© Cambridge University Press 2010

Brian J. Kirby, PhD

Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY

Powerpoint Slides to AccompanyMicro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices

Chapter2

© 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

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• 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

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• The velocity distribution in a Couette flow is linear

• The viscous stress in a Couette flow is uniform

Sec 2.1.1: Couette Flow

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• 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

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• 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

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• 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