Computational Fluid Dynamics of Crossflow Filtration in Suspension-Feeding Fishes Keywords: Crossflow filtration, Suspension feeding

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. Introduction Suspension-feeding fishes filter small particles from enormous volumes of water that enter their mouth. These fishes, belonging to 21 families in 12 orders, are critical components of many ecological communities [1] and comprise approximately 25% of the annual world fish catch [2]. As the details of oral cavity structure are very complex, we focus on the morphological features that are generally considered to serve the most critical functions during suspension feeding [3]. During suspension feeding, water that enters the mouth travels posteriorly to exit the oral cavity via branchial slits between the gill arches on both sides of the head. The gill rakers are fingerlike projections of the gill arch on the opposite side from the gill filaments. Figure 1 shows the arrangement of the gill rakers and gill arch of a bony fish [4]. In this paper, CFD techniques are used to study the feeding mechanism of suspensionfeeding fishes [5-6]. Gill rakers have been postulated to function as a `dead-end' filter, collecting small food items by sieving [7] or by hydrosol filtration, in which particles smaller than the size of the filter pores stick to the filter's elements [8]. A potential problem with dead-end or hydrosol filtration, however, is that the filter gets clogged as tiny food particles become trapped on the gill rakers. Moreover, Sanderson, et al. [9] observed that more than 95% of food particles do not come into contact with the gill rakers but instead remain suspended in fluid flows parallel to the filter surface as water leaves between the gill rakers. Particles become more concentrated as they travel towards the esophagus, and the fish swallows concentrated slurry of food particles. Thus, the gill rakers act like a modern crossflow filtration [10] mechanism similar to those in our water treatment plants. However, unlike most industrial crossflow filtration, particles do not accumulate on the gill rakers. Sanderson et al.[9] estimated the value for one theoretical transport mechanism--radial inertial migration --and found that it is inadequate, by an order of magnitude, to explain * This study is supported in part by NSF grant DMS-0079760, DOE: DE-FG03-99ER25375 and UCD Fellowship to A.Y.C. and by NSF grant IBN-0131293 to S.L.S. particle transport in fishes that feed by crossflow filtration. The underlying physical mechanisms are not yet fully understood. Our goal is to investigate the underlying mechanism of crossflow filtration in suspension feeders. In this study, a 3-D Navier-Stokes flow solver is used to calculate the flow field around the fish rakers and small spherical food particles are released into the flow field so that we can track the particle trajectories. This enables us to compare the effects of different flow conditions (speed and incident angles) on particles of different size and mass inside the oral cavity of the fish. For these calculations, we assume Newtonian flow since the particles we are simulating are small enough that they do not influence the flow field. Overflow In this study, the OVERFLOW code developed at NASA is used to solve the Navier-Stokes (N-S) equations for structured Chimera overset grids (see Figure 2). This code is an outgrowth of the previous computer codes named ARC3D [11] and F3D [12] which have various options of numerical algorithms. Local time step scaling, grid sequencing and multigrid are also implemented for convergence acceleration. Our calculations require the LowMach number preconditioning technique where the resulting matrix equation is solved using the Pulliam-Chaussee diagonalized (scalar pentadiagonal) scheme [13] and the Roe upwind scheme [14]. Particle Traces Algorithm The following algorithm is used to trace the trajectory of food particles that enter the oral cavity of the fish. The velocity field V(x) is obtained from solving the N-S equations and the initial position of a particle x(0) is prescribed. The particle path x(t) is then obtained by first solving the following equation ) (x v dt x d = . Discretizing this equation using the second-order Runge-Kutta integration scheme with adaptive step sizing [15], we get