Fluid Flow and Solute Transfer in a Permeable Tube with Influence of Slip Velocity

Author(s):  
M. Varunkumar ◽  
P. Muthu
2019 ◽  
Vol 74 (12) ◽  
pp. 1057-1067
Author(s):  
M. Varunkumar ◽  
P. Muthu

AbstractWe considered a steady flow of viscous incompressible fluid and solute transfer in an axisymmetric tube of uniform cross section with variable wall permeability, which is relevant to the study of movement of solute across the glomerular capillaries. The solutions for the nonlinear governing equations of the fluid flow and solute transfer are obtained by analytical/numerical methods. The combined effect of variable wall permeability and flow parameters on the hydrostatic pressure, osmotic pressure, velocity profiles, concentration profiles, and the total solute clearance are investigated and are presented in this paper. It is found that an increase in the variable permeability parameter increases the solute concentration at the wall.


Author(s):  
Jian-Fei Xie ◽  
Bing-Yang Cao

This paper presents the fluid flow in nanochannels with permeable walls using the molecular dynamics (MD) simulations. A three-dimensional Couette flow has been carried out to investigate the effect of the permeable surface on the fluid density distributions and the slip velocity. The ordering layer of molecules is constructed near the smooth surface but it was destroyed by the permeable ones resulting in the density drop in porous wall. The fluid density in porous wall is large under strong fluid-structure interaction (FSI) and it is decreased under weak FSI. The negative slip is observed for fluid flow past solid walls under strong FSI, no-slip under medium FSI and positive slip under weak FSI whatever it is smooth or porous. Moreover, the largest slip velocity and slip length occur on the smooth surface of solid wall. As predicted by Maxwell theory, the molecule is bounced back when it impinges on the smooth surface. The molecules, however, can reside in porous wall by replacing the molecules that are trapped in the pores. Moreover, the molecule can escape from the pore and enter the channel becoming a free molecule. After travelling for a period time in the channel, the molecule can enter the pore again. During the molecular movement, the momentum exchange has been implemented not only between fluid molecules and wall but also between the fluid molecules themselves in the pore, and the multi-collision between fluid molecules takes place. The reduced slip velocity at the porous wall results in the larger friction coefficient compared to the smooth surface wall. The molecular boundary condition predicted by Maxwell theory on the smooth surface is no longer valid for flow past the permeable surface, and a novel boundary condition should be introduced.


Author(s):  
Wan Faezah Wan Azmi ◽  
Ahmad Qushairi Mohamad ◽  
Lim Yeou Jiann ◽  
Sharidan Shafie

Casson fluid is a non-Newtonian fluid with its unique fluid behaviour because it behaves like an elastic solid or liquid at a certain condition. Recently, there are several studies on unsteady Casson fluid flow through a cylindrical tube have been done by some researchers because it is related with the real-life applications such as blood flow in vessel tube, chemical and oil flow in pipelines and others. Therefore, the main purpose of the present study is to obtain analytical solutions for unsteady flow of Casson fluid pass through a cylinder with slip velocity effect at the boundary condition. Dimensional governing equations are converted into dimensionless forms by using the appropriate dimensionless variables. Dimensionless parameters are obtained through dimensionless process such as Casson fluid parameters. Then, the dimensionless equations of velocity with the associated initial and boundary conditions are solved by using Laplace transform with respect to time variable and finite Hankel transform of zero order with respect to the radial coordinate. Analytical solutions of velocity profile are obtained. The obtained analytical result for velocity is plotted graphically by using Maple software. Based on the obtained result, it can be observed that increasing in Casson parameter, time and slip velocity will lead to increment in fluid velocity. Lastly, Newtonian fluid velocity is uniform from the boundary to the center of cylinder while Casson fluid velocity is decreased when approaching to the center of cylinder. The present result is validated when the obtained analytical solution of velocity is compared with published result and found in a good agreement.


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