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Microfluidics: Modeling, Mechanics and Mathematics by Bastian E. Rapp

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Chapter 18

Analytical Solutions to Transient Flow Problems

18.1 Time-Dependent Transient Effects: Acceleration and Deceleration

In this section we will study time-dependent phenomena of Poiseuille flow that are important, e.g., during the initiation or deceleration of flows. These are the two important phenomena that we will study primarily in the following sections. Before diving into the physics, we will briefly outline what we expect from accelerating and decelerating fluids. We will start with accelerating fluids. In Fig. 18.1a you can see an exemplary fluid mechanical problem in the form of a circular capillary with liquid at rest. We have already studied this setup during the derivation of the Hagen-Poiseuille flow (see section 16.3). ...

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