Mathematical Modeling And Algorithm Research Of Fluid Surfactant System On Curved Surfaces

Surfactant is a kind of organic compound with unique amphiphilic molecular structure and can change the properties of liquid interface.It has a wide range of practical application value in daily life,medicine,chemical engineering and biological science,such as soap,pesticide,weeding Additives and metal manufacturing additives.For the study of surfactant systems on curved surfaces,due to the complexity of the structure of the system itself and the influence of geometric curvature,its modeling and algorithm analysis have always been a huge challenge.This paper mainly studies the mathematical modeling and algorithm analysis of the fluid surfactant system on the curved surface.First,considering the influence of geometric curvature and fluid flow on the system,a binary fluid surfactant phase field model on the surface and a fluid surfactant phase field model of the coupled incompressible Navier-Stokes equation on the surface are constructed.Secondly,the scalar auxiliary variable method is extended to the two models,and the corresponding equivalent models are obtained respectively.For the new model,the first-order and second-order discrete schemes are constructed using surface finite element method,pressure correction method,stabilization processing,and explicit implicit technology,and it is proved that the first-order scheme satisfies unconditional energy stability.Finally,through a series of numerical experiments,the rationality of the model and the effectiveness of the method were verified,and the influence of geometric curvature and fluid flow on the evolution of the phase separation of the system was explored.The experimental phenomenon shows that the curvature will control the fluid to converge or diverge toward the position with high curvature,and the greater the coupling strength,the faster the system reaches a stable state.For the fluid surfactant phase field model with fluid flow,the above phenomenon is also present,but due to the influence of fluid flow,the system has a deviation from the above situation in the process of phase separation and evolution.