Abstract
Kinematic and dynamic conditions for the existence, or otherwise, of viscous eddies due to point, ring or a line distribution of stokeslets near no-slip boundaries are investigated. Boundaries considered are (i) a single plane boundary, (ii) two parallel plane boundaries, (iii) an infinite cylinder, and (iv) a finite cylinder. It is found that the following constraints on the fluid lead to the existence of eddies (i) a zero flux condition, (ii) confinement due to boundaries, (iii) streamline convergence near the singularity, and (iv) the interaction of flow fields due to adjacent stokeslets. The existence or non-existence of various viscous eddies is illustrated and discussed in detail for the case of infinite line distributions of stokeslets (i.e. a two-dimensional stokeslet). The paper suggests that flow fields produced by sessile micro-organisms are determined primarily by the container geometry in which they are located.
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