Ewald sum for hydrodynamic interactions of rigid spherical microswimmers

2018 ◽  
Vol 149 (14) ◽  
pp. 144110 ◽  
Author(s):  
Tapan Chandra Adhyapak ◽  
Sara Jabbari-Farouji
Keyword(s):  
Hydrodynamic Interactions ◽  
Ewald Sum

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.

scholarly journals Hydrodynamics can determine the optimal route for microswimmer navigation

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Abdallah Daddi-Moussa-Ider ◽  
Hartmut Löwen ◽  
Benno Liebchen
Keyword(s):  
Flow Field ◽  
Hydrodynamic Interactions ◽  
Optimal Trajectories ◽  
Optimal Route ◽  
Active Particles ◽  
Navigation Strategy ◽  
Navigation Strategies

AbstractAs compared to the well explored problem of how to steer a macroscopic agent, like an airplane or a moon lander, to optimally reach a target, optimal navigation strategies for microswimmers experiencing hydrodynamic interactions with walls and obstacles are far-less understood. Here, we systematically explore this problem and show that the characteristic microswimmer-flow-field crucially influences the navigation strategy required to reach a target in the fastest way. The resulting optimal trajectories can have remarkable and non-intuitive shapes, which qualitatively differ from those of dry active particles or motile macroagents. Our results provide insights into the role of hydrodynamics and fluctuations on optimal navigation at the microscale, and suggest that microorganisms might have survival advantages when strategically controlling their distance to remote walls.

scholarly journals Phoretic and hydrodynamic interactions of weakly confined autophoretic particles

2019 ◽  
Vol 150 (4) ◽  
pp. 044902 ◽  
Author(s):  
Eva Kanso ◽  
Sébastien Michelin
Keyword(s):  
Hydrodynamic Interactions
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