In this letter we propose a diffuse interface–lattice Boltzmann model for surfactant transport on an interface. A delta function formulation with a free parameter is given and proved to be equivalent to the interfacial convection–diffusion equation. By replacing the delta function by a discrete form, a diffuse interface formulation is obtained and further reformulated into the regularized form. We develop a multiple-relaxation-time lattice Boltzmann model to solve the regularized diffuse interface equation. A numerical test is performed to validate the present model. The numerical results indicate that appropriately increasing the diffusion coefficient in the normal direction will give more stable and accurate solution.

在这封信中，我们提出了用于界面上表面活性剂传输的扩散界面–格子Boltzmann模型。给出了具有自由参数的增量函数公式，并证明其等效于界面对流扩散方程。通过用离散形式代替增量函数，可以获得扩散界面公式，并进一步将其重新公式化为规则形式。我们开发了一个多重松弛时间晶格玻尔兹曼模型来求解正则化的扩散界面方程。进行数值测试以验证当前模型。数值结果表明，适当增加法线方向的扩散系数将给出更稳定，准确的解决方案。