Session G20: Biological Fluid Dynamics: Locomotion and Movement

Sea-star inspired locomotion

Sea stars have numerous specialized ‘tube feet’, that enable them to achieve highly-controlled locomotion on various terrains from rocky to smooth surfaces. A tube foot consists of soft, water-filled, muscular membranes that extend and contract through changing the hydraulic pressure. Inspired by the biomechanics of the tube feet, we propose a low-order model for a soft actuator consisting of active and passive force elements. The active element can produce either pulling or pushing forces, which correspond to contraction and extension of the tube foot, respectively. We then study the locomotion of a distributed mass driven by several such actuators. Specifically, we investigate the stability of walking by minimally-coupled multiple actuators. We find that even though the dynamics of a single foot is unstable when carrying a load, the interaction of multiple actuators can result in a stable forward locomotion.  This system offers a new paradigm for walking using soft actuators, which exhibits great performance in terms of walking stability.   

A needle-shaped Brownian microswimmer in a channel

We consider a microswimmer modeled as a one-dimensional line segment -- a needle -- with a fixed swimming velocity.  The direction of swimming changes according to a Brownian process, and the swimmer is confined to an infinite channel.  This is a standard model for a simple microswimmer, or a confined wormlike chain polymer.  Using natural assumptions about reflection of the swimmer at boundaries, we compute the invariant distribution across the channel, and the statistics of spreading in the longitudinal direction.  When the needle length is longer than the channel width, we compute the mean drift velocity of the swimmer.  Otherwise, we examine the time it takes for the swimmer to reverse direction, and the effective diffusion constant of its large scale motion.   

Transitions in the synchronization modes of elastic filaments through basal-coupling

Cilia and flagella often beat in synchrony. They can also switch between different synchronization modes. However, the exact mechanisms responsible for such switching remain elusive. While previous evidence suggests that cilia coordination can be a result of hydrodynamic coupling, recent experimental findings show that defects in the intra-cellular basal coupling significantly affect the synchronization modes. Here, we account for basal coupling between two elastic filaments, driven by a geometric switch moment, by introducing a linear elastic spring that connects the two filaments.  We quantitatively examine the effects of this coupling on the synchrony of the filaments. We find that their coordination is strongly affected by the stiffness of the basal spring and the geometric switch parameters. Specifically, we observe a bistable region in the parameter space where the filaments could synchronize in either breast-stroke or free-style fashion depending on their initial conditions. We use the model to explain the transitions between various synchronization modes observed experimentally for the algae cells Chlamydomonas.   

Spontaneous oscillations and hydrodynamics of active micro-filament

Cilia and flagella are thin hair-like cellular projections that play a variety of crucial roles from propulsion at low Reynolds number to long-range hydrodynamic transport. The movement of the cilium is produced by the bending of its core, known as the axoneme that consists of 9 pairs of microtubules. In presence of ATP, molecular motors carrying cargo undergo cycles of attachment and detachment generating sliding forces that are in turn converted to waving motion of the filaments. We present a microscopic bottom-up model that accounts for the detailed stochastic kinetics of molecular motors and as well as feedback from the geometry of the axoneme represented as an Euler elastica. Through direct numerical simulations that account for hydrodynamics, we find that beyond a critical activity of motors the elastica starts beating spontaneously resulting in propagating bending waves similar to those observed in sperm flagella. In the parameter space of the model, we are also able to observe whipping patterns of cilia and the breast stroke of Chlamydomonas. Using PCA, we construct reduced-order representations of the dynamics and flow fields in terms of fundamental singularities of Stokes flow. We also explore hydrodynamic interactions and collective behavior of interacting filaments.   

Wake Pattern Identification Using Graph Matching

Flow patterns generated in the wakes of immersed objects such as bluff bodies and swimming animals are related to the flow generation mechanisms (e.g., vortex shedding) and can provide a window to understanding hydrodynamic performance such as drag or propulsive efficiency.  In this work the essential flow features are represented by critical points of the velocity field.  The pattern is encoded in a graph constructed from the critical points, with node properties determined by the critical point character and graph edges (connections between critical points) carrying a scale-independent “weight” property associated with proximity of the connected points.  Flows are compared by determining a best match between the weighted graphs of the two flows, accounting for constraints based on the character of matched critical points.  Relative similarity is assessed from differences in weights of the matched edges.  The approach is able to correctly match flow fields of the same type from potential flow representations of several bluff body and aquatic locomotion flows, even when distortions of up to 20% of the vortex spacing are applied to the flows.