Session R10: Biofluids: Low Re Swimming III

The effect of temperature on swimming kinematics and hydrodynamics of barnacle cyprids Amphibalanus amphitrite

A barnacle cyprid uses six pairs of thoracic appendages in a metachronal wave to swim through the water. These cyprids are a fraction of a millimeter and move at a Reynolds number that typically ranges from one to ten, so viscosity is potentially important to their swimming performance. Here we observe free swimming cyprids with high-speed imaging to investigate how temperatures ranging from 10 to 40 degrees Celsius affect their swimming. We are able to capture multiple continuous strokes for several individual cyprids at a known temperature and viscosity. For these strokes, we separate the timescales for the power stroke, the recovery stroke, and the time between the strokes, and investigate how the fluid properties including those influenced by temperature impact those time scales.   

Exploring the hydrodynamic advantages of pleopod interaction in shrimp swimming

Shrimp possess closely branched appendages, with the abdomen housing five pairs of specialized appendages known as pleopods. During swimming, these pleopods provide propulsion by metachronal paddling. The close interaction among neighboring pleopods during swimming poses interesting questions regarding their hydrodynamic influence, given that their collective performance likely diverges from the behavior of an individual pleopod. While prevalent research often links these interactions to drag reduction, our findings suggest that the main benefit resides in lowering the power consumption needed to generate hydrodynamic force rather than in drag reduction. We demonstrate this observation by simulating a 3D high-fidelity shrimp model using an in-house immersed-boundary-method-based CFD solver. Our simulation results reveal that the flow interactions between neighboring appendages slightly reduced the thrust generation along the horizontal direction while saving the hydrodynamic power consumption by 21%. As a result, the metachronal movement of the five pairs of pleopods can enhance the cost of transport (COT) by approximately 22% compared to cases where each pleopod pair operates independently. Our research findings aim to guide for optimization of underwater locomotion in similar metachronal underwater robotic designs.   

Unraveling Krill's Metachronal Symphony and Hydrodynamic Secrets

This research aims to investigate the causal flow dynamics associated with the metachronal swimming mode used by krill, along with its correlation to the force generation exhibited by these fascinating creatures. Krill, which possess five legs distributed along their body, propel themselves by coordinating the movement of their legs and body. Our study seeks to comprehend the synchronized paddling motion of these legs and its role in generating two primary types of hydrodynamic forces: kinematic forces resulting from the inertia of the flow and vortex-induced forces originating from vorticity produced by the legs. We will closely examine how the specific kinematic parameters of metachronal swimming influence the contribution of these two forces. Additionally, we will show the impact of the coordinated opening and closure of the interior legs during metachronal swimming in enhancing wake dynamics and better hydrodynamic force generation. Employing a combined immersed body method-boundary element method approach for simulations and flow analysis, the study uses a reciprocal theorem to unify various force partitioning methods and demonstrate its effectiveness in analyzing force contributions.   

Hydrodynamics of cruise locomotion in the adult Euchaeta antarctica

Euchaeta antarctica is a key calanoid copepod species inhabiting the Southern Ocean surrounding Antarctica. In addition to basic propulsion considerations, the flow fields generated by Euchaeta antarctica are significant due to their ecological interactions with other organisms via hydrodynamic signals to predators and prey. In cruise swimming mode, Euchaeta antarctica generates thrust via metachronal stroking of swimming legs located on the dorsal side of their prosome. In the current study, a high-speed tomographic particle image velocimetry (tomo-PIV) system was employed to visualize and quantify the time-resolved 3D velocity field surrounding a free-swimming adult E. antarctica. Comparison of cruising swimming speed among adult E. antarctica and smaller species E. rimana and E. elongata, as well as smaller stage E. antarctica CV, demonstrate a linear dependence on organism length. The fluid velocity, vorticity, dissipation rate, and shear strain rate fields generated by adult E. antarctica during cruise behavior are quantified, with particular attention to turning. The flow fields reveal peak values of vorticity and shear strain rate within a proximity of 1 to 2 mm from the copepod body during straight motion, whereas significant increases in these quantities were observed along the animal tail during turning motion.   

Hydrodynamics of active metachronal swimming modes in Antarctic krill, Euphausia superba

Krill are shrimp-like crustaceans with a high degree of mobility with reported swimming modes including fast forward swimming (FFW), hovering (HOV), and upside down swimming (USD). Krill propel themselves by paddling their five sets of pleopod appendages in a coordinated metachronal wave that generates a fluid wake jet. In this study, 3D velocity and vorticity fields are measured for FFW and USD swimming modes in Antarctic krill (Euphausia superba) using high-speed tomographic Particle Image Velocimetry (tomo-PIV).  The results give novel insight to bio-locomotion of krill and the related fluid flow in this intermediate Reynolds number regime.  The specimens are moving rapidly in each quantified mode: 2.1 body lengths per second (BL/s) for FFW and 2.8 BL/s for USD.  When comparing FFW and (previously reported) HOV results, the krill body velocity has a near eight-fold increase, whereas the flow field data reveal only two-fold increase in the wake velocity around the pleopods during the power stroke. Also, lift-force-generating vortices are observed at the distal tips of the pleopods in each mode, which further supports the hypothesis that vortex formation generates lift force to complement the drag-based propulsion of the pleopod stroke.   

Effects of squeeze-confinement on flow fields around morphologically complex ciliated larvae

Marine invertebrates undergo development through free-swimming larval stages that have a diverse range of shape morphologies and ciliation patterns. These larvae utilize ciliary beating for swimming and feeding at low Reynolds numbers (< 1). The standard microscopic technique used to study flow fields of these larvae involves confining the larvae between a glass slide and cover slip. This induces a quasi-two-dimensional (2D) confinement on them since the larvae swim in three-dimensions (3D) in their natural habitat. We study the effects of quasi-2D confinement of two marine invertebrate species’ larvae with different, complex shape morphologies – sea stars (Patiria miniata) and sea urchins (Lytechinus variegatus). This enables us to understand how morphology may affect the resulting flow fields under different levels of confinement. We measure 2D confinement effects by varying the confinement parameter, defined as the height (h) between glass slide and cover slip. In both species, the number of vortices increase when the confinement is increased (smaller h). Conversely, when the confinement is decreased (larger h), both species create two large counter-rotating vortices. Our results suggest that complex larval shape morphologies are important in determining flow patterns under increased confinement (smaller h), and larval shape plays minimal role in determining flow patterns as confinement decreases.

Squeeze-confinement induced vorticity amplification in ciliated marine larvae

Ciliated marine invertebrate larvae swim and feed in a viscous low Reynolds number (< 1) environment in the ocean. The larvae swim in three-dimensions (3D) using ciliary beating, resulting in flow fields that are often complex and challenging to quantify in experimental studies. The conventional microscopic imaging configuration of trapping larvae in between a glass slide and cover slip induces a quasi-two-dimensional (2D) confinement. We systematically quantify the fluid dynamical effects of 2D squeeze-confinement on flows generated by ciliated larvae at low Reynolds numbers (< 1). We explore both spherical and non-spherical larval morphologies in our study. Spherical morphologies include coral larvae and non-spherical morphologies include sea star and sea urchin larvae. We vary the confinement parameter – the gap between the glass slide and cover slip (h) – and observe changes in the number of vortices, vortex size and intensity. In non-spherical larvae, increasing confinement (smaller h) increases the number of vortices that form, and they come closer to the body surface. In both spherical and non-spherical larvae, decreasing confinement (larger h) gives rise to a pair of counter rotating vortices. Our results are broadly applicable for quantification of the fluid dynamical effects of 2D squeeze confinement for ciliated larvae with a variety of morphologies.   

Effects of 3D confinements on the trajectories of microswimmers

Ciliary beating generates fluid flows that determine the direction of microswimmers at low Reynolds numbers. The trajectories of microswimmers can be significantly influenced by confinement (i.e. the presence of walls), and the degree of confinement: strong versus weak. We numerically study this problem by confining a squirmer in 3D channels under different conditions: (i) no confinement, (ii) weak confinement, (iii) strong confinement. Our results show that the presence of confinement effects can result in a more directed trajectory compared to no confinement. In weak 3D confinement, pusher type squirmers (e.g. E.coli) exhibit oscillatory trajectories spanning the entire cross-section of the channel. However, the puller (e.g. Chlamydomonas) and neutral (e.g. Volvox) type squirmers show directed motion near to the centerline of the channels. In this work, we carry out a detailed study of parameters that can influence squirmer trajectories: (a) type of squirmer, (b) size of channel, (c) aspect ratio of channel and (d) ratio of squirmer size to channel size. Our goal is to group all the above parameters into a landscape of energy injection vs energy dissipation and develop comprehensive phase diagrams that quantify trajectories of microswimmers.