Droplet collision dynamic behavior prediction method

Abstract

The invention discloses a liquid drop collision dynamic behavior prediction method, which comprises the following steps of S1, analyzing a relationship between stress and deformation of an elastomer in a collision process of liquid drops, and establishing a dynamic model of a first liquid drop and a second liquid drop in the collision process; s2, solving the kinetic model according to the initial distance and the initial speed of the first liquid drop and the second liquid drop to obtain the speed of the first liquid drop and the second liquid drop and the sphere center distance in the collision process, and further calculating the interaction force of the first liquid drop and the second liquid drop in the collision process; s3, calculating the surface tension when the interaction force of the liquid drops in the collision process reaches the maximum value; and S4, determining the fusion condition of the liquid drops according to the surface tension when the interaction force of the liquid drops in the collision process reaches the maximum value. The method is simple in calculation and high in accuracy, fusion and splitting behaviors of the liquid drops can be predicted, and a calculation result is matched with experimental data.

Description

Technical Field

[0001] The invention belongs to the interdisciplinary field of fluid mechanics and interface science, and specifically relates to a method for predicting the dynamic behavior of droplet collision. Background Art

[0002] The importance of droplet collision research in daily life and industrial production is increasingly recognized. The emergence of bionics has further promoted the development of superhydrophobic surfaces. Studying the collision behavior of droplets on superhydrophobic surfaces helps to deepen the understanding of the movement patterns and interaction mechanisms of droplets on complex surfaces. Yi et al. studied binary droplet collisions by considering temperature changes. The researchers elucidated the effect of temperature on the aggregation of binary droplets after collision on superhydrophobic surfaces by examining three different cases: room temperature to room temperature, high temperature to high temperature, and room temperature to high temperature. As the temperature of the droplets increases, the collision of two droplets tends to aggregate. Nilsson et al. studied the effect of contact angle hysteresis on droplet aggregation and mixing, and identified three different aggregation mechanisms based on the Weber number and impact angle. Mertaniemi et al. used experimental methods to demonstrate the distribution of different states after collision on superhydrophobic surfaces, and established liquid logic gates using the rebound characteristics of droplets after collision.

[0003] So far, many scholars have studied the collision behavior of freely moving droplets from the perspective of droplet size ratio, collision parameters and Weber number through theoretical analysis, numerical simulation and experimental methods. Amani et al. proposed five different collision results by numerically simulating the collision phenomenon of freely moving droplets, and studied the energy distribution during the droplet collision process. Al-Dirawi et al. studied the evolution of the collision behavior of droplets with equal diameters but different viscosities, and proposed a theoretical model to predict the collision state boundary of droplets with different viscosities. Pan et al. used computational simulation to study the collision dynamics of two identical droplets, proposed the concepts of soft collision and hard collision, and analyzed the influence of van der Waals force on droplet aggregation. Pal et al. used numerical simulation to analyze the head-on collision of two droplets in the evaporation state, and established an evaporation model that can predict the phase transition of droplets from liquid to vapor.

[0004] The study found that there are relatively many studies on droplet collisions in the air, but the research on droplet collisions on two-dimensional surfaces mainly relies on experimental methods. Researchers have not yet analyzed the motion displacement and velocity changes of droplets after collision on super-hydrophobic surfaces, and have not established a reliable theory to explore the critical conditions for droplet collisions on super-hydrophobic surfaces. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, a method for predicting the dynamic behavior of droplet collision provided by the present invention solves the problem that it is difficult to accurately predict the fusion or bounce behavior of droplets when they collide on a super-hydrophobic surface.

[0006] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a method for predicting the dynamic behavior of droplet collision, comprising the following steps:

[0007] S1. Analyze the relationship between the force and deformation of the elastic body during the collision of the droplets, and establish a dynamic model of the first droplet and the second droplet during the collision;

[0008] S2. Solving the dynamic model according to the initial distance and initial velocity of the first droplet and the second droplet to obtain the velocity of the first droplet and the second droplet and the distance between the sphere centers during the collision process, and then calculating the interaction force between the first droplet and the second droplet during the collision process;

[0009] S3. Calculate the surface tension when the interaction force of the droplets reaches the maximum value during the collision process;

[0010] S4. Determine the fusion of the droplets based on the surface tension when the interaction force of the droplets reaches a maximum value during the collision process.

[0011] Further: In S1, the expression of the relationship between the force and deformation of the elastic body is specifically the following formula;

[0012]

[0013] Wherein, α is the sum of the distances between the centers of the first droplet and the second droplet during the collision process, P is the force applied to the droplet, K1 is the elastic constant of the first droplet, K2 is the elastic constant of the second droplet, R1 is the radius of the first droplet, and R2 is the radius of the second droplet;

[0014] The expression of the dynamic model of the first droplet and the second droplet during the collision process is specifically as follows:

[0015]

[0016] Where x1 is the distance between the center of the first droplet during the collision, x2 is the distance between the center of the second droplet during the collision, m1 is the mass of the first droplet, and m2 is the mass of the second droplet. is the acceleration of the first droplet, is the acceleration of the second droplet.

[0017] Further: In S2, the expression for calculating the interaction force P between the first droplet and the second droplet during the collision process is specifically:

[0018]

[0019] Where E is the equivalent Young's modulus.

[0020] Further: In S3, the expression for calculating the surface tension when the interaction force of the droplet during the collision reaches the maximum value is specifically:

[0021]

[0022] In the formula, γ t is the surface tension of the droplet at time t, time t is the moment when the interaction force between the first droplet and the second droplet reaches the maximum value during the collision, γ is the internal tension of the elastic film, v0 is the initial velocity of the droplet, m is the mass of the droplet, R0 is the radius of the droplet, ρ is the density of the droplet, and R t is the radius of the droplet during the droplet collision process, p t is the static pressure of the droplet at time t, g is the acceleration due to gravity, h0 is the height of the moving liquid inside the droplet before collision, and h t is the height of the liquid collision inside the droplet.

[0023] Further: In S4, the method for determining the fusion status of the droplets is specifically:

[0024] The droplets merge when the following equation is satisfied;

[0025] γ t ≥λγ.

[0026] The beneficial effects of the present invention are:

[0027] (1) The present invention provides a method for predicting the dynamic behavior of droplet collision. In order to stably manipulate droplets and predict the dynamic behavior of droplet collision, the droplets are regarded as elastic balls, the collision behavior of droplets on super-hydrophobic surfaces is observed, the relative speed and fusion of droplets before collision are counted, and the speed and displacement changes of fusion and ejection after droplet collision are analyzed. From a mechanical point of view, a dynamic model is established using Hertz contact theory to calculate the interaction force between the first droplet and the second droplet during the collision process. The calculation is simple and accurate. It can accurately calculate the interaction force of the droplets during the collision process and the direction of the surface tension at the contact circle after the collision deformation, and predict the fusion and splitting behavior of the droplets. The calculation results of the theoretical model are consistent with the experimental data.

[0028] (2) The present invention can predict the two different states of droplet fusion and bounce after collision, and control the droplet bounce and fusion by adjusting the droplet size and the relative speed between the droplets, thereby providing a guarantee for subsequent microfluidics, droplet transport and chemical reactions.

[0029] (3) The present invention introduces the Hertz contact theory to analyze the droplet collision behavior, which is quite different from the prior art and provides new ideas for other researchers to analyze the droplet theory. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 The present invention is a flow chart of a method for predicting the dynamic behavior of droplet collision.

[0031] Figure 2 Schematic diagram of droplet collision deformation.

[0032] Figure 3 Schematic diagram of the droplet force balance.

[0033] Figure 4 Schematic diagram of force balance during droplet collision.

[0034] Figure 5 This is a diagram showing the displacement change during the collision process of a droplet with a diameter of 0.00245 m according to the present invention.

[0035] Figure 6 This is a velocity variation diagram of a droplet with a diameter of 0.00285 m during the collision process of the present invention.

[0036] Figure 7 This is a statistical diagram of the collision of droplets with a diameter of 0.00245 m according to the present invention.

[0037] Figure 8 This is a statistical diagram of the collision of droplets with a diameter of 0.00285 m according to the present invention.

[0038] Fig. 9 This is the relationship between the droplet size and the critical velocity of the present invention. DETAILED DESCRIPTION

[0039] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0040] like Figure 1 As shown, in one embodiment of the present invention, a method for predicting the dynamic behavior of droplet collision includes the following steps:

[0041] S1. Analyze the relationship between the force and deformation of the elastic body during the collision of the droplets, and establish a dynamic model of the first droplet and the second droplet during the collision;

[0042] S2. Solving the dynamic model according to the initial distance and initial velocity of the first droplet and the second droplet to obtain the velocity of the first droplet and the second droplet and the distance between the sphere centers during the collision process, and then calculating the interaction force between the first droplet and the second droplet during the collision process;

[0043] S3. Calculate the surface tension when the interaction force of the droplets reaches the maximum value during the collision process;

[0044] S4. Determine the fusion of the droplets based on the surface tension when the interaction force of the droplets reaches a maximum value during the collision process.

[0045] like Figure 2 As shown, in S1, according to the geometric relationship, the droplet is assumed to be an elastic sphere, and the expression of the relationship between the force and deformation of the elastic body during the collision of the droplet is specifically as follows:

[0046]

[0047] Wherein, α is the sum of the distances between the centers of the first droplet and the second droplet during the collision process, P is the force applied to the droplet, K1 is the elastic constant of the first droplet, K2 is the elastic constant of the second droplet, R1 is the radius of the first droplet, and R2 is the radius of the second droplet;

[0048] Ignoring the effects of gravity and friction, a dynamic model of the first droplet and the second droplet during the collision process can be established. The expression of the dynamic model of the first droplet and the second droplet during the collision process is specifically as follows:

[0049]

[0050] Where x1 is the distance between the center of the first droplet during the collision, x2 is the distance between the center of the second droplet during the collision, m1 is the mass of the first droplet, and m2 is the mass of the second droplet. is the acceleration of the first droplet, is the acceleration of the second droplet.

[0051] in:

[0052]

[0053] Wherein, v1 and v2 are the Poisson's ratios of the droplet, and the value thereof is 0.5 in this embodiment, and E is the equivalent Young's modulus, and its specific expression is:

[0054]

[0055] In the formula, λ is the correction coefficient, λ=2, and R is the radius.

[0056] In S2, the expression for calculating the interaction force P between the first droplet and the second droplet during the collision process is specifically:

[0057]

[0058] Where E is the equivalent Young's modulus.

[0059] Analyzing the dynamic equation, when x2-x1 is the smallest, α is the largest, that is, when the distance between the two droplets is the shortest, the interaction force P reaches its maximum value. At this moment, the speeds of the two droplets are equal. According to the law of conservation of momentum, we have:

[0060]

[0061] In S3, the expression for calculating the surface tension when the interaction force of the droplet during the collision reaches the maximum value is specifically:

[0062]

[0063] In the formula, γ t is the surface tension of the droplet at time t, time t is the moment when the interaction force between the first droplet and the second droplet reaches the maximum value during the collision, γ is the internal tension of the elastic film, v0 is the initial velocity of the droplet, m is the mass of the droplet, R0 is the radius of the droplet, ρ is the density of the droplet, and R t is the radius of the droplet during the droplet collision process, p t is the static pressure of the droplet at time t, g is the acceleration due to gravity, h0 is the height of the moving liquid inside the droplet before collision, and h t is the height of the liquid collision inside the droplet.

[0064] In this embodiment, the surface tension γ of the droplet at time t is calculated t The specific principle is:

[0065] The droplet is considered as a sphere surrounded by an elastic film and filled with liquid. The surface tension of the droplet is equivalent to the tension in the elastic film, such as Figure 3 shown.

[0066] When the droplets do not collide, considering the force balance condition under the action of internal and external pressure and elastic film tension, we can get formula 1:

[0067] 2πR0γ+πR0 2 p a =πR0 2 p0

[0068] Among them, R0 is the radius of the droplet, γ is the tension in the elastic film, that is, the surface tension of the droplet, p0 is the static pressure in the droplet, and p a is the atmospheric pressure.

[0069] During the collision of droplets, there will be a change in the pressure difference between the inside and outside of the "elastic film" due to the flow of internal liquid. Due to the collision, the forward speed of the liquid in the "elastic film" is reduced, so that it moves radially along the contact surface of the droplet, such as Figure 4 As shown, the formula 2 can be obtained through the dynamic force balance condition:

[0070]

[0071] Where m is the mass of the droplet, a t is the equivalent acceleration of the liquid in the "elastic film" perpendicular to the collision direction at time t, p t is the pressure inside the droplet at time t.

[0072] From the Bernoulli equation, we know that the sum of the kinetic energy, potential energy and pressure potential energy of the droplet during the collision is always a constant. Therefore, the pressure inside the "elastic film" can be estimated by formula 3:

[0073]

[0074] Combining formulas 1 to 3, we get formula 4:

[0075]

[0076] When the interaction force between the droplets reaches its maximum value during the collision, the velocities of the two droplets are equal at this moment. According to the law of conservation of momentum:

[0077]

[0078] Substituting the above formula into Formula 4, we can get the surface tension γ of the droplet at time t: t expression.

[0079] In S4, the method for determining the fusion status of the droplets is specifically as follows:

[0080] When the following equation is satisfied, the droplets merge, otherwise the droplets split;

[0081] γ t ≥λγ.

[0082] In this embodiment, the height of the liquid inside the droplet remains unchanged during the droplet collision, that is, h0 = h t When the lateral acceleration of the liquid is neglected, calculate the surface tension γ of the droplet at time t t The expression is simplified to:

[0083]

[0084] In this embodiment, it is assumed that the tension in the “elastic film” on the surface of the droplet reaches a threshold value, i.e., γ t When ≥λγ, the “film” breaks and causes the droplets to merge. Then the criterion for droplet fusion can be obtained as follows:

[0085]

[0086] When R t ≈R0:

[0087]

[0088] It can be seen that the left side of the above formula is the dimensionless Weber number. Therefore, this embodiment provides the conditions for fusion when droplets collide using the Weber number definition through qualitative deduction. In this embodiment, the rationality of the above formula is verified by experiment, and the specific value of λ is determined, in order to achieve accurate prediction of droplet collision behavior and provide a reliable theoretical basis for subsequent research and application.

[0089] In this embodiment, the present invention provides an experimental analysis process to verify the rationality and correctness of the method of the present invention.

[0090] In this embodiment, three different diameter needles are used to generate droplets with diameters of 0.00245m, 0.00285m and 0.00325m. The size of the generated droplets is controlled by changing the diameter of the needle. Pure water droplets are used as the research object, and the experiment is carried out at room temperature of 20°C. Its movement and deformation process are observed. The first droplet is made to rest at a fixed position on the super-hydrophobic substrate, and the second droplet is allowed to slide steadily down the slope of the super-hydrophobic substrate to reduce the impact of droplet bouncing and droplet deformation on the experiment.

[0091] According to experimental phenomena, this embodiment regards the droplet as a balloon filled with liquid, and the surface tension is approximately the tension of the balloon on the internal liquid. The Hertz contact theory is used to calculate the change in the velocity of the two droplets during the droplet collision process. Figure 5 A droplet with a diameter of 0.00245m collides at a relative speed of 0.25m / s. The speed of the moving droplet gradually slows down after the collision until the collision ends.

[0092] In analyzing the droplet collision process, the present invention found that surface tension is a key factor. In order to verify the model, the present invention conducted a series of experiments to analyze. By measuring the speed of droplets of different sizes, observing the state of droplets bouncing and merging after collision at different relative speeds, and conducting statistical analysis. Figure 6 and Figure 7 It is a statistical diagram of the states of droplets of different sizes after colliding at a certain speed. The present invention finds that when two droplets collide at a relatively low relative speed, they often show a bouncing phenomenon, while when they collide at a relatively high relative speed, they often show a fusion phenomenon. Some fusion phenomena still occur at a relatively low speed. The present invention infers that this is because the state of the droplets is unstable when they fall, and the violent shaking increases the possibility of droplet fusion. At a relatively high speed, some droplets may also bounce off. This phenomenon may be due to the fact that the two droplets are not colliding head-on, but there is a certain angle, that is, the first droplet brushes past the second droplet, showing the characteristics of separation.

[0093] During the experimental statistics, it was observed that droplets of different sizes overlap repeatedly within a certain velocity range, e.g. Figure 6 The fusion and separation of droplets of this size can occur within the relative speed range of 0.3m / s-0.34m / s, but not within other speed ranges. A statistical analysis of the state of the other two sizes of droplets after collision shows that a speed range can be found. Based on this phenomenon, the theoretical model is used to calculate the direction of the surface tension at the contact surface, determine the size of the component force that can tear the liquid film at the contact surface, and then find the critical speed for the fusion of the two droplets during the collision. Calculated by the theoretical model, Figure 6 and Figure 7 The green solid line indicates that the critical speed for the fusion and bounce of the droplets with a diameter of 0.00245m after collision is 0.32m / s, and the critical speeds for the droplets with diameters of 0.00285m and 0.00325m are 0.295m / s and 0.276m / s respectively. When the movement speed of the two droplets does not exceed the critical speed, the "pulling force" at the contact surface does not reach the critical value, and they will separate after the collision; if the movement speed exceeds the critical speed, the "pulling force" exceeds the bearing limit of the liquid film, and fusion occurs at the moment of collision. Based on collision theory and experience, it can be known that after the droplets collide under a certain state, the critical condition for the rupture of the liquid film must be determined. The phenomenon that appeared in experimental statistics is believed to be caused by three reasons in the present invention: the first is that there are subtle changes in the temperature of the droplets during the collision process, the second is that the two droplets have an eccentric collision with a small angle that is not easy to observe, and it is not a standard head-on collision, and the third reason is that the state of the second droplet is relatively unstable during the rolling process.

[0094] By comparing the experimental statistical data with the theoretical model calculation data, the calculated critical speed is within the overlapping range of the experimental statistical data, such as Figure 8 The calculated critical velocity of the droplet of this size is 0.295m / s, and the critical velocity range of the experimental statistics is 0.28m / s-0.31m / s. By comparing the collision data statistics of droplets of three sizes, it can be found that the theoretical model is consistent with the experimental results, which verifies the correctness of the model.

[0095] like Fig. 9 As shown, by comparing the critical speeds of droplets of different sizes, it is found that the smaller the droplet size, the higher the critical speed; the larger the droplet size, the lower the critical speed and the easier it is to merge.

[0096] The beneficial effects of the present invention are as follows: the present invention provides a method for predicting the dynamic behavior of droplet collision. In order to stably manipulate droplets and predict the dynamic behavior of droplet collision, the droplets are regarded as elastic balls, the collision behavior of droplets on super-hydrophobic surfaces is observed, the relative speed and fusion of droplets before collision are counted, and the speed and displacement changes of fusion and ejection after droplet collision are analyzed. From a mechanical point of view, a dynamic model is established using Hertz contact theory to calculate the interaction force between the first droplet and the second droplet during the collision process. The calculation is simple and accurate. It can accurately calculate the interaction force of the droplet during the collision process and the direction of the surface tension at the contact circle after the collision deformation, and predict the fusion and splitting behavior of the droplet. The calculation results of the theoretical model are consistent with the experimental data.

[0097] The present invention can predict the two different states of droplet fusion and bounce after collision, and control the droplet bounce and fusion by adjusting the droplet size and the relative speed between the droplets, thereby providing a guarantee for subsequent microfluidics, droplet transport and chemical reactions.

[0098] The present invention introduces the Hertz contact theory to analyze the droplet collision behavior, which is quite different from the prior art and provides new ideas for other researchers on the theory of droplet analysis.

[0099] In the description of the present invention, it is necessary to understand that the orientation or positional relationship indicated by the terms "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", and "third" are used only for descriptive purposes, and cannot be understood as indicating or implying the relative importance or the number of implicitly specified technical features. Therefore, the features defined by "first", "second", and "third" may explicitly or implicitly include one or more of the features.

Claims

1. A method for predicting the dynamic behavior of droplet collision, characterized in that: The following steps are involved: S1. Analyze the relationship between the force and deformation of the elastic body during the collision of the droplets, and establish a dynamic model of the first droplet and the second droplet during the collision; S2. Solving the dynamic model according to the initial distance and initial velocity of the first droplet and the second droplet to obtain the velocity of the first droplet and the second droplet and the distance between the sphere centers during the collision process, and then calculating the interaction force between the first droplet and the second droplet during the collision process; S3. Calculate the surface tension when the interaction force of the droplets reaches the maximum value during the collision process; S4. Determine the fusion of the droplets based on the surface tension when the interaction force of the droplets reaches a maximum value during the collision process.

2. The method for predicting the dynamic behavior of droplet collision according to claim 1, characterized in that: In S1, the expression of the relationship between the force and deformation of the elastic body is specifically as follows: Wherein, α is the sum of the distances between the centers of the first droplet and the second droplet during the collision process, P is the force applied to the droplet, K1 is the elastic constant of the first droplet, K2 is the elastic constant of the second droplet, R1 is the radius of the first droplet, and R2 is the radius of the second droplet; The expression of the dynamic model of the first droplet and the second droplet during the collision process is specifically as follows: Where x1 is the distance between the center of the first droplet during the collision, x2 is the distance between the center of the second droplet during the collision, m1 is the mass of the first droplet, and m2 is the mass of the second droplet. is the acceleration of the first droplet, is the acceleration of the second droplet.

3. The method for predicting the dynamic behavior of droplet collision according to claim 2, characterized in that: In S2, the expression for calculating the interaction force P between the first droplet and the second droplet during the collision process is specifically: Where E is the equivalent Young's modulus.

4. The method for predicting the dynamic behavior of droplet collision according to claim 3, characterized in that: In S3, the expression for calculating the surface tension when the interaction force of the droplet during the collision reaches the maximum value is specifically: In the formula, γ t is the surface tension of the droplet at time t, time t is the moment when the interaction force between the first droplet and the second droplet reaches the maximum value during the collision, γ is the internal tension of the elastic film, v0 is the initial velocity of the droplet, m is the mass of the droplet, R0 is the radius of the droplet, ρ is the density of the droplet, and R t is the radius of the droplet during the droplet collision process, p t is the static pressure of the droplet at time t, g is the acceleration due to gravity, h0 is the height of the moving liquid inside the droplet before collision, and h t is the height of the liquid collision inside the droplet.

5. The method for predicting the dynamic behavior of droplet collision according to claim 3, characterized in that: In S4, the method for determining the fusion status of the droplets is specifically as follows: The droplets merge when the following equation is satisfied; c t ≥λγ。

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