Projects per year
Abstract
We study exact solutions for the slow viscous flow of an infinite liquid caused by two rigid spheres approaching each either along or parallel to their line of centres, valid at all separations. This goes beyond the applicable range of existing solutions for singular hydrodynamic interactions (HIs) which, for practical applications, are limited to the nearcontact or far field region of the flow. For the normal component of the HI, by use of a bipolar coordinate system, we derive the stream function for the flow as Re→0 and a formula for the singular (squeeze) force between the spheres as an infinite series. We also obtain the asymptotic behaviour of the forces as the nondimensional separation between the spheres goes to zero and infinity, rigorously confirming and improving upon known results relevant to a widely accepted lubrication theory. Additionally, we recover the force on a sphere moving perpendicularly to a plane as a special case. For the tangential component, again by using a bipolar coordinate system, we obtain the corresponding infinite series expression of the (shear) singular force between the spheres. All results hold for retreating spheres, consistent with the reversibility of Stokes flow. We demonstrate substantial differences in numerical simulations of colloidal fluids when using the present theory compared with existing multipole methods. Furthermore, we show that the present theory preserves positive definiteness of the resistance matrix R in a number of situations in which positivity is destroyed for multipole/perturbative methods
Original language  English 

Article number  062001 
Number of pages  28 
Journal  Physics of Fluids 
Volume  32 
Issue number  6 
Early online date  3 Jun 2020 
DOIs  
Publication status  Published  30 Jun 2020 
Fingerprint Dive into the research topics of 'The Singular Hydrodynamic Interactions Between Two Spheres In Stokes Flow'. Together they form a unique fingerprint.
Projects
 2 Finished

4D printing using programmable soft materials: from rheology to technology
1/08/17 → 31/07/18
Project: Research
