Mathematical modelling of couple stresses on fluid flow in constricted tapered artery in presence of slip velocity-effects of catheter

2014 ◽  
Vol 35 (8) ◽  
pp. 947-958 ◽  
Author(s):  
J. V. R. Reddy ◽  
D. Srikanth ◽  
S. K. Murthy
Keyword(s):  
Fluid Flow ◽  
Mathematical Modelling ◽  
Slip Velocity ◽  
Couple Stresses ◽  
Tapered Artery

scholarly journals Mathematical modelling of fluid flow and solute transport to define operating parameters for in vitro perfusion cell culture systems

2020 ◽  
Vol 10 (2) ◽  
pp. 20190045 ◽  
Author(s):  
Lauren Hyndman ◽  
Sean McKee ◽  
Nigel J. Mottram ◽  
Bhumika Singh ◽  
Steven D. Webb ◽  
...  
Keyword(s):  
Cell Culture ◽  
Fluid Flow ◽  
Mathematical Modelling ◽  
Solute Transport ◽  
Computational Modelling ◽  
Operating Parameters ◽  
Perfusion Cell Culture ◽  
Culture Systems ◽  
Cell Culture Systems

In recent years, there has been a move away from the use of static in vitro two-dimensional cell culture models for testing the chemical safety and efficacy of drugs. Such models are increasingly being replaced by more physiologically relevant cell culture systems featuring dynamic flow and/or three-dimensional structures of cells. While it is acknowledged that such systems provide a more realistic environment within which to test drugs, progress is being hindered by a lack of understanding of the physical and chemical environment that the cells are exposed to. Mathematical and computational modelling may be exploited in this regard to unravel the dependency of the cell response on spatio-temporal differences in chemical and mechanical cues, thereby assisting with the understanding and design of these systems. In this paper, we present a mathematical modelling framework that characterizes the fluid flow and solute transport in perfusion bioreactors featuring an inlet and an outlet. To demonstrate the utility of our model, we simulated the fluid dynamics and solute concentration profiles for a variety of different flow rates, inlet solute concentrations and cell types within a specific commercial bioreactor chamber. Our subsequent analysis has elucidated the basic relationship between inlet flow rate and cell surface flow speed, shear stress and solute concentrations, allowing us to derive simple but useful relationships that enable prediction of the behaviour of the system under a variety of experimental conditions, prior to experimentation. We describe how the model may used by experimentalists to define operating parameters for their particular perfusion cell culture systems and highlight some operating conditions that should be avoided. Finally, we critically comment on the limitations of mathematical and computational modelling in this field, and the challenges associated with the adoption of such methods.

Molecular Dynamics Study on Fluid Flow in Nanochannels With Permeable Walls

2016 ◽  
Author(s):  
Jian-Fei Xie ◽  
Bing-Yang Cao
Keyword(s):  
Molecular Dynamics ◽  
Boundary Condition ◽  
Fluid Flow ◽  
Slip Velocity ◽  
Smooth Surface ◽  
Porous Wall ◽  
Permeable Surface ◽  
Fluid Density ◽  
Maxwell Theory ◽  
Permeable Walls

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.

Analytical Solution of Unsteady Casson Fluid Flow Through a Vertical Cylinder with Slip Velocity Effect

2021 ◽  
Vol 87 (1) ◽  
pp. 68-75
Author(s):  
Wan Faezah Wan Azmi ◽  
Ahmad Qushairi Mohamad ◽  
Lim Yeou Jiann ◽  
Sharidan Shafie
Keyword(s):  
Fluid Flow ◽  
Analytical Solution ◽  
Newtonian Fluid ◽  
Analytical Solutions ◽  
Slip Velocity ◽  
Fluid Velocity ◽  
Real Life ◽  
Casson Fluid ◽  
Flow Through ◽  
Velocity Effect

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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