Modeling Chemotaxis of Microswimmers: From Individual to Collective Behavior

Liebchen, Benno; Löwen, Hartmut

doi:10.1142/9781786347015_0020

Cited by 12 publications

(18 citation statements)

References 55 publications

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“…Minimal model for chemically interacting particles: Let us consider an ensemble of N overdamped Brownian point particles representing microorganisms or colloids responding to the gradient of a concentration field c( r, t) either by chemotaxis (microorganisms) [22,38,39] or by (diffusio)phoresis (synthetic colloids) [40]. The position of the i-th particle evolves in time as ˙ r i (t) = β∇c( r i , t)…”

Section: Chemotaxis and Phoretic Interactionsmentioning

confidence: 99%

“…(1,2) describe an auto-chemotactic agent interacting with its selfproduced (or self-consumed) chemical field. While the concentration field due to a stationary agent at position r 0 is isotropic and reads (if assuming that the production is instantaneously switched on at time zero) [39,52]:…”

Section: Autochemotaxismentioning

confidence: 99%

“…In 3D the steady state solution of equation (2) for k d = 0 and constant r i (t) = r i reads (see e.g. [39] for variants of this solution and considerations in other dimensions):…”

Section: Autochemotaxismentioning

confidence: 99%

“…a degradation in microorganisms, or an effective "decay" of the chemical species which are relevant for phoretic interactions in autophoretic Janus colloids, due to bulk reactions (including association-dissociation reactions), the steady state solution of Eq. ( 2) reads [39]:…”

Section: Autochemotaxismentioning

confidence: 99%

“…For a single point source moving with a constant velocity r 1 (t) = vt, the solution of Eq. ( 2) reads instead [39]…”

Section: Far-field Interactions In Janus Colloidsmentioning

confidence: 99%

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Which interactions dominate in active colloids?

Liebchen

Löwen

2019

The Journal of Chemical Physics

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Despite a mounting evidence that the same gradients which active colloids use for swimming, induce important crossinteractions (phoretic interaction), they are still ignored in most many-body descriptions, perhaps to avoid complexity and a zoo of unknown parameters. Here we derive a simple model, which reduces phoretic far-field interactions to a pair-interaction whose strength is mainly controlled by one genuine parameter (swimming speed). The model suggests that phoretic interactions are generically important for autophoretic colloids (unless effective screening of the phoretic fields is strong) and should dominate over hydrodynamic interactions for the typical case of half-coating and moderately nonuniform surface mobilities. Unlike standard minimal models, but in accordance with canonical experiments, our model generically predicts dynamic clustering in active colloids at low density. This suggests that dynamic clustering can emerge from the interplay of screened phoretic attractions and active diffusion.

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Section: Chemotaxis and Phoretic Interactionsmentioning

confidence: 99%

Section: Autochemotaxismentioning

confidence: 99%

“…In 3D the steady state solution of equation (2) for k d = 0 and constant r i (t) = r i reads (see e.g. [39] for variants of this solution and considerations in other dimensions):…”

Section: Autochemotaxismentioning

confidence: 99%

Section: Autochemotaxismentioning

confidence: 99%

“…For a single point source moving with a constant velocity r 1 (t) = vt, the solution of Eq. ( 2) reads instead [39]…”

Section: Far-field Interactions In Janus Colloidsmentioning

confidence: 99%

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Which interactions dominate in active colloids?

Liebchen

Löwen

2019

The Journal of Chemical Physics

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Active and Passive Motion in Complex pH‐Fields

et al. 2021

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We create pH landscapes of increasing spatial complexity by placing ion exchange resin beads of different types and sizes in a closed cell featuring a negatively charged bottom substrate. We thus extend previous measurements in a chemically homogeneous background to investigations in chemically structured backgrounds, which evolve in time. We determine local pH gradients by photometry and study the resulting solvent flows along the substrate by tracking passive tracer particles. Analytical modelling of the dispersion of chemicals is possible for situations with dominantly diffusive transport. We then release phoretic swimmers in differently shaped pH fields and study their motion for selected examples. Catalytic Janus swimmers assembled in the wake of a mobile pH source form a modular swimmer showing a noise‐dominated trajectory. For standard modular swimmers with passive cargo, we identify well‐defined and reproducible swimming trajectory types at and around single pH sources. These include swimmer deflection and swing‐by maneuvers, swimmer trapping and escape, as well as circular orbits. More complicated paths result from combining the pH fields of multiple pH sources. Finally, we address swimmer‐swimmer interactions resulting from the superposition of their own pH fields. Our findings clearly demonstrate the high potential of chemically structured environments for swimmer steering. They can further be rationalized in a simple heuristic model considering the interplay of phoretic flows on different length and time scales and its influence on swimmer speed, orientation and emerging propulsion direction. In view of the vast range of possible combinations, our study has to remain preliminary. We anticipate, however, that it will aid the general understanding of transport experiments in pH‐driven systems and other types of phoresis and thus also help design novel and useful strategies for directed transport on the micro‐scale.

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High-Resolution Positivity and Asymptotic Preserving Numerical Methods for Chemotaxis and Related Models

Chertock

Kurganov

2019

Active Particles, Volume 2

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Modeling Chemotaxis of Microswimmers: From Individual to Collective Behavior

Cited by 12 publications

References 55 publications

Which interactions dominate in active colloids?

Which interactions dominate in active colloids?

Active and Passive Motion in Complex pH‐Fields

High-Resolution Positivity and Asymptotic Preserving Numerical Methods for Chemotaxis and Related Models

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