The hydrodynamic quantification of superhydrophobic slipperiness has traditionally employed two canonical problems – namely, shear flow about a single surface and pressuredriven channel flow. We here advocate the use of a new class of canonical problems, defined by the motion of a superhydrophobic particle through an otherwise quiescent liquid. In these problems the superhydrophobic effect is naturally measured by the enhancement of the Stokes mobility relative to the corresponding mobility of a homogeneous particle. We focus upon what may be the simplest problem in that class – the rotation of an infinite circular cylinder whose boundary is periodically decorated bymore »
Slender body theory for particles with noncircular crosssections with application to particle dynamics in shear flows
This paper presents a theory to obtain the force per unit length acting on a slender filament with a noncircular crosssection moving in a fluid at low Reynolds number. Using a regular perturbation of the inner solution, we show that the force per unit length has $O(1/\ln (2A))+O(\unicode[STIX]{x1D6FC}/\ln ^{2}(2A))$ contributions driven by the relative motion of the particle and the local fluid velocity and an $O(\unicode[STIX]{x1D6FC}/(\ln (2A)A))$ contribution driven by the gradient in the imposed fluid velocity. Here, the aspect ratio ( $A=l/a_{0}$ ) is defined as the ratio of the particle size ( $l$ ) to the crosssectional dimension ( $a_{0}$ ) and $\unicode[STIX]{x1D6FC}$ is the amplitude of the noncircular perturbation. Using thought experiments, we show that twolobed and threelobed crosssections affect the response to relative motion and velocity gradients, respectively. A twodimensional Stokes flow calculation is used to extend the perturbation analysis to crosssections that deviate significantly from a circle (i.e. $\unicode[STIX]{x1D6FC}\sim O(1)$ ). We demonstrate the ability of our method to accurately compute the resistance to translation and rotation of a slender triaxial ellipsoid. Furthermore, we illustrate novel dynamics of straight rods in a simple shear flow that translate and rotate quasiperiodically if they have twolobed crosssection, more »
 Award ID(s):
 1803156
 Publication Date:
 NSFPAR ID:
 10162408
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 877
 Page Range or eLocationID:
 1098 to 1133
 ISSN:
 00221120
 Sponsoring Org:
 National Science Foundation
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