Nonlinear hydrodynamic phenomena in Stokes flow regime

2010 ◽  
Vol 239 (14) ◽  
pp. 1214-1224 ◽  
Author(s):  
J. Blawzdziewicz ◽  
R.H. Goodman ◽  
N. Khurana ◽  
E. Wajnryb ◽  
Y.-N. Young
Keyword(s):  
Flow Regime ◽  
Stokes Flow

Double-Layer Representation of Model Microorganisms by a Boundary Element Method

2012 ◽  
Author(s):  
Kohei Kyoya ◽  
Yohsuke Imai ◽  
Takami Yamaguchi ◽  
Takuji Ishikawa
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Flow Regime ◽  
Double Layer ◽  
Stokes Flow ◽  
Biomedical Engineering ◽  
Many Body ◽  
Body Interaction ◽  
Many Body Interactions ◽  
Element Method

Analysis of a suspension of microorganisms is important in environmental and biomedical engineering. Previous studies had problems of high computational load in simulating many-body interaction of non-spherical swimmers. In this study, we propose a boundary element method (BEM), based on the double-layer representation, for calculating interactions of two squirmers in Stokes flow regime. By comparing the trajectories of squirmers calculated by both single- and double-layer representations, we show the accuracy of the method. The developed method has potential to deal with many-body interactions of non-spherical microorganisms.

Plane Poiseuille flow of miscible layers with different viscosities: instabilities in the Stokes flow regime

2011 ◽  
Vol 686 ◽  
pp. 484-506 ◽  
Author(s):  
L. Talon ◽  
E. Meiburg
Keyword(s):  
Flow Regime ◽  
Stokes Flow ◽  
Poiseuille Flow ◽  
Long Wave ◽  
Interface Location ◽  
Large Growth ◽  
Diffusive Modes ◽  
Reynolds Number Flows ◽  
Sharp Interfaces ◽  
And Diffusion

AbstractWe investigate the linear stability of miscible, viscosity-layered Poiseuille flow. In the Stokes flow regime, diffusion is observed to have a destabilizing effect very similar to that of inertia in finite-Reynolds-number flows. For two-layer flows, four types of instability can dominate, depending on the interface location. Two interfacial modes exhibit large growth rates, while two additional bulk modes grow more slowly. Three-layer Stokes flows give rise to diffusive modes for each interface. These two diffusive interface modes can be in resonance, thereby enhancing the growth rate. Furthermore, modes without inertia and diffusion are also observed, consistent with a previous long-wave analysis for sharp interfaces. In contrast to that earlier investigation, the present analysis demonstrates that instability can also occur when the more viscous layer is in the centre, at larger wavenumbers.

Computational Modeling of 3D Printed Tissue-on-a-Chip Microfluidic Devices as Drug Screening Platforms

2014 ◽  
Author(s):  
Filippos Tourlomousis ◽  
Robert C. Chang
Keyword(s):  
Flow Regime ◽  
Concentration Profile ◽  
Drug Screening ◽  
Stokes Flow ◽  
Drug Concentration ◽  
Human Liver ◽  
Shear Stresses ◽  
Convection Diffusion ◽  
Micro Scale

Physiological tissue-on-a-chip technology is enabled by adapting microfluidics to create micro scale drug screening platforms that replicate the complex drug transport and reaction processes in the human liver. The ability to incorporate three-dimensional (3d) tissue models using layered fabrication approaches into devices that can be perfused with drugs offer an optimal analog of the in vivo scenario. The dynamic nature of such in vitro metabolism models demands reliable numerical tools to determine the optimum tissue fabrication process, flow, material, and geometric parameters for the most effective metabolic conversion of the perfused drug into the liver microenvironment. Thus, in this modeling-based study, the authors focus on modeling of in vitro 3d microfluidic microanalytical microorgan devices (3MD), where the human liver analog is replicated by 3d cell encapsulated alginate hydrogel based tissue-engineered constructs. These biopolymer constructs are hosted in the chamber of the 3MD device serving as walls of the microfluidic array of channels through which a fluorescent drug substrate is perfused into the microfluidic printed channel walls at a specified volumetric flow rate assuring Stokes flow conditions (Re<<1). Due to the porous nature of the hydrogel walls, a metabolized drug product is collected as an effluent stream at the outlet port. A rigorous modeling approached aimed to capture both the macro and micro scale transport phenomena is presented. Initially, the Stokes Flow Equations (free flow regime) are solved in combination with the Brinkman Equations (porous flow regime) for the laminar velocity profile and wall shear stresses in the whole shear mediated flow regime. These equations are then coupled with the Convection-Diffusion Equation to yield the drug concentration profile by incorporating a reaction term described by the Michael-Menten Kinetics model. This effectively yields a convection-diffusion–cell kinetics model (steady state and transient), where for the prescribed process and material parameters, the drug concentration profile throughout the flow channels can be predicted. A key consideration that is addressed in this paper is the effect of cell mechanotransduction, where shear stresses imposed on the encapsulated cells alter the functional ability of the liver cell enzymes to metabolize the drug. Different cases are presented, where cells are incorporated into the geometric model either as voids that experience wall shear stress (WSS) around their membrane boundaries or as solid materials, with linear elastic properties. As a last step, transient simulations are implemented showing that there exists a tradeoff with respect the drug metabolized effluent product between the shear stresses required and the residence time needed for drug diffusion.

Numerical Study on Mixing in a Chaotic Serpentine Mixer Using a Mapping Method

2009 ◽  
Author(s):  
T. G. Kang ◽  
M. K. Singh ◽  
P. D. Anderson ◽  
H. E. H. Meijer
Keyword(s):  
Reynolds Number ◽  
Flow Regime ◽  
Stokes Flow ◽  
Mapping Method ◽  
Creeping Flow ◽  
Chaotic Mixing ◽  
Original Design ◽  
Two Fluids ◽  
Serpentine Channel ◽  
Design Variables

We introduce a chaotic serpentine mixer (CSM), which is motivated by the three-dimensional serpentine channel [Liu et al., 2000, J. Microelectromech. Syst. 9, pp. 190–197], and demonstrate a systematic way of utilizing the mapping method [Singh et al., 2008, Microfluid Nanofluid 5, pp. 313–325] to find out an optimal set of design variables for the new mixer. The new mixer shows globally chaotic mixing even in the Stokes flow regime, while maintaining the benefits of the original design. One geometrical period of the mixer consists of two functional units, inducing two flow portraits with crossing streamlines. Each half period of the mixer consists of an “L-shaped” bend and a bypass channel. The two flow portraits may be either co-rotational or counter-rotational. As a preliminary study, first of all, mixing in the original serpentine channel has been analyzed to demonstrate the flow characteristics and to find out a critical Reynolds number showing chaotic mixing above the limit. The working principle of the newly proposed mixer is explained by the manifold of the deforming interface between two fluids. To optimize the mixer, we choose three key design variables: the sense of rotation of the two flows, the aspect ratio of the rectangular channel, and the lateral location of the bypass channel. Then, simulations for all possible combinations of the variables are carried out. At proper combinations of the variables, almost global chaotic mixing is observed in the creeping flow regime. The design windows, provided as a result of the parameter study, can be used to determine a proper set of the design variables to fit with a specific application. The deforming interface of the two fluids shows that, even in a poor mixer in Stokes flow regime, as the Reynolds number increases, more efficient mixing is resulted in due to the enhanced cross-sectional vertical motion and back flows near the bends.

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