Basic Concepts of Stokes Flows

Abstract

Stokes flows have many applications in both physical theory and practice. For example, they have been used to describe dynamics of complex fluids in microfluidics, lab-on-chip technologies [1], medical applications [2, 3], design of innovative materials [4-6] and micro-devices-e.g. to carry drugs [7, 8] or act as fuel cells [9]-and in biological systems [10-15]. In this chapter, we discuss some fundamental properties of Stokes flows, namely: negligibility of inertial forces, reversibility and the minimum energy dissipation theorem. First we will briefly discuss how the neglecting of inertial forces simplifies the nonlinear Navier-Stokes equations to the linear Stokes equations. We then discuss two basic aspects of Stokes flows: reversibility and the minimum energy dissipation theorem. In order to bring out the nature of the three principles, we will demonstrate by example how these properties can be used to obtain conclusions about investigated fluid systems without laborious construction of analytical solutions. We then move beyond the Stokes approximation in various ways in order to see how the principles work in a general context. Finally, we conclude by discussing the logical structure of the principles as revealed by the examples considered.

Control of Nanostructured Polysulfone Membrane Preparation by Phase Inversion Method

“…The relationship between the mobility of the ion, m PSf , and the characteristics of the polymer could be described through a simple Stoke model [64] that follows the velocity of a small particle (spherical with a radius r PSf ) in a homogeneous fluid material with a viscosity η PSf when a force (i.e., electrical q PSf E) acts on it.…”

Experimental and Numerical Investigation of Polymer Pore-Clogging in Micromodels

“…In the conducted experiments, the injection rate is very low, resulting in a Reynolds number far less than 1. Therefore, the Stokes flow governing equations are used to solve the flow of polymer solution, where inertial forces are negligible compared to viscous and pressure forces (Durbin et al, 2010;Trombley and Ekiel-Jeżewska, 2019). As the simulation time steps are small and the two-way coupling solves the flow equations for the updated conditions each time step, steady-state conditions for fluid flow modeling can be used within a time-step interval.…”

Experimental and Numerical Investigation of Polymer Pore-Clogging in Micromodels

“…where inertial forces are negligible compared to viscous and pressure forces (Durbin et al, 2010;Trombley and Ekiel-Jeżewska, 2019). As the simulation time steps are small and the two-way coupling solves the flow equations for the updated conditions each time step, steady-state conditions for fluid flow modeling can be used within a time-step interval.…”