere Ni,Nj with a diameter equal to the major axis of the particulate component. A simplified determination is then made for at least one of the following: the overlap between the sphere and the top surface of the computational grid (coating surface), the overlap between the sphere and the bottom surface of the computational grid (coating plane), and the overlap between one sphere and another. The position correction is then performed. The effect can be obtained by detecting and resolving any one of the overlaps with the top surface, the bottom surface, or the overlap between spheres. However, to further improve the calculation accuracy, it is preferable to detect and resolve all of these overlaps. In the initial simplified overlap determination and correction process, the calculation can be simplified by assuming that non-spherical particulate components are circumscribing spheres, thereby reducing calculation time and cost.

[0067] In Figure 6, the sphere Ni has radius ri and coordinate (x i ,y i ,z i ), the sphere Nj has radius rj and coordinate (x j ,y j ,z j ), dz is the amount of protrusion in the z-axis direction, and Lp is the allowable amount of protrusion, where Lp = r ij × Allowable protrusion ratio prtlim, the thick arrow indicates the z-axis direction correction process according to the amount of protrusion. If the amount of protrusion exceeds the allowable protrusion amount, an overlap is detected, and the protrusion correction process is performed by moving in the z-axis direction. For overlap with the coating surface, it is possible to set the allowable amount by which the sphere protrudes from the coating surface, as follows: -z j = 1.01 × (dz-rj ×prtlim) As shown, the sphere is corrected by moving it in the -z direction by 1% of the distance obtained by subtracting the length determined by the ratio of the sphere's radius from the allowable protrusion amount. For overlap with the bottom surface of the coating, the allowable protrusion amount is 0, and the following equation zi = 1.01 × ri As shown, the correction is made by moving the sphere in the z direction by 1% of its radius.

[0068] Regarding the overlap of spheres, as shown in Figure 7, the diameter of sphere i is 2r, based on the coordinates of the particles and their diameters. i Within the range, the diameter of sphere j is 2r j If an overlap exists, that is, if an overlap of two spheres is detected, the distance R between the spheres is calculated using the coordinates of the two particles from equation (8) below, and from equation (9) below, the coordinates x, y, and z of each sphere are shifted by a random number XSRND × coefficient × (ratio of overlap distance to inter-particle distance) on the straight line connecting the centers of the two spheres i and j.

[0069]

number

[0070] In equation (8), R is the interparticle distance, x i y i z i x is the coordinate of particle i, x j y j z j is the coordinate of particle j. In equation (9), X is the initial x-direction cell size (m), r i r is the radius of particle i. j is the radius of particle j. Equation (9) allows us to find the x-coordinate of particle i after its movement. The y-coordinates and z-coordinates of particle i, and the x-coordinates, y-coordinates and z-coordinates of particle j can be found in the same way as in equation (9).

[0071] Next, a coordinate scan is performed within the non-spherical particulate components to determine in detail the overlap between the particulate components and the coating surface, and the overlap between the particulate components and the coating bottom surface. Specifically, as shown in Figure 8, the scanning mesh pitch set before the calculation is reflected in the region of a sphere circumscribing the non-spherical particulate components 22, and it is checked whether the non-spherical particulate components protrude from the coating surface or the coating bottom surface for each mesh section. In Figure 8, the check marks indicate mesh sections that were determined to protrude within the non-spherical particulate components 22.

[0072] Thus, if it is determined that there is overlap between particulate components and the coating surface, and overlap between particulate components and the bottom surface of the coating, the particulate components are moved linearly and rotationally by vector calculation. Specifically, for example, regarding the overlap between particulate components and the coating surface, as shown in Figure 9, first, a vector t is obtained that is perpendicularly downward from the centroid C2 of the mesh section in which particulate component 22 protrudes most significantly from the coating surface. Next, a vector b is obtained from the centroid C1 of particulate component 22 to the centroid C2. Next, the vector t is decomposed into components, and as shown in Figure 10, the vector t is obtained as the vector component of vector t perpendicular to vector b. ⊥b We determine the particulate component 22 as vector t. ⊥b Then, move it vertically. Also, vector b and vector t ⊥b We find the vector d obtained by the addition of vectors d and b. We find the angle θ in the zy-plane and the angle φ in the xy-plane formed by vectors d and b, and rotate the particulate component 22 by these angles θ and φ.

[0073] Detailed determination of overlap between particulate components is shown in Figure 11. First, the scanning region is determined from the coordinate values ​​of the spheres circumscribing each of the particulate components 22i and 22j. The selection of the spatial scanning region is set to the minimum possible overlap range + α. The smallest x-coordinate of the outer diameter of particulate component 22i is given by x0 = px1 - area[i]. The minimum x-coordinate of the outer diameter of particulate component 22j is given by dx = px2 - area[j]. In that case, The larger of x0 and dx is selected. if (dx > x0) x0 = dx The maximum x-coordinate of the outer diameter of particulate component 22i is given by x1 = px1 + area[i]. The maximum x-coordinate of the outer diameter of particulate component 22j is given by dx = px² + area[j]. In that case, The smaller of x1 and dx is selected if(dx <x1)x1=dxとする。 This calculation determines the scanning region shown by the dashed rectangle in Figure 11. Within this scanning region, region A where two particulate components overlap is identified as an overlap. Next, the centroid position of region A, which has been identified as an overlap, is determined. The centroid position of overlapping region A is calculated by dividing the sum of the mesh coordinates identified as overlaps by the number of mesh sections identified as overlaps.

[0074] If it is determined that there is overlap between particulate components, the direction for eliminating the overlap is then determined. Specifically, as shown in Figures 12 and 13, for each of the particulate components 22i and 22j, the direction for eliminating the overlap is determined to be the region where the other particulate component does not exist, and the centroid position C of the overlapping region A. A The position that is the shortest distance from is scanned again to determine the direction of overlap elimination. Note that, unlike the overlap elimination process when the particulate component is assumed to be spherical, the scanning area is wider by two divisions of the scanning mesh pitch, taking into account that the particulate component will rotate afterward. In Figure 12, the rectangle with a dashed line shows the scanning area, and C Ai The centroid C of the overlapping region is the region where particle j does not exist, as seen from particle i, and is the region at the minimum distance from the centroid CA of the overlapping region A. A This is the planned destination, C Aj This is the region where particle i does not exist, as seen from particle j, and is the centroid position C of the overlapping region A. A The centroid C of the overlapping region, which is the closest to the centroid C. A This is the planned destination.

[0075] Next, the particulate components 22i and 22j are moved linearly and rotationally, respectively, using vector calculations. Specifically, taking the particulate component 22i as an example, as shown in Figure 13, which is an enlarged view of the overlapping region A in Figure 12, first, the centroid position C of the overlapping region A is... ATherefore, the planned point C of the centroid of the overlapping region, which was determined earlier, is now located there. Ai We find the vector t to [the point]. Next, we find the centroid C of the particulate component 22i from the centroid Ci. A Find the vector b to . Next, decompose the vector t into its components, and find the vector component of vector t that is perpendicular to vector b. ⊥b We find the particulate component 22i into vector t. ⊥b Then, move it vertically. Also, vector b and vector t ⊥b We find the vector d obtained by the addition of vectors d and b. We find the angle θ in the zy-plane and the angle φ in the xy-plane formed by vectors d and b, and rotate the particulate component 22 by these angles θ and φ. We do the same for the other particulate component j.

[0076] Through the above process, at least one of the following is detected: overlap between particulate components and the top surface of the computational grid, overlap between particulate components and the bottom surface of the computational grid, and overlap between one particulate component and another. The overlap is then resolved by translating and rotating the particulate components using vector calculations.

[0077] Next, in the porosity calculation step S24, the porosity of each layer within the computational grid is calculated. Here, porosity is the ratio of particulate components and components other than nanoparticles, i.e., resin binder and solvent, within the computational grid. Porosity = (Volume of resin binder and solvent) / Volume of the entire calculation grid That is the case.

[0078] Next, in the Brownian motion calculation step S25, the movement of particulate components in the paint is calculated. Specifically, the particulate components are moved in their x, y, and z directions by Brownian motion, and the coordinates after the movement are calculated using the random number generation command XSRAND and the diffusion coefficient. The calculation formula for Brownian motion is shown in equation (10), and the calculation formula for the coordinates after the movement is shown in equation (11).

[0079]

number

[0080] In equation (10), D is the diffusion coefficient of the particulate component, k is the Boltzmann constant, T is the temperature, μ is the viscosity, and a is the radius of the particulate component. In equation (11), D is the diffusion coefficient of the particulate component, s is the time step (seconds), x int The initial x-axis cell size (m), V x This represents the partial coordinate position relative to the cell size.

[0081] Next, in the particle terminal velocity calculation step S26, the movement of particulate components in the paint is calculated. Specifically, using Stokes' equation (12) below, the movement of the particles by floating and sinking is calculated from the difference between the settling of the particulate components due to gravity and the flow of solvent around the particles. In equation (12), if the viscosity η (Pa·s) is high, the resistance increases and the particles become more difficult to move.

[0082]

number

[0083] In formula (12), ν s is the terminal velocity of the particulate component, p p D is the density of particulate components. p is the particle size of the particulate component, p f η is the fluid density (components of the coating other than particulate matter), and η is the viscosity.

[0084] Next, in the particle overlap correction step S27, the same process as in the particle overlap correction step S23 is performed to detect at least one of the overlaps between particulate components and the bottom surface of the computational grid, and the overlap between one particulate component and another particulate component, and to eliminate the overlap. In the actual wet coating, particulate components may collide with the top or bottom surface of the coating or with each other during the drying process, and it is thought that the direction of movement will change due to these collisions. Therefore, in this step, if any one of the overlaps between the top and bottom surfaces of the computational grid and particulate components, or overlaps between particulate components, is detected, a process is performed to eliminate the overlap by translating and rotating the particulate components. This makes the movement of the particulate components closer to actual movement, and improves the accuracy of predicting the position and orientation angle of particulate components in the dry coating.

[0085] Next, in the porosity calculation step S28 for each layer, the porosity is calculated for the computational grid of each layer in the z-axis direction. The porosity is the ratio of particulate components to components other than nanoparticles within the computational grid, similar to the porosity calculation step S24.

[0086] Next, in the solvent volatilization calculation step S29, the amount of solvent volatilizing from the top surface of the computational grid, which is located at the outermost layer, is calculated, assuming that the solvent volatilizes from the top surface. Specifically, the volatilization rate of a single solvent, or, if the solvent is a mixture of multiple solvents, the interaction coefficients of each solvent in the mixture, are used as input information, and the amount of solvent volatilizing from the top surface of the computational grid is calculated by calculating the following equation (13) as the volatilization calculation equation.

[0087]

number

[0088] In equation (13), n is an integer greater than or equal to 1, indicating that n types of solvents, from the first solvent to the nth solvent, are used. Jn is the amount of solvent n volatilized in the computational grid located at the outermost layer, Rn is the volatilization rate when solvent n is a single solvent, S is the area of ​​the top surface of the computational grid located at the outermost layer, Δt is the time step, Cn is the molar concentration of solvent n, and α is the interaction coefficient of solvent n in the mixed solvent when the solvents are mixed solvents. The interaction coefficient α is the driving force for solvent movement and diffusion.

[0089] In equation (13), the interaction coefficient α is an experimentally determined value. Figure 15 shows graphs of experimentally obtained and calculated volatilization rates when a mixed solvent of hydrocarbon solvent A and alcohol solvent B is prepared at various mole fractions. As shown by the dashed line in Figure 15, if we assume that hydrocarbon solvent A and alcohol solvent B are an ideal solution with no interaction between them, the volatilization rate and mole fraction will be proportional. However, in reality, interactions exist between the solvents, so the volatilization rate and mole fraction are not proportional. Experimentally, the weight change was measured while volatilizing a mixed solvent of hydrocarbon solvent A and alcohol solvent B at room temperature, and the value of the volatilization rate as a function of the mole fraction of the mixed solvent was obtained. As shown in Figure 15, the interaction coefficient α of each solvent in the mixed solvent can be derived from the experimentally obtained relationship between the volatilization rate and the mole fraction of the mixed solvent. For example, in this example of a mixed solvent of hydrocarbon solvent A and alcohol solvent B, the volatilization rate of hydrocarbon solvent A is 0.067 g / (m³). 2 s) The interaction coefficient of xylene in a mixed solvent of hydrocarbon solvent A and alcohol solvent B is 0.92, and the volatilization rate of alcohol solvent B is 0.052 g / (m³). 2 s) In a mixed solvent of hydrocarbon solvent A and alcohol solvent B, the interaction coefficient of alcohol solvent B is 0.69.

[0090] In equation (13), the area S is determined based on the coordinates of the particulate components obtained by particulate component movement calculations such as the Brownian motion calculation step S25, the particle terminal velocity calculation step S26, and the particle overlap correction step S27. Figures 16A and 16B show schematic diagrams of the computational grid A located at the outermost layer and particulate components 22 protruding from the upper surface a of the computational grid, with Figure 16A being a front view and Figure 16B being a top view. The solvent can volatilize in the area of ​​the upper surface a of the computational grid located at the outermost layer, but as shown in Figures 16A and 16B, if the particulate components 22 protrude from the upper surface a, the volatilization of the solvent will be hindered by the area occupied by the particulate components. Therefore, when the particulate components 22 protrude from the upper surface a, it is preferable that the area from which the solvent can volatilize is obtained by subtracting the sum of the areas occupied by the particulate components protruding from the upper surface a of the computational grid located at the outermost layer (shaded area in Figure 16).

[0091] Next, in the solvent transfer calculation step S30, the solvent concentration is assumed to decrease as it moves from the calculation grid on the substrate side to the calculation grid on the surface side (in the z-axis direction of the calculation grid), and the calculation of solvent transfer and diffusion is performed. Specifically, the diffusion coefficient as a single solvent is experimentally determined and input, and the solvent transfer and diffusion state is calculated by calculating the following equation (14) as the volatile flux calculation equation (Fick equation).

[0092]

number

[0093] In equation (14), Dn is the diffusion coefficient of solvent n, x is the position in the z-axis direction on the computational grid, J'n is the amount of solvent n transferred between layers (between computational grids), and Cn is the molar concentration of solvent n. Since the solvent concentration decreases from the computational grid on the substrate side to the computational grid on the surface side (in the z-axis direction of the computational grid), in equation (14), the concentration c with respect to position x has a negative gradient, and J has a positive value.

[0094] Next, in the film thickness update step S31, based on the calculation results of the solvent volatilization calculation step S29 and the solvent transfer calculation step S30, the volume of the computational grid reduced by the amount of volatilization, the coordinate values ​​of the particulate components, and the concentration of the paint are updated, and the film thickness (the z-axis length of the entire computational grid) is also updated.

[0095] Next, in the drying process completion determination step S32, it is determined whether the drying process is complete based on whether the specified number of steps have been executed. If the specified number of steps have not yet been executed, the process returns to the porosity calculation step S24 and performs calculations for all time steps. At this point, various film thickness information may be output in time history format.

[0096] Once calculations are complete for all time steps, the dry coating information output process S33 outputs the position coordinates and orientation angles of each particulate component in the dry coating from the final calculation results. Specifically, the relative position coordinates (x,y,z) of each particulate component with respect to the dry coating, along with the first angle θ and the second angle φ, are output.

[0097] In the above configuration, the movement of non-spherical particulate components in the computational grid considers not only the translation but also the rotational movement of the particulate components, thereby improving the accuracy of predicting the position and orientation angle of the particulate components in the dry coating film after drying. When the top and bottom surfaces of the computational grid overlap with particulate components, or when particulate components overlap with each other, the process of resolving the overlap by translating and rotating the particulate components makes the movement of the particulate components closer to actual movement, thereby improving the accuracy of predicting the position and orientation angle of the particulate components in the dry coating film. For overlap detection, the calculation can be simplified and computation time and cost can be reduced by assuming that the particulate components are circumscribing spheres.

[0098] <Applications of coating film state prediction methods> In the coating state prediction method configured as described above, the positional information and orientation angle of the filler are obtained as output information. By using this output information and coupling it with further calculation methods, it is thought that it will be easier to calculate, for example, the dispersion state of a filler that can transmit electromagnetic waves, or the dispersion state and orientation angle of a filler that can obtain high aesthetic appeal. Requirements for the simulation software to be coupled include the ability to use the finite element method, the presence of electromagnetic configuration relationships and a UI (User Interface) that can use them, and the ability to handle three-dimensional shapes. Examples of products include COMSOL Multiphysics from COMSOL, HFSS from Ansys which is capable of electromagnetic field analysis (FEM), and Speos from Ansys which is capable of aesthetic appeal analysis.

[0099] <Program for predicting coating state and recording medium thereof> At least a portion of each step of the prediction method described above is programmed as a program for predicting the state of the coating film. That is, the program for predicting the state of the coating film according to this disclosure is a program that causes a computer to execute the following steps of each of the above steps: the computational grid creation step S22, the overlap correction steps S23 and S27, the Brownian motion calculation step S25, the particle terminal velocity calculation step S26, the solvent volatilization amount calculation step S29, and the solvent transfer calculation step S30 in the drying step S2. The analysis program may also be configured to cause the computer to execute the steps of other steps in addition to the above steps. Specifically, for example, the analysis program may be configured to execute each step of the drying step S2 following each step of the coating step S1, or it may be configured to execute only the drying step S2 independently. This analysis program can be stored in, for example, a storage unit 120 and executed by a processor 130. Furthermore, the analysis program is not limited to being stored in the storage unit 120, but can also be recorded on various well-known computer-readable recording media such as optical discs or magnetic tape media. Then, by attaching such a recording medium to the reading unit 160 and reading the analysis program, the program can be executed. [Industrial applicability]

[0100] This disclosure is extremely useful because it can improve the accuracy of analysis when dealing with coatings formed by paints containing particulate components, in a method for predicting the state of a coating, a prediction device, a prediction program, and a recording medium. [Explanation of Symbols]

[0101] 10 Base material 20 paint 21 Solvent 22 Particulate components 100 Coating film state prediction device 130 Processor (Arithmetic Unit) 131 Wet coating information calculation unit 132 Computational grid formation part 133 Particle Coordinate Calculation Unit 134 Volatility calculation unit 135 Dry coating information calculation unit 136 Duplicate detection unit 137 Duplication Resolution Section 170 Recording media S1 Coating process S2 Drying process S11 Setting of coating conditions S12 Numerical Analysis Process S13 Wet coating information calculation process S14 Wet coating information output process S21 Drying condition setting process S22 Computational grid creation process S23 Duplicate correction process S24 Porosity calculation process S25 Brownian motion calculation process S26 Particle terminal velocity calculation process S27 Duplicate correction process S28 Porosity calculation process S29 Solvent Volatility Calculation Process S30 Solvent transfer calculation process S31 Film Thickness Renewal Process S32 Termination Decision Process S33 Dry coating information output process

Claims

1. A method for predicting the state of a dry coating film after drying using computer simulation, In a drying model in which a wet coating film formed by applying a paint containing non-spherical particulate components and a solvent to a substrate surface is dried to obtain a dry coating film, The input information includes the shape information of the particulate component, orientation information including the angle and proportion of the particulate component in the wet coating, and physical property information of paint components other than the particulate component. The steps include dividing the computational domain of the wet coating into multiple computational grids, The steps include: performing a calculation of the movement of the particulate components in the paint; The steps include: performing calculations of the diffusion state and volatilization amount of the solvent; Assuming the particulate component is a sphere circumscribing it, the calculation of the movement of the particulate component includes the step of detecting at least one of the following: the overlap between the sphere and the upper surface of the computational grid, the overlap between the sphere and the bottom surface of the computational grid, and the overlap between one sphere and another sphere. The process includes the step of, if an overlap is detected, translating and rotating the particulate components to eliminate the overlap by the shortest distance. A method for predicting the state of a coating film, characterized by the following features.

2. In claim 1, The shape information includes the average major axis and average minor axis of the particulate component. A method for predicting the state of a coating film, characterized by the following features.

3. In claim 1, The aforementioned translation and rotation are calculated using the horizontal and rotational vector components obtained from the center of gravity of the particulate components and the center of gravity of the overlapping region. A method for predicting the state of a coating film, characterized by the following features.

4. In a coating model in which a coating containing the particulate component and the solvent is applied to the surface of a substrate to form the wet coating film, The method includes a step of setting coating conditions and performing a fluid analysis to calculate the coating state of the paint applied to the substrate surface from the coating device, and using the film thickness of the wet coating and the solid content of the coated paint obtained in this step as input information for performing the prediction method described in claim 1. A method for predicting the state of a coating film, characterized by the following features.

5. In claim 1, A method for predicting the state of a coating film, characterized in that the movement of the particulate components is derived using Stokes' equation for deriving the terminal velocity of the particles.

6. In claim 1, Output the coordinates and orientation angles of each particulate component in the dry coating. A method for predicting the state of a coating film, characterized by the following features.

7. A device for predicting the state of a dry coating film after drying using computer simulation, In a drying model in which a wet coating film formed by applying a paint containing non-spherical particulate components and a solvent to a substrate surface is dried to obtain a dry coating film, The input information includes the shape information of the particulate component, orientation information including the angle and proportion of the particulate component in the wet coating, and physical property information of paint components other than the particulate component. A computational grid forming unit that divides the computational area of ​​the wet coating into a plurality of computational grids, A particle coordinate calculation unit that performs calculations for the movement of the particulate components in the paint, A volatilization amount calculation unit that performs calculations of the diffusion state and volatilization amount of the solvent, Assuming the particulate component is a sphere circumscribing it, the system includes an overlap detection unit that detects at least one of the following in the movement calculation of the particulate component: the overlap between the sphere and the upper surface of the computational grid, the overlap between the sphere and the bottom surface of the computational grid, and the overlap between one sphere and another sphere. The system includes an overlap removal unit that, when an overlap is detected, moves the particulate components in parallel and rotates them to eliminate the overlap by the shortest distance. A device for predicting the state of a coating film, characterized by the following features.

8. A program for predicting the state of a dry coating film after drying using computer simulation, On the computer, Using a drying model in which a wet coating film formed by applying a paint containing non-spherical particulate components and a solvent to a substrate surface is dried to obtain a dry coating film, The input information includes the shape information of the particulate component, orientation information including the angle and proportion of the particulate component in the wet coating, and physical property information of paint components other than the particulate component. The computational domain of the wet coating is divided into multiple computational grids, Perform a calculation of the movement of the particulate component in the paint. The system is instructed to perform calculations on the diffusion state and volatilization amount of the aforementioned solvent. Assuming the particulate component is a sphere circumscribing it, in the calculation of the movement of the particulate component, at least one of the following is detected: the overlap between the sphere and the upper surface of the computational grid, the overlap between the sphere and the bottom surface of the computational grid, and the overlap between one sphere and another sphere. If overlap is detected, the particulate components are moved in parallel and rotation to eliminate the overlap along the shortest distance. A program for predicting the state of a coating film, characterized by the following features.

9. A computer-readable recording medium that stores the coating state prediction program described in claim 8.

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