Stochastic Hydrodynamic Model Mixing By Multiple Swimmers

This paper focuses on the displacement of a passive scalar particle which is influenced by the locomotion of bodies through it. Then based on the diffusion model of thermodynamics, we calculate the effective diffusivity, which can be used to help us to quantitatively describe the multiple transportation problem of the setting, with the displacement of the target particle.In reality, the relevant phenomena appear in the chemical industry, medical treatment, environmental engineering and other scientific and engineering fields.Therefore, this study has important theoretical and practical significance.With generalizing the model proposed by Thiffeault,Childress [1] (Phys.Lett.A, 372,3487-3490,2010) into the case which swimmers swim in the anisotropic randomly direction, the effective diffusivity & diffusion tensor are calculated with Ito diffusion process theory. Demonstrating the effect induced by anisotropic stirring, the mean diffusivity may reduce.We concretely calculate the effective diffusivity in any direction and then deduce the relationship between effective diffusivity and probability density function. That’s to say it can quantitatively describe how the anisotropic degree of scalar effective diffusion in the model is affected by the anisotropy of swimming. Then, we study the relationship between anisotropy of swimming and anisotropy of diffusion tensor, and proposed two dimensionless numbers which measure the two anisotropy respectively. From those numbers we can easily judge the anisotropism of them.