A LBM-IBM simulation method for surfactant-responsive flotation bubble slip flow

Abstract

The present invention discloses an LBM-IBM simulation method for surfactant-responsive flotation bubble slip flow, which relates to the technical fields of fluid mechanics and multiphase flow simulation. The method comprises the following steps: analyzing a fluid field based on a lattice Boltzmann method to obtain a velocity field and a pressure field of a fluid in the fluid field; analyzing a concentration field of a surfactant in the fluid to obtain a volume concentration, obtaining an interface adsorption / desorption source term based on the volume concentration calculation, and updating a particle distribution function in the concentration field; collecting a diffusion coefficient and a tangential velocity of the surfactant on a bubble interface of the fluid, and updating the surfactant concentration on the bubble interface based on the interface adsorption / desorption source term, the diffusion coefficient, and the tangential velocity; and constructing an LBM-IBM simulation mechanism that couples surfactant concentration changes with bubble interface slip behavior, thereby achieving synchronous feedback of the dynamic response of the bubble interface and the evolution of the flow field during the flotation process, and improving the numerical analysis capability of the fine evolution characteristics of the interface slip flow.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid mechanics and multiphase flow simulation, and in particular to an LBM-IBM simulation method for surfactant-responsive flotation bubble slip flow. Background Art

[0002] In the flotation separation process, bubbles are important carriers of mineral particles, and their interfacial dynamic behavior has a direct impact on the separation efficiency. Especially in the presence of surfactants, the spatial distribution and temporal changes of surfactants on the interface will significantly affect the slip behavior of bubbles and the local flow field structure.

[0003] To address this issue, researchers have recently introduced coupled simulation strategies based on the Lattice Boltzmann method (LBM) and the Immersed Boundary Method (IBM). Leveraging the LBM's strengths in solving complex flow structures and the IBM's capabilities in modeling interfacial motion, these methods numerically characterize the behavior of bubble interfaces. These methods maintain good numerical stability when dealing with dynamic boundaries and shear forces between gas and liquid phases, and exhibit a degree of scalability. Consequently, they are widely used in the simulation of microscale flotation fluid processes.

[0004] Although existing methods can achieve slip velocity estimation of interfacial fluids and modeling of fluid-interface interactions to a certain extent, most methods only use the surfactant concentration field as an additional term in the boundary conditions, failing to form a closed-loop mechanism between interfacial concentration evolution, shear stress response, and slip velocity feedback.

[0005] Especially under complex working conditions where the interface concentration changes significantly and the fluid has non-uniform disturbances, the existing model has difficulty in synchronously updating the position and concentration state of the bubble interface and cannot fully reflect the impact of surfactant transport behavior on the formation mechanism of bubble slip flow.

[0006] In addition, some methods ignore the feedback regulation effect of interfacial adsorption / desorption behavior on local concentration evolution, which makes the simulation results prone to numerical deviations under high concentration gradient conditions, affecting the accuracy and physical consistency of the simulation. Summary of the Invention

[0007] In order to solve the above technical problems, the present invention provides an LBM-IBM simulation method for surfactant response flotation bubble slip flow, the method comprising:

[0008] S11, analyze the fluid field based on the lattice Boltzmann method to obtain the velocity field and pressure field of the fluid in the fluid field;

[0009] S12, analyzing the concentration field of the surfactant in the fluid to obtain the volume concentration, obtaining the interface adsorption / desorption source term based on the volume concentration, and updating the particle distribution function in the concentration field;

[0010] S13, collecting the diffusion coefficient and tangential velocity of the surfactant on the bubble interface of the fluid, and updating the surfactant concentration on the bubble interface based on the interface adsorption / desorption source term, the diffusion coefficient and the tangential velocity;

[0011] S14, calculating the shear stress and slip velocity of the bubble interface based on the surfactant concentration field and the velocity field of the fluid at the bubble interface, collecting the boundary velocity of the bubble interface, and calculating the target velocity of the bubble interface based on the slip velocity and the boundary velocity;

[0012] S15, based on the immersed boundary method, the target velocity on the bubble interface is fed back to the fluid field, and the position of the bubble interface and the surfactant concentration on the bubble interface are updated according to the target velocity.

[0013] Furthermore, the logic for obtaining the velocity field and pressure field of the fluid is:

[0014] S111, based on the particle distribution function in the lattice Boltzmann method, obtain the evolution equation used to characterize the microscopic dynamic behavior of the fluid;

[0015] S112, calculating the density of the generated fluid according to the particle distribution function;

[0016] S113, based on the density of the fluid, calculate and obtain the velocity field and pressure field of the fluid.

[0017] Furthermore, the logic for obtaining the volume concentration of the surfactant is:

[0018] Define the particle distribution function of surfactants;

[0019] The volume concentration of the surfactant in the fluid is obtained by summing the particle distribution functions of the surfactant.

[0020] Furthermore, the logic for obtaining the interface adsorption / desorption source term based on volume concentration calculation and updating the particle distribution function in the concentration field is as follows:

[0021] The interfacial adsorption / desorption source terms were calculated using the Langmuir adsorption kinetics model and the volume concentration of the surfactant.

[0022] The particle distribution function is updated based on the convection-diffusion equation and the interfacial adsorption / desorption source terms used to characterize the mass transfer behavior of surfactants.

[0023] Furthermore, the logic for updating the surfactant concentration on the bubble interface is:

[0024] Based on the interfacial adsorption / desorption source terms, the characterization equation for the transport behavior of surfactants on the bubble interface is obtained:

[0025] Expressed as: , where is the surfactant concentration at the bubble interface, is the tangential velocity of the bubble interface; is the diffusion coefficient at the bubble interface, is the interface adsorption / desorption source term, is the rate of change of surfactant concentration over time, is the Laplace operator, is the interface gradient operator;

[0026] The surfactant concentration is obtained and updated based on the characterization equation.

[0027] Furthermore, the logic for calculating the shear stress at the bubble interface is:

[0028] The dynamic viscosity of the fluid, the tangential velocity component on the bubble interface and the gradient of the tangential velocity along the normal direction are collected to calculate the interface shear stress;

[0029] Expressed as: , where is the interfacial shear stress, is the dynamic viscosity of the fluid, is the tangential velocity component on the bubble interface, is the gradient of the tangential velocity along the normal direction.

[0030] Furthermore, the logic for calculating the slip velocity of the bubble interface is:

[0031] Based on the shear stress and the dynamic viscosity of the fluid, the initial slip velocity caused by the shear stress on the bubble surface is calculated;

[0032] Based on the initial slip velocity, discretization processing is performed, and the slip velocity is obtained according to the velocity field of the fluid, where the velocity field of the fluid is discretized using an Euler grid.

[0033] Furthermore, the logic for calculating the target velocity of the bubble interface based on the slip velocity and boundary velocity is:

[0034] The collected boundary velocity and slip velocity are accumulated to generate the target velocity;

[0035] Expressed as: , where is the target speed, is the boundary velocity of the acquisition, is the slip speed.

[0036] Furthermore, the logic for updating the position of the bubble interface and the surfactant concentration on the bubble interface according to the target velocity is as follows:

[0037] S151, extracting the fluid velocity at the boundary point of the bubble interface by using an interpolation kernel function;

[0038] S152, calculating a boundary feedback force based on the target velocity and the fluid velocity;

[0039] S153, propagating the feedback force to the Euler grid and applying it to the fluid field;

[0040] S154, updating the position of the bubble interface according to the target speed to obtain an updated position;

[0041] S155, based on the updated position, updating the surfactant concentration on the bubble interface.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] This invention introduces a particle distribution function evolution equation based on the lattice Boltzmann model during fluid evolution, combined with microscopic dynamic behavior modeling, to achieve a detailed restoration of the velocity and pressure fields. This in turn improves the ability to express the distribution characteristics of physical quantities within the fluid, thereby enhancing the perception of interfacial dynamic behavior. Furthermore, by introducing interfacial adsorption / desorption source terms to feedback-regulate the surfactant concentration field, the concentration evolution is made responsive to the transport effects of bubble interfaces, effectively enhancing the spatiotemporal consistency of the simulation of mass transfer behavior driven by changes in interfacial activity.

[0044] Furthermore, when dealing with interfacial mass transfer problems, the present invention establishes a feedback model based on the Langmuir adsorption model and the convection-diffusion mechanism to achieve continuous tracking of the changes in surfactant concentration on the bubble interface with diffusion, tangential velocity and adsorption state, thereby improving the response accuracy to the evolution law of interfacial shear stress and slip velocity, thereby enhancing the dynamic update capability of local interfacial velocity boundary changes.

[0045] Furthermore, based on the immersed boundary method, the present invention constructs an interface-fluid coupling feedback pathway driven by a target velocity. This mapping of the boundary velocity, feedback force, and fluid velocity field is accomplished while the interface position changes over time. This synchronizes the physical movement of the bubble interface with the evolution of the interface concentration, thereby improving the ability to model the continuous evolution of interface behavior in flotation environments and ensuring the accuracy of coupled simulations of microscale interface mechanics and mass transfer characteristics under dynamic conditions. These components form a complete feedback loop for the coupled effects of the bubble interface physical behavior and the flow field, maintaining physical consistency throughout the entire process.

[0046] In summary, the present invention realizes the synchronous feedback of the dynamic response of the bubble interface and the flow field evolution during the flotation process by constructing an LBM-IBM simulation mechanism that couples the change of surfactant concentration with the slip behavior of the bubble interface, effectively improving the numerical analysis capability of the fine evolution characteristics of the interface slip flow. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, a brief introduction to the drawings required for use in the embodiments will be given below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0048] Figure 1 This is a flow chart of an LBM-IBM simulation method for surfactant-responsive flotation bubble slip flow provided in Example 1 of the present invention. DETAILED DESCRIPTION

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0050] Example 1

[0051] See also Figure 1 As shown, this embodiment discloses an LBM-IBM simulation method for surfactant response flotation bubble slip flow, the method comprising:

[0052] S11, analyze the fluid field based on the lattice Boltzmann method to obtain the velocity field and pressure field of the fluid in the fluid field;

[0053] It should be noted that the fluid field refers to the physical quantities of the fluid at each point in a specific spatial area, including but not limited to the distribution of physical quantities such as velocity, pressure, density, and temperature.

[0054] Specifically, the logic for obtaining the velocity field and pressure field of the fluid is:

[0055] S111, based on the particle distribution function in the lattice Boltzmann method, obtain the evolution equation used to characterize the microscopic dynamic behavior of the fluid;

[0056] Expressed as: ,in, For particles at time and location The particle distribution function on For particles at time and location The particle distribution function on The particle in the time step Inner edge direction The distance of propagation, is the collision operator, is the external force term, is the index identifier, An integer greater than 0.

[0057] It should be noted that: Location is the spatial node coordinate on the Euler grid in the lattice Boltzmann method, which is used to define the particle distribution function The spatial position vector of the location, whose spatial dimension can be two-dimensional or three-dimensional (i.e. position =( , ) or location =( , , )), depending on the discrete velocity model used (such as D2Q9 or D3Q19);

[0058] The microscopic dynamic behavior of the fluid refers to the behavior process of particles in the fluid, such as molecules or bubbles, moving, interacting and colliding with each other in space. The particle distribution function is an existing function content and will not be elaborated on.

[0059] In the demonstration equation, the left side It describes the change of particle distribution function over time. Specifically, it represents the change of particle position and velocity within a time step, reflecting the change of particle from its current position to its velocity. Along the direction of speed Move to a new location process;

[0060] The right side of the demonstration equation They represent the influence of collision process and external force on particle distribution respectively.

[0061] The movement (propagation) of particles is determined by the particle distribution function Expressed by the evolution equation, each particle in time Inward along its direction Propagating to the next position simulates the random motion of particles in the fluid.

[0062] Among them, the collision operator It describes the collision process between particles, that is, the movement of particles in the fluid will be affected by the collision, and the collision operator is responsible for describing this collision behavior; in the lattice Boltzmann method, that is, LBM, the collision operator is used to make the particle distribution function Towards a local equilibrium Evolution, that is, the particle distribution function will gradually return to the equilibrium distribution according to the local state of the fluid.

[0063] External force , describes the effect of external forces on the particle distribution function. External forces include but are not limited to gravity, interface feedback force and electromagnetic force. During the flotation process, bubble interface feedback force, interaction force between mineral particles, etc. will be reflected through external force terms. Affects the movement of fluid particles. The external force term is used to simulate the influence of these external forces on the state of fluid microscopic particles; and adjust the particle distribution function of the particles.

[0064] S112, calculating the density of the generated fluid according to the particle distribution function;

[0065] Expressed as: ,in, For the location , time is The density of the fluid at .

[0066] S113, calculating and obtaining the velocity field and pressure field of the fluid based on the density of the fluid;

[0067] The velocity field calculation formula is expressed as: ,in, is the velocity field of the fluid, is the pressure field of the fluid, is the sound velocity constant in the fluid, preferably, The value is .

[0068] It should be noted that: In the calculation formula, It does not mean × , but the particle distribution function and discrete velocity directions The weighted sum of By discretizing the velocity directions and assigning a numerical scalar to each direction.

[0069] S12, analyzing the concentration field of the surfactant in the fluid to obtain the volume concentration, obtaining the interface adsorption / desorption source term based on the volume concentration, and updating the particle distribution function in the concentration field.

[0070] It should be noted that the fluid in this step is liquid phase;

[0071] Specifically, the logic for obtaining the volume concentration of the surfactant is:

[0072] Define the particle distribution function of surfactants;

[0073] Expressed as: ,in, For the location and time Active agent particle distribution function on ;

[0074] It should be noted that: Indicates the distribution of surfactants;

[0075] The volume concentration of the surfactant in the fluid is obtained by summing the surfactant particle distribution functions;

[0076] Expressed as: Specifically, the logic for obtaining the interface adsorption / desorption source term based on volume concentration calculation and updating the particle distribution function in the concentration field is as follows:

[0077] The interfacial adsorption / desorption source terms were calculated using the Langmuir adsorption kinetics model and the volume concentration of the surfactant.

[0078] Expressed as: ,in, is the interface adsorption / desorption source term, and are the adsorption and desorption rate constants, respectively, is the maximum saturated adsorption capacity of the interface, is the amount of interfacial adsorption.

[0079] Update the particle distribution function based on the convection-diffusion equation and the interface adsorption / desorption source term used to characterize the mass transfer behavior of surfactants;

[0080] Expressed as: ,in, For particles at time and location The particle distribution function of the surfactant on For particles at time and location The particle distribution function of the surfactant on is the collision operator of the concentration field, is the interface adsorption / desorption source term;

[0081] Output updated particle distribution function based on the formula .

[0082] It should be noted that mass transfer behavior is the process of a substance moving from one location or phase to another, usually through mechanisms such as diffusion and convection. That is, mass transfer behavior describes the migration process of a substance between different media (such as gas, liquid, solid).

[0083] S13, collecting the diffusion coefficient and tangential velocity of the surfactant on the bubble interface of the fluid, and updating the surfactant concentration on the bubble interface based on the interface adsorption / desorption source term, the diffusion coefficient and the tangential velocity.

[0084] It should be noted that the diffusion coefficient of the surfactant on the bubble interface can be collected by optical microscopy and fluorescent labeling technology to observe the diffusion process of the surfactant on the bubble interface; the tangential velocity on the bubble interface can be collected by particle imaging velocimetry (PIV) or laser Doppler velocimetry (LDA) to measure the tangential velocity of the bubble surface.

[0085] Specifically, the logic for updating the surfactant concentration on the bubble interface is:

[0086] Based on the interfacial adsorption / desorption source terms, the characterization equation for the transport behavior of surfactants on the bubble interface is obtained:

[0087] Expressed as: , where is the surfactant concentration at the bubble interface, is the tangential velocity of the bubble interface; is the diffusion coefficient at the bubble interface, is the interface adsorption / desorption source term, is the rate of change of surfactant concentration over time, is the Laplace operator, is the interface gradient operator;

[0088] Obtain and update surfactant concentration based on the characterization equation;

[0089] It should be noted that the Laplace operator and the interface gradient operator are obtained by calculating the Lagrangian boundary point position and the neighborhood concentration difference in the immersed boundary method. This is a prior art and will not be described in detail.

[0090] S14, calculating the shear stress and slip velocity of the bubble interface according to the surfactant concentration field of the bubble interface and the velocity field of the fluid, collecting the boundary velocity of the bubble interface, and calculating the target velocity of the bubble interface based on the slip velocity and the boundary velocity.

[0091] Specifically, the logic for calculating the shear stress at the bubble interface is:

[0092] The dynamic viscosity of the fluid, the tangential velocity component on the bubble interface and the gradient of the tangential velocity along the normal direction are collected to calculate the interface shear stress;

[0093] Expressed as: , where is the interfacial shear stress, is the dynamic viscosity of the fluid, is the tangential velocity component on the bubble interface, is the gradient of the tangential velocity along the normal direction;

[0094] It should be noted that the dynamic viscosity of the fluid is measured by a rotational viscometer or a capillary viscometer, the tangential velocity component on the bubble interface is measured by a particle imaging velocimeter (PIV) or a laser Doppler velocimeter (LDA), and the velocity difference at different positions on the bubble interface is measured by a particle imaging velocimeter (PIV) or a laser Doppler velocimeter (LDA), and the gradient of the tangential velocity is then calculated.

[0095] Specifically, the logic for calculating the slip velocity of the bubble interface is:

[0096] Based on the shear stress and the dynamic viscosity of the fluid, the initial slip velocity caused by the shear stress on the bubble surface is calculated;

[0097] Expressed as: ,in, is the initial slip velocity.

[0098] Discretization is performed based on the initial slip velocity, and the slip velocity is obtained according to the velocity field of the fluid, where the velocity field of the fluid is discretized using an Euler grid;

[0099] The calculation formula for slip velocity is: , where is the slip velocity, is the spatial discrete step length along the normal direction of the bubble interface, is the velocity field interpolated from the centers of the neighboring Euler grids.

[0100] It should be noted that the velocity field of the fluid is discretized using an Euler grid and is defined on a fixed spatial grid constructed by the lattice Boltzmann method (LBM).

[0101] Specifically, the logic for calculating the target velocity of the bubble interface based on the slip velocity and boundary velocity is:

[0102] The collected boundary velocity and slip velocity are accumulated to generate the target velocity;

[0103] Expressed as: , where is the target speed, is the boundary velocity of the acquisition.

[0104] It should be noted that the boundary velocity of the bubble interface is collected by analyzing the motion trajectory of the tracer particles in the flow field around the bubble using particle image velocimetry (PIV).

[0105] S15, based on the immersed boundary method, the target velocity on the bubble interface is fed back to the fluid field, and the position of the bubble interface and the surfactant concentration on the bubble interface are updated according to the target velocity.

[0106] Specifically, the logic for updating the position of the bubble interface and the surfactant concentration on the bubble interface according to the target velocity is as follows:

[0107] S151, extracting the fluid velocity at the boundary point of the bubble interface by using an interpolation kernel function;

[0108] Expressed as: , where The bubble interface The fluid velocity at the boundary point, The first Boundary points, To sum over all boundary points, For location The fluid velocity vector, is the interpolation kernel function.

[0109] It should be noted that: is the Euler grid node The fluid velocity vector of each node, the interpolation kernel function represents the Lagrange point Euler point The weights of , satisfy the normalization and compact support properties, are usually discrete approximations of cubic B-splines or Dirac delta functions and are dimensionless.

[0110] S152, calculating a boundary feedback force based on the target velocity and the fluid velocity;

[0111] Expressed as: ,in, The bubble interface The boundary feedback force on the boundary points, For the The density at the boundary points, For the The target velocity at each boundary point.

[0112] S153, propagating the feedback force to the Euler grid and applying it to the fluid field;

[0113] Expressed as: , where is the Euler grid point The feedback force at .

[0114] S154, updating the position of the bubble interface according to the target speed to obtain an updated position;

[0115] Expressed as: , where The first Boundary point at time spatial location, is the time step, The first Boundary point at time Updated spatial location.

[0116] Will Output as the updated position.

[0117] S155, updating the surfactant concentration on the bubble interface based on the updated position;

[0118] Expressed as: ,in, is the updated surfactant concentration at the bubble interface.

[0119] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A LBM-IBM simulation method for surfactant-responsive flotation bubble slip flow, characterized in that: The method comprises: S11, analyze the fluid field based on the lattice Boltzmann method to obtain the velocity field and pressure field of the fluid in the fluid field; The logic for obtaining the velocity field and pressure field of the fluid is: S111, based on the particle distribution function in the lattice Boltzmann method, obtain the evolution equation used to characterize the microscopic dynamic behavior of the fluid; S112, calculating the density of the generated fluid according to the particle distribution function; S113, calculating and obtaining the velocity field and pressure field of the fluid based on the density of the fluid; S12, analyzing the concentration field of the surfactant in the fluid to obtain the volume concentration, obtaining the interface adsorption / desorption source term based on the volume concentration, and updating the particle distribution function in the concentration field; The logic for obtaining the interface adsorption / desorption source term based on volume concentration calculation and updating the particle distribution function in the concentration field is as follows: The interfacial adsorption / desorption source terms were calculated using the Langmuir adsorption kinetics model and the volume concentration of the surfactant. Update the particle distribution function based on the convection-diffusion equation and the interface adsorption / desorption source term used to characterize the mass transfer behavior of surfactants; The logic for obtaining the volume concentration of surfactant is: Define the particle distribution function of surfactants; The volume concentration of the surfactant in the fluid is obtained by summing the particle distribution functions of the surfactant; S13, collecting the diffusion coefficient and tangential velocity of the surfactant on the bubble interface of the fluid, and updating the surfactant concentration on the bubble interface based on the interface adsorption / desorption source term, the diffusion coefficient and the tangential velocity; The logic for updating the surfactant concentration at the bubble interface is: Based on the interfacial adsorption / desorption source terms, the characterization equation for the transport behavior of surfactants on the bubble interface is obtained: Expressed as: ； Where, is the surfactant concentration at the bubble interface, is the tangential velocity of the bubble interface; is the diffusion coefficient at the bubble interface, is the interface adsorption / desorption source term, is the rate of change of surfactant concentration over time, is the Laplace operator, is the interface gradient operator; Obtain and update the surfactant concentration based on the characterization equation; S14, calculating the shear stress and slip velocity of the bubble interface based on the surfactant concentration field and the velocity field of the fluid at the bubble interface, collecting the boundary velocity of the bubble interface, and calculating the target velocity of the bubble interface based on the slip velocity and the boundary velocity; S15, based on the immersed boundary method, the target velocity on the bubble interface is fed back to the fluid field, and the position of the bubble interface and the surfactant concentration on the bubble interface are updated according to the target velocity.

2. The LBM-IBM simulation method for surfactant-responsive flotation bubble slip flow according to claim 1, characterized in that: The logic for calculating the shear stress at the bubble interface is: The dynamic viscosity of the fluid, the tangential velocity component on the bubble interface and the gradient of the tangential velocity along the normal direction are collected to calculate the interface shear stress; Expressed as: ； Where, is the interfacial shear stress, is the dynamic viscosity of the fluid, is the tangential velocity component on the bubble interface, is the gradient of the tangential velocity along the normal direction.

3. The LBM-IBM simulation method for surfactant-responsive flotation bubble slip flow according to claim 2, characterized in that: The logic for calculating the slip velocity of the bubble interface is: Based on the shear stress and the dynamic viscosity of the fluid, the initial slip velocity caused by the shear stress on the bubble surface is calculated; Based on the initial slip velocity, discretization processing is performed, and the slip velocity is obtained according to the velocity field of the fluid, where the velocity field of the fluid is discretized using an Euler grid.

4. The LBM-IBM simulation method for surfactant-responsive flotation bubble slip flow according to claim 3, characterized in that: The logic for calculating the target velocity of the bubble interface based on the sliding velocity and boundary velocity is: The collected boundary velocity and slip velocity are accumulated to generate the target velocity; Expressed as: ； Where, is the target speed, is the boundary velocity of the acquisition, is the slip speed.

5. The LBM-IBM simulation method for surfactant-responsive flotation bubble slip flow according to claim 4, characterized in that: The logic for updating the position of the bubble interface and the surfactant concentration on the bubble interface according to the target velocity is: S151, extracting the fluid velocity at the boundary point of the bubble interface by using an interpolation kernel function; S152, calculating a boundary feedback force based on the target velocity and the fluid velocity; S153, propagating the feedback force to the Euler grid and applying it to the fluid field; S154, updating the position of the bubble interface according to the target speed to obtain an updated position; S155, based on the updated position, updating the surfactant concentration on the bubble interface.

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