© Cambridge University Press 2010 Brian J. Kirby, PhD Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY Powerpoint Slides to Accompany Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices Chapter 4

© Cambridge University Press 2010 Fick’s law and diffusivity describe scalar transport by random microscopic processes Microfluidic devices often have flows in the high-Pe, low-Re regime High Pe and low Re means that mixing is difficult to accomplish but laminar flow patterning is easy to accomplish Ch 4: Passive Scalar Transport: Dispersion, Patterning, Mixing

© Cambridge University Press 2010 passive scalars are properties that are scalar (not vector) whose convective velocity component is that of the fluid this ignores vector properties like momentum or vorticity this ignores transport effects that move scalars relative to fluid, such as gravity acting on a dense particle or electric fields acting on a charged molecule the two scalar fluxes are diffusion and convection Sec 4.1: Passive Scalar Transport Equation

© Cambridge University Press 2010 applying the scalar fluxes to a differential control volume leads to the passive scalar transport equation Sec 4.1: Passive Scalar Transport Equation

© Cambridge University Press 2010 nondimensionalizing the passive scalar transport equation leads to the Peclet number Sec 4.1: Passive Scalar Transport Equation

© Cambridge University Press 2010 mixing can be thought of as a two-step process: stirring from fluid motion, followed by diffusion across the steep scalar gradients generated by the stirring the diffusive part can be explained by studying a 1-D diffusion problem: diffusion across the interface between two species Sec 4.2: Physics of Mixing

© Cambridge University Press 2010 many microfluidic systems create flows with no stirring, so the result is close to the 1D diffusion case (VERY LITTLE MIXING) Sec 4.2: Physics of Mixing

© Cambridge University Press 2010 when there is very little mixing, multiple streams of fluid can be used to pattern the chemical species inside a microchannel the widths of the fluid streams are algebraic functions of the flow rates Sec 4.5: Laminar Flow Patterning

© Cambridge University Press 2010 low mixing enables patterning, but high mixing is required for chemical assays mixing is enhanced by “stirring”, or increasing the interfacial area between regions of different scalar concentration, i.e., shortening diffusion length scales Sec 4.3: Microfluidic Mixing