scholarly journals The raspberry model for hydrodynamic interactions revisited. I. Periodic arrays of spheres and dumbbells

2015 ◽  
Vol 143 (8) ◽  
pp. 084107 ◽  
Author(s):  
Lukas P. Fischer ◽  
Toni Peter ◽  
Christian Holm ◽  
Joost de Graaf
Keyword(s):  
Hydrodynamic Interactions ◽  
Periodic Arrays ◽  
Arrays Of Spheres

Permeability of periodic arrays of spheres

2005 ◽  
Vol 32 (6) ◽  
pp. 659-665 ◽  
Author(s):  
A. Kadaksham ◽  
S.B. Pillapakkam ◽  
P. Singh
Keyword(s):  
Periodic Arrays ◽  
Arrays Of Spheres

Directional locking and deterministic separation in periodic arrays

2009 ◽  
Vol 627 ◽  
pp. 379-401 ◽  
Author(s):  
JOELLE FRECHETTE ◽  
GERMAN DRAZER
Keyword(s):  
External Force ◽  
Hydrodynamic Interactions ◽  
Square Lattice ◽  
Stokesian Dynamics ◽  
Particle Mobility ◽  
Periodic Arrays ◽  
Moving Particle ◽  
Dynamics Simulations ◽  
Solid Obstacles ◽  
Vector Separation

We investigate the dynamics of a non-Brownian sphere suspended in a quiescent fluid and moving through a periodic array of solid obstacles under the action of a constant external force by means of Stokesian dynamics simulations. We show that in the presence of non-hydrodynamic, short-range interactions between the solid obstacles and the suspended sphere, the moving particle becomes locked into periodic trajectories with an average orientation that coincides with one of the lattice directions and is, in general, different from the direction of the driving force. The locking angle depends on the details of the non-hydrodynamic interactions and could lead to vector separation of different species for certain orientations of the external force. We explicitly show the presence of separation for a mixture of suspended particles with different roughness, moving through a square lattice of spherical obstacles. We also present a dilute model based on the two-particle mobility and resistance functions for the collision between spheres of different sizes. This simple model predicts the separation of particles of different size and also suggests that microdevices that maximize the differences in interaction area between the different particles and the solid obstacles would be more sensitive for size separation based on non-hydrodynamic interactions.

Stokes flow through periodic arrays of spheres

1982 ◽  
Vol 115 (-1) ◽  
pp. 13 ◽  
Author(s):  
A. A. Zick ◽  
G. M. Homsy
Keyword(s):  
Stokes Flow ◽  
Periodic Arrays ◽  
Flow Through ◽  
Arrays Of Spheres

scholarly journals Stirring by periodic arrays of microswimmers

2016 ◽  
Vol 811 ◽  
pp. 487-498 ◽  
Author(s):  
Joost de Graaf ◽  
Joakim Stenhammar
Keyword(s):  
Theoretical Work ◽  
Difficult Problem ◽  
Hydrodynamic Interactions ◽  
Bulk Fluid ◽  
Enhanced Diffusion ◽  
Periodic Arrays ◽  
Ewald Sum ◽  
Tracer Particles ◽  
Micro Organisms ◽  
New Strategies

The interaction between swimming micro-organisms or artificial self-propelled colloids and passive (tracer) particles in a fluid leads to enhanced diffusion of the tracers. This enhancement has attracted strong interest, as it could lead to new strategies to tackle the difficult problem of mixing on a microfluidic scale. Most of the theoretical work on this topic has focused on hydrodynamic interactions between the tracers and swimmers in a bulk fluid. However, in simulations, periodic boundary conditions (PBCs) are often imposed on the sample and the fluid. Here, we theoretically analyse the effect of PBCs on the hydrodynamic interactions between tracer particles and microswimmers. We formulate an Ewald sum for the leading-order stresslet singularity produced by a swimmer to probe the effect of PBCs on tracer trajectories. We find that introducing periodicity into the system has a surprisingly significant effect, even for relatively small swimmer–tracer separations. We also find that the bulk limit is only reached for very large system sizes, which are challenging to simulate with most hydrodynamic solvers.

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