Session LL: Bio-Fluids: Wakes and Mixing I

LCS analysis of a biologically inspired wake

Particle Image Velocimetry (PIV) was used to investigate the wakes of rigid pitching panels with a trapezoidal panel geometry, chosen to model idealized fish caudal fins. Experiments were performed for Strouhal numbers from 0.23 to 0.65. The three dimensional flow field around the panel is reconstructed by integrating two-dimensional PIV results across the volume surrounding the panel. A Lagrangian coherent structure (LCS) analysis is employed to investigate the formation and evolution of the panel wake. A classic reverse von K$\acute{a}$rm$\acute{a}$n vortex street pattern was observed along the mid-span of the near wake, but the complexity and three-dimensionality of the wake increases away from the mid-span as streamwise vortices interact with the swept edges of the panel.   

The Hydrodynamic Wake of Two Species of Swimming Krill

Krill are often found in unorganized swarms or coordinated schools depending on the species. To test if group organization is related to the hydrodynamic wake produced by swimming krill we quantified the flow structure in the wake of \textit{Euphausia superba, }a schooling Antarctic krill, and \textit{Euphausia pacifica, }a swarming Pacific krill. In this study, we used infrared Particle Image Velocimetry (PIV) to analyze the structure of the hydrodynamic disturbance of free-swimming individual specimens. The downward directed jet produced by \textit{E. pacifica }has a lower maximum velocity (3.4 +/- 1.1 cm/s vs. 6.2 +/- 1.3 cm/s), has a steeper wake angle (59 +/- 20 degrees vs. 48 +/- 14 degrees), and decays faster (0.3 s vs. 0.6 s) than the jet of \textit{E. superba}, which suggests that the wake is less persistent for signaling in the smaller krill species (\textit{E. pacifica}). Time record analysis reveals that the wake flow is very weak beyond 0.5 body length for \textit{E. pacifica} and beyond 1 body length for \textit{E. superba}. Since \textit{E. superba} separation distances within a school range from 1 to 3 body lengths (from previous data), it appears that \textit{E. superba} may not be using solely the hydrodynamic signal to facilitate schooling.   

Mixing efficiency of swimming animals in stratified fluids

The potential role of animal-fluid energy interactions in ocean mixing is a topic of increasing study that has been limited by the need for data at the scale of individual animals. Previous findings suggest that the energetic input by swimming animals to the ocean mixing energy budget may impact mixing at the same level as winds and tides, whose respective rates of kinetic energy dissipation are of the same order of magnitude. However, these results equate dissipation of mechanical energy with mixing; not all mechanical energy that is dissipated goes into mixing a fluid. The mixing efficiency should instead be an indicator of mixing. We present a method to determine the mixing efficiency of swimming animals that combines the techniques of DPIV, PLIF and dye visualizations. This methodology is then applied to multiple swimming cycles of \textit{Aurelia labiata} to answer whether mechanical energy at small animal scales can achieve any substantial mixing before it is dissipated as heat.   

A fluid mechanical model for current-generating-feeding jellyfish

Many jellyfish species, e.g. moon jellyfish \textit{Aurelia aurita,} use body motion to generate fluid currents which carry their prey to the vicinity of their capture appendages. In this study, a model was developed to understand the fluid mechanics for this current-generating-feeding mode of jellyfish. The flow generated by free-swimming \textit{Aurelia aurita} was measured using digital particle image velocimetry. The dynamics of prey (e.g., brine shrimp \textit{Artemia}) in the flow field were described by a modified Maxey-Riley equation which takes into consideration the inertia of prey and the escape forces, which prey exert in the presence of predator. A Lagrangian analysis was used to identify the region of the flow in which prey can be captured by the jellyfish and the clearance rate was quantified. The study provides a new methodology to study biological current-generating-feeding and the transport and mixing of particles in fluid flow in general.   

Flow field around \textit{Vorticella}: Mixing with a reciprocal stroke

\textit{Vorticella }is a stalked protozoan. It has an extremely fast biological spring, whose contraction is among the fastest biological motions relative to size. Though the \textit{Vorticella }body is typically only 30 $\mu $m across, the contracting spring accelerates it up to speeds of centimeters per second. \textit{Vorticella }live in an aqueous environment attached to a solid substrate and use their spring to retract their body towards the substrate. The function of the rapid retraction is not known. Many hypothesize that it stirs the surrounding liquid and exposes the \textit{Vorticella }to fresh nutrients. We evaluate this hypothesis by modeling the \textit{Vorticella }as a sphere moving normal to a wall, with a stroke that moves towards the wall at high Reynolds number, and away from the wall at low Reynolds number. We approximate the flow during contraction as potential flow, while the flow during re-extension is considered Stokes flow. The analytical results are compared to the flow field obtained with a finite element (Comsol Multiphysics) simulation of the full Navier-Stokes equations.   

Instabilities, pattern formation and mixing in active suspensions

Suspensions of self-propelled particles are known to undergo complex dynamics as a result of hydrodynamic interactions. To elucidate these dynamics, a kinetic theory is developed and applied to study the linear stability and the non-linear pattern formation in these systems. The evolution of a suspension of self-propelled particles is modeled using a conservation equation for the particle configurations, coupled to a mean-field description of the flow arising from the stress exerted by the particles on the fluid. Based on this model, the stability of isotropic suspensions of particles is first investigated. We demonstrate the existence of an instability in which shear stresses are eigenmodes and grow exponentially at long scales, and propose an interpretation in terms of the system entropy. Non-linear effects are also studied using numerical simulations in two dimensions. These simulations confirm the results of the stability analysis, and the long- time non-linear behavior is shown to be characterized by the formation of strong density fluctuations, which merge and break up in time in a quasi-periodic fashion. These complex motions result in very efficient fluid mixing, which we quantify by means of a multiscale mixing norm.   

Bacterial chemotaxis in the ocean: microfluidic studies

Bacteria are key players in the biogeochemistry of the ocean. We present microfluidic experiments to mimic nutrient conditions experienced by marine bacteria. Using videomicroscopy, we quantified the intensity and time scale of the response of bacteria to nutrient pulses. We found that marine bacteria are capable of superior chemotaxis compared to {\em Escherichia coli} (the classic model of chemotactic motility), likely an adaptation to the ephemeral nutrient conditions in the ocean. For moving nutrient sources, performance depends on the speed of the source: we present the first experimental evidence that marine bacteria can colonize plumes of marine snow particles, for slow to moderate particle settling speeds. Finally, preliminary numerical results reveal that turbulence can play a significant role in bacterial foraging in the ocean.   

Life at high Deborah number

Many biologically-relevant situations in cell locomotion involve non-Newtonian fluids. Important examples include the motion of spermatozoa in cervical mucus, or the movement of bacteria in biofilms. In this work, we present quantitative models of cell locomotion in polymeric solutions by deriving integral theorems which allow a general determination of the swimming kinematics of a small-amplitude swimmer for arbitrarily large Deborah numbers.   

Waltzing {\it Volvox\/}: Orbiting Bound States of Flagellated Multicellular Algae

The spherical colonial alga {\it Volvox} swims by means of flagella on thousands of surface somatic cells. This geometry and its large size makes it a model organism for the fluid dynamics of multicellularity. Remarkably, when two nearby colonies swim close to a solid surface, they are attracted together and can form a stable bound state in which they continuously waltz around each other. A surface-mediated hydrodynamic attraction between colonies combined with the rotational motion of bottom-heavy {\it Volvox} are shown to explain the stability and dynamics of the bound state. This phenomenon is suggested to underlie observed clustering of colonies at surfaces.   

Can unicells increase their nutrient uptake by swimming?

We introduce two simple models for the flow generated by a self-propelled flagellate: a sphere propelled by a cylindrical flagellum and one propelled by an external point force. We use these models to examine the role of advection in enhancing feeding rates in 3 situations: (i) osmotroph feeding on dissolved molecules, (ii) interception feeding flagellates feeding on non-motile prey particles, and (iii) interception feeders feeding on motile prey (such as bacteria). We show that the Sherwood number is close to unity for osmotrophic flagellates, as suggested by most previous models. However, a more correct representation of the flow field than that predicted by a naive sinking sphere model leads to substantially higher clearance rates for interception feeding flagellates. We finally demonstrate that prey motility significantly enhances prey encounter rates in interception feeding flagellates and in fact often is much more important for food acquisition than the feeding current.   

No many-scallop theorem: Collective locomotion of reciprocal swimmers

To achieve propulsion at low Reynolds number, a swimmer must deform in a way that is not invariant under time-reversal symmetry; this result is known as the scallop theorem. However, there is no many-scallop theorem. We demonstrate that two active particles undergoing reciprocal deformations can swim collectively; moreover, polar particles also experience effective long-range interactions. These results are derived for a minimal dimers model, and generalized to more complex geometries on the basis of symmetry and scaling arguments. We explain how such cooperative locomotion can be realized experimentally by shaking a collection of soft particles with a homogeneous external field.