© 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 2

© Cambridge University Press 2010 The Navier-Stokes equations can be solved analytically if certain simplifications are made The convection term is zero for flow in long, unidirectional channels Two simple solutions include Couette Flow and Poiseuille Flow Ch 2: Unidirectional Flow

© Cambridge University Press 2010 Couette flow is the flow between two infinite parallel plates with no pressure gradient Couette flow has no acceleration, no net pressure forces, no net convective transport, and no net viscous forces Sec 2.1.1: Couette Flow

© Cambridge University Press 2010 The velocity distribution in a Couette flow is linear The viscous stress in a Couette flow is uniform Sec 2.1.1: Couette Flow

© Cambridge University Press 2010 Hagen-Poiseuille flow is the flow in an infinite circular tube driven by a uniform pressure gradient Poiseuille flow describes a steady balance between net pressure forces and net viscous forces Sec 2.1.2: Poiseuille Flow

© Cambridge University Press 2010 The concavity of the velocity in a Poiseuille flow is uniform The Reynolds number indicates whether the laminar solution is observed Sec 2.1.2: Poiseuille Flow

© Cambridge University Press 2010 Startup describes the temporal dependence of a flow as the boundary starts moving or the pressure is applied Development describes the spatial dependence of a flow as it moves from an entrance to a region where entrance effects can be ignored Sec 2.2: Startup and Development of Unidirectional Flows