Motion of an aerosol sphere in hydrogel medium under thermal gradient

In this work the thermophoretic migration of an aerosol sphere embedded in a hydrogel medium has been analytically investigated. The porous medium containing microstructure fluid of a micropolar type can be viewed as a hydrogel medium. The Reynolds and Péclet numbers are considered to be very small. We solve the governing equations of momentum and energy by applying a temperature jump, continuity of heat flux, and hydrodynamic boundary conditions such as viscous slip, thermal creep and thermal stress slip at the particle surface. Analytical expressions for thermophoretic velocity and thermophoretic force are obtained. The influence of the permeability, micropolarity, frictional slip, spin slip, thermal stress slip parameters, and thermal properties of particle and medium on thermophoretic velocity and force are discussed numerically. Our results show that the thermophoretic velocity and force are decreasing functions of micropolarity and microrotation thermal conductivity parameters, while the effect of thermal stress slip is to increase the thermophoretic velocity and force of the particle. The novelty of the research is the micropolarity parameter and permeability that characterizes the micropolar fluid flow through a porous medium. The results are also compared with previously published work. The study is applied to capture ash particles conducting thermophoresis in a porous filter formed by interconnected spherical pores in a hydrogel medium.