Convective Shear flow, role

In practice, one often deals with the case in which particles are completely entrained by the flow and convective transfer due to the shear flow plays the main role. In studying the corresponding diffusion processes, it is convenient to attach the frame of reference to the particle center of gravity then this frame moves translationally at the particle velocity, and the particle itself can freely rotate around the origin. For linear shear flow, the fluid velocity components have the form... 

The liver is a vital organ in the body that plays a primary role in the digestive system in detoxification, protein synthesis, and filtering of blood [56]. Liver-on-a-chip platforms have been developed to understand liver function better and to study drug hepatotoxicity and metabolism [29, 57, 58]. A microfluidic-based device fabricated to mimic the permeable sinusoid endothelial barrier between hepa-tocytes and liver [29] includes three main sections—a central channel to pack the hepatocytes, a microfluidic sinusoid barrier consisting of a set of narrow (2 mm wide) microchannels to model the endothelial barrier, and a convection microfluidic channel surrounding the barrier (Fig. 5A). The flow of nutrients through the convection microfluidic channel feeds the hepatocytes. This system mimics the transportation between blood flow and hepatocytes, and the shear stress over hepatocytes with a patterned set of microchannels. 

Fluid flow in small devices acts differently from those in macroscopic scale. The Reynolds number (Re) is the most often mentioned dimensionless number in fluid mechanics. The Re number, defined by pUL/jj, represents the ratio of inertial forces to viscous ones. In most circumstances involved in micro- and nanofluidics, the Re number is at least one order of magnitude smaller than unity, ruling out any turbulence flows in micro/nanochannels. Inertial force plays an insignificant role in microfluidics, and as systems continue to scale down, it will become even less important. For such small Re number flows, the convective term pu Vm) of Navier-Stokes equations can be dropped. Without this nonlinear convection, simple micro/nanofluidic systems have laminar, deterministic flow patterns. They have parabolic velocity profile in pressure-driven flows, plug-like velocity profile in elec-froosmotic flows, or a superposition of both. One of the benefits from the low Re number flow is that genomic material can be transported easily without shearing in Lab-... 

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