Imperial College London
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ProfessorDarrenCrowdy

Faculty of Natural Sciences, Department of Mathematics

Professor in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8587d.crowdy Website

 
 
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Location

 

735Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Crowdy:2022:10.1017/jfm.2021.936,
author = {Crowdy, D},
doi = {10.1017/jfm.2021.936},
journal = {Journal of Fluid Mechanics},
pages = {1--11},
title = {Equilibrium tilt of slippery elliptical rods in creeping simple shear},
url = {http://dx.doi.org/10.1017/jfm.2021.936},
volume = {931},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - It is shown that shape anisotropy and intrinsic surface slip lead to equilibrium tilt of slippery particles in a creeping simple shear flow, even for nearly shape-isotropic particles with a cross-section that is close to circular provided the Navier-slip length is sufficiently large. We study a rigid particle with an elliptical cross-section, and of infinite extent in the vorticity direction, in simple shear. A Navier-slip boundary condition is imposed on its surface. When a Navier-slip length parameter  λ  is infinite, an analytical solution is derived for the Stokes flow around a particle tilting in equilibrium at an angle  (1/2)cos−1((1−k)/(1+k))  to the flow direction where  0≤k≤1  is the ratio of the semi-minor to semi-major axes of its elliptical cross-section. A regular perturbation analysis about this analytical solution is then performed for small values of  1/λ  and a numerical continuation method implemented for larger values. It is found that an equilibrium continues to exist for any anisotropic particle  k<1  provided  λ≥λcrit(k)  where  λcrit(k)  is a critical Navier-slip length parameter determined here. As the case  k→1  of a circular cross-section is approached, it is found that  λcrit(k)→∞ , so the range of Navier-slip lengths allowing equilibrium tilt shrinks as shape anistropy is lost. Novel theoretical connections with equilibria for constant-pressure gas bubbles with surface tension are also pointed out.
AU  - Crowdy,D
DO  - 10.1017/jfm.2021.936
EP  - 11
PY  - 2022///
SN  - 0022-1120
SP  - 1
TI  - Equilibrium tilt of slippery elliptical rods in creeping simple shear
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2021.936
UR  - https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/equilibrium-tilt-of-slippery-elliptical-rods-in-creeping-simple-shear/F25C2C1515ED3861D4AEECDE6A407726
UR  - http://hdl.handle.net/10044/1/92748
VL  - 931
ER  -
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