Modeling of active swimmer suspensions and their interactions with the environment

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.

Emergent collective dynamics of bottom-heavy squirmers under gravity

We present the results of hydrodynamic simulations using the method of multi-particle collision dynamics for a system of squirmer microswimmers moving under the influence of gravity at low Reynolds numbers. In addition, the squirmers are bottom-heavy so that they experience a torque which aligns them along the vertical. The squirmers interact hydrodynamically by the flow fields of a stokeslet and rotlet, which are initiated by the acting gravitational force and torque, respectively, and by their own flow fields. By varying the ratio of swimming to bulk sedimentation velocity and the torque, we determine state diagrams for the emergent collective dynamics of neutral squirmers as well as strong pushers and pullers. For low swimming velocity and torque we observe conventional sedimentation, while the sedimentation profile becomes inverted when their values are increased. For neutral squirmers we discover convective rolls of circulating squirmers between both sedimentation states, which sit at the bottom of the system and are fed by plumes made of collectively sinking squirmers. At larger torques porous clusters occur that spawn single squirmers. The two latter states can also occur transiently starting from a uniform squirmer distribution and then disappear in the long-time limit. For strong pushers and pullers only weak plume formation is observed.

Biofilms at interfaces: microbial distribution in floating films

Cellular motility is a key function guiding microbial adhesion to interfaces, which is the first step in the formation of biofilms. The close association of biofilms and bioremediation has prompted extensive research aimed at comprehending the physics of microbial locomotion near interfaces. We study the dynamics and statistics of microorganisms in a 'floating biofilm', i.e., a confinement with an air-liquid interface on one side and a liquid-liquid interface on the other. We use a very general mathematical model, based on a multipole representation and probabilistic simulations, to ascertain the spatial distribution of microorganisms in films of different viscosities. Our results reveal that microorganisms can be distributed symmetrically or asymmetrically across the height of the film, depending on their morphology and the ratio of the film's viscosity to that of the fluid substrate. Long-flagellated, elongated bacteria exhibit stable swimming parallel to the liquid-liquid interface when the bacterial film is less viscous than the underlying fluid. Bacteria with shorter flagella on the other hand, swim away from the liquid-liquid interface and accumulate at the free surface. We also analyze microorganism dynamics in a flowing film and show how a microorganism's ability to resist 'flow-induced-erosion' from interfaces is affected by its elongation and mode of propulsion. Our study generalizes past efforts on understanding microorganism dynamics under confinement by interfaces and provides key insights on biofilm initiation at liquid-liquid interfaces.

Experiments and Agent Based Models of Zooplankton Movement within Complex Flow Environments

The movement of plankton is often dictated by local flow patterns, particularly during storms and in environments with strong flows. Reefs, macrophyte beds, and other immersed structures can provide shelter against washout and drastically alter the distributions of plankton as these structures redirect and slow the flows through them. Advection-diffusion and agent-based models are often used to describe the movement of plankton within marine and fresh water environments and across multiple scales. Experimental validation of such models of plankton movement within complex flow environments is challenging because of the difference in both time and spatial scales. Organisms on the scale of 1 mm or less swim by beating their appendages on the order of 1 Hz and are advected meters to kilometers over days, weeks, and months. One approach to study this challenging multiscale problem is to insert actively moving agents within a background flow field. Open source tools to implement this sort of approach are, however, limited. In this paper, we combine experiments and computational fluid dynamics with a newly developed agent-based modeling platform to quantify plankton movement at the scale of tens of centimeters. We use Artemia spp., or brine shrimp, as a model organism given their availability and ease of culturing. The distribution of brine shrimp over time was recorded in a flow tank with simplified physical models of macrophytes. These simplified macrophyte models were 3D-printed arrays of cylinders of varying heights and densities. Artemia nauplii were injected within these arrays, and their distributions over time were recorded with video. The detailed three-dimensional flow fields were quantified using computational fluid dynamics and validated experimentally with particle image velocimetry. To better quantify plankton distributions, we developed an agent-based modeling framework, Planktos, to simulate the movement of plankton immersed within such flow fields. The spatially and temporally varying Artemia distributions were compared across models of varying heights and densities for both the experiments and the agent-based models. The results show that increasing the density of the macrophyte bed drastically increases the average time it takes the plankton to be swept downstream. The height of the macrophyte bed had less of an effect. These effects were easily observed in both experimental studies and in the agent-based simulations.

Collective dynamics in a monolayer of squirmers confined to a boundary by gravity

We present a hydrodynamic study of a monolayer of squirmer model microswimmers confined to a boundary by strong gravity using the simulation method of multi-particle collision dynamics. The squirmers interact with each other via their self-generated hydrodynamic flow fields and thereby form a variety of fascinating dynamic states when density and squirmer type are varied. Weak pushers, neutral squirmers, and pullers have an upright orientation. With their flow fields they push neighbors away and thereby form a hydrodynamic Wigner fluid at lower densities. Furthermore, states of fluctuating chains and trimers, of kissing, and at large densities a global cluster exist. Finally, pushers at all densities can tilt against the wall normal and their in-plane velocities align to show swarming. It turns into chaotic swarming for strong pushers at high densities. We characterize all these states quantitatively.

Chemotaxis mediated interactions can stabilize the hydrodynamic instabilities in active suspensions

Ordered phases in active suspensions of polar swimmers are under long-wavelength hydrodynamic mediated instabilities. In this article, we show that chemical molecules dissolved in aqueous suspensions, as an unavoidable part of most wet active systems, can mediate long-range interactions and subsequently stabilize the polar phase. Chemoattractants in living suspensions and dissolved molecules in synthesized Janus suspensions are reminiscent of such chemical molecules. Communication between swimmers through the gradients of such chemicals is the foundation of this stabilization mechanism. To classify the stable states of such active systems, we investigate the detailed phase diagrams for two classes of systems with momentum conserving and non-conserving dynamics. Our linear stability analysis shows that the proposed stabilization mechanism can work for swimmers with different dynamical properties, e.g., pushers or pullers and with various static characteristics, e.g., spherical, oblate or prolate geometries.

Hydrodynamic Interaction Enhances Colonization of Sinking Nutrient Sources by Motile Microorganisms

In this study, we document hydrodynamics-mediated trapping of microorganisms around a moving spherical nutrient source such as a settling marine snow aggregate. There exists a range of size and excess density of the nutrient source, and motility and morphology of the microorganism under which hydrodynamic interactions enable the passive capture of approaching microorganisms onto a moving nutrient source. We simulate trajectories of chemotactic and non-chemotactic bacteria encountering a sinking marine snow particle effusing soluble nutrients. We calculate the average nutrient concentration to which the bacteria are exposed, under regimes of strong and weak hydrodynamic trapping. We find that hydrodynamic trapping can significantly amplify (by ≈40%) the nutrient exposure of bacteria, both chemotactic and non-chemotactic. The subtle interactions between hydrodynamic and chemotactic effects reveal non-trivial variations in this “hydrodynamic amplification,” as a function of relevant biophysical parameters. Our study provides a consistent description of how microorganism motility, fluid flow and nutrient distribution affect foraging by marine microbes, and the formation of biofilms on spherical nutrient sources under the influence of fluid flow.

Swimming sheet near a plane surfactant-laden interface

In this work we analyze the velocity of a swimming sheet near a plane surfactant-laden interface by assuming the Reynolds number and the sheet's deformation to be small. We observe a nonmonotonic dependence of the sheet's velocity on the Marangoni number (Ma) and the surface Péclet number (Pe_{s}). For a sheet passing only transverse waves, the swimming velocity increases with an increase in Ma for any fixed Pe_{s}. When Pe_{s} is increasing, on the other hand, the swimming velocity of the same sheet either increases (at large Ma) or it initially increases and then decreases (at small Ma). This dependence of the swimming velocity on Ma and Pe_{s} is altered if the sheet is passing longitudinal waves in addition to the transverse waves along its surface.

Ideal circle microswimmers in crowded media

Microswimmers are exposed in nature to crowded environments and their transport properties depend in a subtle way on the interaction with obstacles. Here, we investigate a model for a single ideal circle swimmer exploring a two-dimensional disordered array of impenetrable obstacles. The microswimmer moves on circular orbits in the freely accessible space and follows the surface of an obstacle for a certain time upon collision. Depending on the obstacle density and the radius of the circular orbits, the microswimmer displays either long-range transport or is localized in a finite region. We show that there are transitions from two localized states to a diffusive state each driven by an underlying static percolation transition. We determine the non-equilibrium state diagram and calculate the mean-square displacements and diffusivities by computer simulations. Close to the transition lines transport becomes subdiffusive which is rationalized as a dynamic critical phenomenon.