The behavior of fluid interfaces far from equilibrium plays central roles in nature and in industry. Active swimmers trapped at interfaces can alter transport at fluid boundaries with far reaching implications. Swimmers can become trapped at interfaces in diverse configurations and swim persistently in these surface adhered states. The self-propelled motion of bacteria makes them ideal model swimmers to understand such effects. We have recently characterized the swimming of interfacially-trapped Pseudomonas aeruginosa PA01 moving in pusher mode. The swimmers adsorb at the interface with pinned contact lines, which
fix the angle of the cell body at the interface and constrain their motion. Thus, most interfacially-trapped bacteria swim along circular paths. Fluid interfaces form incompressible two-dimensional layers, altering leading order interfacial flows generated by the swimmers from those in bulk. In our previous work, we have visualized the interfacial flow around a pusher bacterium and described the flow field using two dipolar hydrodynamic modes; one stresslet mode whose symmetries differ from those in bulk, and another bulk mode unique to incompressible fluid interfaces. Based on this understanding, swimmers-induced tracer displacements and swimmer-swimmer pair interactions are explored using analysis and experiment. The settings in which multiple interfacial swimmers with circular motion can significantly enhance interfacial transport of tracers or promote mixing of other swimmers on the interface are identified through simulations and compared to experiment. This study identifies important factors of general interest regarding swimmers on or near fluid boundaries, and in the design of biomimetic swimmers to enhance transport at interfaces.
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Curve Lengthening via Regularized Motion Against Curvature from the Strong FCH Flow
We present a rigorous analysis of the transient evolution of nearly circular bilayer interfaces evolving under the thin interface limit, ε ≪ 1, of the mass preserving L2-gradient flow of the strong scaling of the functionalized Cahn–Hilliard equation. For a domain Ω ⊂ R2 we construct a bilayer manifold with boundary comprised of quasi-equilibria of the flow and a projection onto the manifold that associates functions u in an H2 tubular neighborhood of the manifold with an interface Γ embedded in Ω. The linearization of the flow about the manifold does not present a clear spectral separation of modes normal and tangential to the manifold. The dimension of the parameterization of the interfaces and the bilayer manifold controls both the normal coercivity of the manifold and the coupling between normal and tangential modes, both of which increase with this dimension. The key step in the analysis is the identification of a range of dimensions in which coercivity dominates the coupling, permitting the closure of the nonlinear estimates that establish the asymptotic stability of the manifold. Orbits originating in a thin, forward invariant, tubular neighborhood ultimately converge to an equilibrium associated to a circular interface. Projections of these orbits yield interfacial evolution equivalent at leading order to the regularized curve-lengthening motion characterized by normal motion against mean curvature, regularized by a higher order Willmore expression. The curve lengthening is driven by absorption of excess mass from the regions of Ω away from the interface, leading to high dimensional dynamics that are ill-posed in the ε → 0+ limit.
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- Award ID(s):
- 1813203
- NSF-PAR ID:
- 10359255
- Date Published:
- Journal Name:
- Journal of Dynamics and Differential Equations
- ISSN:
- 1040-7294
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s10884-022-10178-7
