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Register a new userHydrodynamics of a Semipermeable Vesicle Under Flow and Confinement
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Lipid bilayer membranes have a native (albeit small) permeability for water molecules. Under an external load, provided that the bilayer structure stays intact and does not suffer from poration or rupture, a lipid membrane deforms and its water influx/efflux is often assumed negligible in the absence of osmolarity. In this work we use boundary integral simulations to investigate the effects of water permeability on the vesicle hydrodynamics due to a mechanical load, such as the viscous stress from an external flow deforming a vesicle membrane in free space or pushing it through a confinement. Incorporating the membrane permeability into the framework of Helfrich free energy for an inextensible, elastic membrane as a model for a semipermeable vesicle, we illustrate that, in the absence of an osmotic stress gradient, the semipermeable vesicle is affected by water influx/efflux over a sufficiently long time or under a strong confinement. Our simulations quantify the conditions for water permeation to be negligible in terms of the time scales, flow strength, and confinement. These results shed light on how microfluidic confinement can be utilized to estimate membrane permeability.
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Although the behavior of fluid-filled vesicles in steady flows has been extensively studied, far less is understood regarding the shape dynamics of vesicles in time-dependent oscillatory flows. Here, we investigate the nonlinear dynamics of vesicles in large amplitude oscillatory extensional (LAOE) flows using both experiments and boundary integral (BI) simulations. Our results characterize the transient membrane deformations, dynamical regimes, and stress response of vesicles in LAOE in terms of reduced volume (vesicle asphericity), capillary number ($Ca$, dimensionless flow strength), and Deborah number ($De$, dimensionless flow frequency). Results from single vesicle experiments are found to be in good agreement with BI simulations across a wide range of parameters. Our results reveal three distinct dynamical regimes based on vesicle deformation: pulsating, reorienting, and symmetrical regimes. We construct phase diagrams characterizing the transition of vesicle shapes between pulsating, reorienting, and symmetrical regimes within the two-dimensional Pipkin space defined by $De$ and $Ca$. Contrary to observations on clean Newtonian droplets, vesicles do not reach a maximum length twice per strain rate cycle in the reorienting and pulsating regimes. The distinct dynamics observed in each regime result from a competition between the flow frequency, flow time scale, and membrane deformation timescale. By calculating the particle stresslet, we quantify the nonlinear relationship between average vesicle stress and strain rate. Additionally, we present results on tubular vesicles that undergo shape transformation over several strain cycles. Broadly, our work provides new information regarding the transient dynamics of vesicles in time-dependent flows that directly informs bulk suspension rheology.
Colloid or nanoparticle mobility under confinement is of central importance to a wide range of physical and biological processes. Here, we introduce a minimal model of particles in a hydrodynamic continuum to examine how particle shape and concentration affect the transport of particles in spherical confinement. Specifically, an immersed boundary-General geometry Ewald-like approach is adopted to simulate the dynamics of spheres and cylinders under the influence of short-and long-range fluctuating hydrodynamic interactions with appropriate non-slip conditions at the confining walls. An efficient $it{O(N)}$ parallel finite element algorithm is used, thereby allowing simulations at high concentrations, while a Chebyshev polynomial approximation is implemented in order to satisfy the fluctuation-dissipation theorem. A concentration-dependent anomalous diffusion is observed for suspended particles. It is found that introducing cylinders in a background of spheres, i.e. particles with a simple degree of anisotropy, has a pronounced influence on the structure and dynamics of the particles. First, increasing the fraction of cylinders induces a particle segregation effect, where spheres are pushed towards the wall and cylinders remain near the center of the cavity. This segregation leads to lower mobility for the spheres relative to that encountered in a system of pure spheres at the same volume fraction. Second, the diffusive-to-anomalous transition and the degree of anomaly--quantified by the power-law exponent in the mean square displacement vs. time relation-both increase as the fraction of cylinders becomes larger. These findings are of relevance for studies of diffusion in the cytoplasm, where proteins exhibit a distribution of size and shapes that could lead to some of the effects identified in the simulations reported here.
With the continuing rapid development of artificial microrobots and active particles, questions of microswimmer guidance and control are becoming ever more relevant and prevalent. In both the applications and theoretical study of such microscale swimmers, control is often mediated by an engineered property of the swimmer, such as in the case of magnetically propelled microrobots. In this work, we will consider a modality of control that is applicable in more generality, effecting guidance via modulation of a background fluid flow. Here, considering a model swimmer in a commonplace flow and simple geometry, we analyse and subsequently establish the efficacy of flow-mediated microswimmer positional control, later touching upon a question of optimal control. Moving beyond idealised notions of controllability and towards considerations of practical utility, we then evaluate the robustness of this control modality to sources of variation that may be present in applications, examining in particular the effects of measurement inaccuracy and rotational noise. This exploration gives rise to a number of cautionary observations, which, overall, demonstrate the need for the careful assessment of both policy and behavioural robustness when designing control schemes for use in practice.
We present a study of the hydrodynamics of an active particle, a model squirmer, in an envi- ronment with a broken rotational symmetry: a nematic liquid crystal. By combining simulations with analytic calculations, we show that the hydrodynamic coupling between the squirmer flow field and liquid crystalline director can lead to re-orientation of the swimmers. The preferred orientation depends on the exact details of the squirmer flow field. In a steady state, pushers are shown to swim parallel with the nematic director while pullers swim perpendicular to the nematic director. This behaviour arises solely from hydrodynamic coupling between the squirmer flow field and anisotropic viscosities of the host fluid. Our results suggest that an anisotropic swimming medium can be used to characterise and guide spherical microswimmers in the bulk.
Despite their importance in many biological, ecological and physical processes, microorganismal fluid flows under tight confinement have not been investigated experimentally. Strong screening of Stokelets in this geometry suggests that the flow fields of different microorganisms should be universally dominated by the 2D source dipole from the swimmers finite-size body. Confinement therefore is poised to collapse differences across microorganisms, that are instead well-established in bulk. Here we combine experiments and theoretical modelling to show that, in general, this is not correct. Our results demonstrate that potentially minute details like microswimmers spinning and the physical arrangement of the propulsion appendages have in fact a leading role in setting qualitative topological properties of the hydrodynamic flow fields of micro-swimmers under confinement. This is well captured by an effective 2D model, even under relatively weak confinement. These results imply that active confined hydrodynamics is much richer than in bulk, and depends in a subtle manner on size, shape and propulsion mechanisms of the active components.
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