A Direct Boundary Integral Method for a Mobility Problem

2000 ◽  
Vol 7 (1) ◽  
pp. 73-84
Author(s):  
Mirela Kohr
Keyword(s):  
Solid Particle ◽  
Integral Method ◽  
Surface Force ◽  
Rigid Wall ◽  
Uniqueness Result ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Fredholm Integral Equations ◽  
Total Force ◽  
Mobility Problem

Abstract The problem of a Stokes flow in the presence of a solid particle, a rigid wall and a viscous cell is formulated as a system of Fredholm integral equations of the second kind, with the surface force on the boundary of the solid particle and the velocity on the interface as unknowns. The particularity of the problem consists in the fact that the total force and the total torque of the flow on the solid particle are zero. The existence and the uniqueness result of solution is obtained when the boundaries are curves of the class C 2.

scholarly journals Motion of a solid particle in a shear flow along a porous slab

2012 ◽  
Vol 713 ◽  
pp. 271-306 ◽  
Author(s):  
Sondes Khabthani ◽  
Antoine Sellier ◽  
Lassaad Elasmi ◽  
François Feuillebois
Keyword(s):  
Shear Flow ◽  
Green’S Function ◽  
Solid Particle ◽  
Green's Function ◽  
Integral Method ◽  
Particle Surface ◽  
Slip Boundary Condition ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Darcy Problem

AbstractThe flow field around a solid particle moving in a shear flow along a porous slab is obtained by solving the coupled Stokes–Darcy problem with the Beavers and Joseph slip boundary condition on the slab interfaces. The solution involves the Green’s function of this coupled problem, which is given here. It is shown that the classical boundary integral method using this Green’s function is inappropriate because of supplementary contributions due to the slip on the slab interfaces. An ‘indirect boundary integral method’ is therefore proposed, in which the unknown density on the particle surface is not the actual stress, but yet allows calculation of the force and torque on the particle. Various results are provided for the normalized force and torque, namely friction factors, on the particle. The cases of a sphere and an ellipsoid are considered. It is shown that the relationships between friction coefficients (torque due to rotation and force due to translation) that are classical for a no-slip plane do not apply here. This difference is exhibited. Finally, results for the velocity of a freely moving particle in a linear and a quadratic shear flow are presented, for both a sphere and an ellipsoid.

scholarly journals UGUCA: A spectral-boundary-integral method for modeling fracture and friction

SoftwareX ◽  
2021 ◽  
Vol 15 ◽  
pp. 100785 ◽  
Author(s):  
David S. Kammer ◽  
Gabriele Albertini ◽  
Chun-Yu Ke
Keyword(s):  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Modeling Fracture
Sign in / Sign up

Export Citation Format

Share Document