© 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 3

© Cambridge University Press 2010 The fully developed Poiseuille flow solution approximates the flow rate- pressure relation in long, narrow channels Fluid channels can be modeled using electrical circuit theory with equivalent component properties The hydraulic resistance is a parameter that measures the resistance of a channel to volumetric flow hydraulic impedance adds the capacity of the fluid interfaces (channel walls or bubbles) to deform Ch 3: Hydraulic Circuit Analysis

© Cambridge University Press 2010 Integrating the Hagen-Poiseuille flow distribution leads to a relation for volumetric flow rate in terms of the pressure gradient This can be discretized to describe the hydraulic resistance of a long, circular tube Sec 3.1 : Hydraulic Circuits

© Cambridge University Press 2010 For tubes with noncircular cross sections, a hydraulic radius can be defined to approximate the hydraulic resistance The hydraulic resistance leads to the Hagen-Poiseuille law, which is analogous to Ohm’s law Sec 3.1 : Hydraulic Circuits

© Cambridge University Press 2010 Hydraulic resistance describes the system response for steady pressure gradients Unsteady pressure gradients are described using compliance i.e. hydraulic capacitance Sec 3.2 : Hydraulic Circuit Elements

© Cambridge University Press 2010 Hydraulic resistance describes the system response for steady pressure gradients Unsteady pressure gradients are described using compliance i.e. hydraulic capacitance Sec 3.2 : Hydraulic Circuit Elements

© Cambridge University Press 2010 Conservation of mass is analogous to Kirchoff’s Current Law Sec 3.2 : Hydraulic Circuit Elements

© Cambridge University Press 2010 Sec 3.2 : Hydraulic Circuit Elements Series and parallel circuit laws follow from conservation of mass at nodes combined with the component flow relations

© Cambridge University Press 2010 Sec 3.2 : Hydraulic Circuit Elements Solving for the steady flow in a microfluidic system involves solving a set of real algebraic equations For sinusoidally oscillating flow, a set of complex algebraic equations is solved