8.6 Supplementary reading [Stokes flow top]

Some further concepts are covered in related texts. Low-Re number flows from the standpoint of perturbation expansions are covered in [57, 8, 63], including discussions of Stokes’ and Whitehead’s paradoxes and the Oseen linearization of flow around a circular cylinder. Faxén laws are covered in [63, 64, 65, 6]. The Lorentz reciprocal theorem is covered in [65]. A variety of theorems and velocity/stress properties of the Stokes flow fields are discussed in [57, 64, 65]. A stochastic description of Brownian motion of particles can be found in [64] and a similar description with a focus on macromolecules can be found in [66]. Descriptions of droplet motion with surfactant effects can be found in [6].

Stokes flow can be viewed from a thermodynamic standpoint as the fluid-mechanical regime in which the system departs only slightly from equilibrium. Because of this, the thermodynamics of irreversible processes with slight deviations from equilibrium [67, 68] is applicable, and reciprocal relations apply when we link fluid flow with ion flow, as is important in Chapters 9, 10, 13, and 15.

Specialized results relevant to discussion of particle transport in this chapter can be found in [69, 70, 64, 71, 72, 73], and specialized results related to particle-image velocimetry are discussed for macroscale flows in [74] and for microscale flows in [16].

Some examples of our research where Stokes flow analysis is relevant include our circulating tumor cell capture microchips and our dielectrophoretic manipulation of microparticles.

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