Angela Cheer

Paddles and rakes: Fluid flow through bristled appendages of small organisms

Many small organisms capture food particles, locomote through water or air, or create currents using appendages bearing arrays of long bristles. The performance of these arrays of hairs depends on the movement of fluid relative to them. We have modeled the fluid flow around such hairs, and have used the model to predict, for a range of biologically-relevant circumstances: (1) the steepness of the shear gradients adjacent to the hairs, (2) the leakiness of the gaps between pairs of hairs, and (3) the drag force on hairs with neighbors. We point out the circumstances under which bristled appendages function as rakes versus those under which they operate as paddles. Our results suggest that a simple change in size or speed of a bristled appendage can lead to a novel mode of functioning under some circumstances, whereas in other situations differences in morphology or behavior have little effect on performance.

Spatial and temporal patterns of water flow generated by suction-feeding bluegill sunfish Lepomis macrochirus resolved by Particle Image Velocimetry

SUMMARY The suction-feeding fish generates a flow field external to its head in order to draw prey into the mouth. To date there are very few empirical measurements that characterize the fluid mechanics of suction feeding, particularly the temporal and spatial patterns of water velocity in front of the fish. To characterize the flow in front of suction-feeding bluegill sunfish Lepomis macrochirus, measurements with high spatial (<1 mm) and temporal (500 Hz) resolution were taken using Particle Image Velocimetry (PIV). In an analysis separate from the PIV, high-speed video sequences were used for a novel method of visually tracking every seed particle for the duration of each feeding in order to determine directly the total parcel of water that the fish ingests. PIV measurements and particle tracking show that water is drawn from all around the mouth. Fluid velocity decreases rapidly with distance from the mouth and is only significant (>5% of speed at the mouth) within roughly 1 mouth diameter of the fish. Suction feeders gain little in terms of extending this flow field by even substantial increases in the fluid speed at the mouth opening. Instead, the chief advantage of increased flow speed at the mouth may be the increased magnitude of generated forces within the space very close to the mouth. After scaling of the velocity field based on size of the mouth opening and the measured fluid speed at a fixed position, the measured velocity profiles for all feedings are very similar to one another, so that a functional relationship for the magnitude of fluid speed as a function of distance from the predator mouth is presented and shown to be accurate over the range of kinematic variables tested. This relationship describes the velocity field both along the centerline of the fish and along transects lying at an angle to the centerline within both the mid-sagittal and frontal planes. Comparison of the time-resolved fluid velocity measurements to gape kinematics demonstrate that peak fluid speed occurs simultaneously with 95% of peak gape, showing that the bluegill maximizes nearly simultaneously both the generated forces and size of the region over which these forces act. The magnitude of peak fluid speed during each strike decreases as a function of increasing time to peak gape (r2=0.87), demonstrating a strong relationship between the rate of buccal cavity expansion and maximum generated flow speed.

Cortical activity in vertebrate eggs I: The activation waves

We present a physical model for the propagation of chemical and mechanical waves on the surface of vertebrate eggs. As a first step we analyzed the propagation of the calcium wave observed to sweep over the surface of the Medaka egg (Gilkey et al., 1978). It has been assumed that this wave is driven by a mechanism of calcium-stimulated-calcium-release. By formulating this hypothesis mathematically we can use the observed wavefront data to obtain a map of cortical reactivity. This map indicates a gradient of reactivity along the egg: highest in the animal hemisphere and tapering off towards the vegetal hemisphere. The cortex of Xenopus eggs is also capable of propagating a calcium wave (Busa & Nuccitelli, 1985). At about the same time a wave of expansion followed by a wave of contraction sweeps across the egg surface (Takeichi et al., 1984). We have proposed a mechanism for this wave pair based on the physical chemistry of actomyosin gels. The calcium wave activates solation factors which sever some of the actin chains which leads to an osmotic swelling of the gel. Calcium also activates the contractile machinery of the actomyosin system which causes the gel to contract. The contraction lags the swelling because of the nature of the kinetics: solation and swelling is a more rapid process than contraction. By writing the equations for gel expansion and contraction we can mimic the mechanical and chemical wave propagation by a computer simulation. If the model is correct this provides a method for using the waves as a diagnostic of the mechanochemical properties of the egg cortex.

Modeling the Hydraulics of Root Growth in Three Dimensions with Phloem Water Sources

Primary growth is characterized by cell expansion facilitated by water uptake generating hydrostatic (turgor) pressure to inflate the cell, stretching the rigid cell walls. The multiple source theory of root growth hypothesizes that root growth involves transport of water both from the soil surrounding the growth zone and from the mature tissue higher in the root via phloem and protophloem. Here, protophloem water sources are used as boundary conditions in a classical, three-dimensional model of growth-sustaining water potentials in primary roots. The model predicts small radial gradients in water potential, with a significant longitudinal gradient. The results improve the agreement of theory with empirical studies for water potential in the primary growth zone of roots of maize (Zea mays). A sensitivity analysis quantifies the functional importance of apical phloem differentiation in permitting growth and reveals that the presence of phloem water sources makes the growth-sustaining water relations of the root relatively insensitive to changes in root radius and hydraulic conductivity. Adaptation to drought and other environmental stresses is predicted to involve more apical differentiation of phloem and/or higher phloem delivery rates to the growth zone.

The benefits of planar circular mouths on suction feeding performance.

Suction feeding is the most common form of prey capture across aquatic feeding vertebrates and many adaptations that enhance efficiency and performance are expected. Many suction feeders have mechanisms that allow the mouth to form a planar and near-circular opening that is believed to have beneficial hydrodynamic effects. We explore the effects of the flattened and circular mouth opening through computational fluid dynamics simulations that allow comparisons with other mouth profiles. Compared to mouths with lateral notches, we find that the planar mouth opening results in higher flow rates into the mouth and a region of highest flow that is positioned at the centre of the mouth aperture. Planar mouths provide not only for better total fluid flow rates through the mouth but also through the centre of the mouth near where suction feeders position their prey. Circular mouths are shown to provide the quickest capture times for spherical and elliptical prey because they expose the prey item to a large region of high flow. Planar and circular mouths result in higher flow velocities with peak flow located at the centre of the mouth opening and they maximize the capacity of the suction feeders to exert hydrodynamic forces on the prey.

Use of computational fluid dynamics to study forces exerted on prey by aquatic suction feeders

Suction feeding is the most commonly used mechanism of prey capture among aquatic vertebrates. Most previous models of the fluid flow caused by suction feeders involve making several untested assumptions. In this paper, a Chimera overset grids approach is used to solve the governing equations of fluid dynamics in order to investigate the assumptions that prey do not interact with the flow and that the flow can be modelled as a one-dimensional flow. Results show that, for small prey, both neglecting the prey and considering prey interaction give similar calculated forces exerted on the prey. However, as the prey item increases in size toward the size of the gape, its effect on the flow becomes more pronounced. This in turn affects both the magnitude of the hydrodynamic forces imparted to the prey and the time when maximum force is delivered. Maximum force is delivered most quickly to intermediate sized prey, about one-third of mouth diameter, and most slowly to prey less than 7 per cent or greater than 67 per cent of mouth diameter. This suggests that the effect of prey size on the timing of suction forces may have substantial consequences for the feeding ecology of suction feeders that are known to prefer prey between 25 and 50 per cent of mouth diameter. Moreover, for a 15 cm fish with a 15 mm gape, assuming a radial one-dimensional flow field can result in underestimating the maximum force exerted on a 5 mm diameter spherical prey 1 gape distance from the mouth by up to 28.7 per cent.

Computational Fluid Dynamics of Crossflow Filtration in Suspension-Feeding Fishes

Suspension-feeding fishes such as herring and anchovies engulf particle-concentrated water through their mouths and release the water through the posterior oral cavity. Food particles are separated from the water at the gill rakers that act like modern crossflow filters. This paper uses Computational Fluid Dynamic (CFD) techniques to study the feeding mechanism of these suspension feeders. By understanding how food is separated from the water, we can elucidate why fish gill rakers do not get clogged with particles in the same manner that industrial crossflow filters eventually become fouled.

Convergence acceleration of viscous and inviscid hypersonic flow calculations

The convergence of inviscid and viscous hypersonic flow calculations using a two-dimensional flux-splitting code is accelerated by applying a Richardson-type overrelaxation method. Successful results are presented for various cases; and a 50 percent savings in computer time is usually achieved. An analytical formula for the overrelaxation factor is derived, and the performance of this scheme is confirmed numerically. Moreover, application of this overrelaxation scheme produces a favorable preconditioning for Wynns epsilon-algorithm. Both techniques have been extended to viscous three-dimensional flows and applied to accelerate the convergence of the compressible Navier-Stokes code. A savings of 40 percent in computer time is achieved in this case.

Bio-inspired particle separator design based on the food retention mechanism by suspension-feeding fish.

A new particle separator is designed using a crossflow filtration mechanism inspired by suspension-feeding fish in this study. To construct the model of the bio-inspired particle separator, computational fluid dynamics techniques are used, and parameters related to separator shape, fluid flow and particle properties that might affect the performance in removing particles from the flow, are varied and tested. The goal is to induce a flow rotation which enhances the separation of particles from the flow, reduce the particle-laden flow that exits via a collection zone at the lower/posterior end of the separator, while at the same time increase the concentration of particles in that flow. Based on preliminary particle removal efficiency tests, an exiting flow through the collection zone of about 8% of the influent flow rate is selected for all the performance tests of the separator including trials with particles carried by air flow instead of water. Under this condition, the simulation results yield similar particle removal efficiencies in water and air but with different particle properties. Particle removal efficiencies (percentage of influent particles that exit through the collection zone) were determined for particles ranging in size from 1 to 1500 µm with a density between 1000 and 1150 kg m(-3) in water and 2 and 19 mm and 68 and 2150 kg m(-3) in air. As an example, removal efficiencies are 66% and 64% for 707 µm diameter particles with a density of 1040 kg m(-3) in water and for 2 mm particles with a density of 68 kg m(-3) in air, respectively. No significant performance difference is found by geometrically scaling the inlet diameter of the separator up or down in the range from 2.5 to 10 cm.

Analysis of the convergence history of flow through nozzles with shocks

Acceleration techniques such as Wynns (1986) epsilon algorithm and analysis techiques such as eigensystem analysis are used here to study numerically the convergence properties of an iterative scheme applied to the quasi-one-dimensional Euler and Navier-Stokes equations for flow through nozzles with shocks. The convergence and stability properties are studied by analyzing the dependence of convergence of the code on the discretization technique, boundary conditions, time-step, number of grid points, and the physics of the problem.