We present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary velocity to enclose the body at all times. The moving box is aligned with Cartesian grid faces, which makes the integral evaluation straightforward in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of velocity and pressure at the fluid–structure interface are avoided and far-field (smooth) velocity and pressure information is used. We re-visit the approach to compute hydrodynamic forces and torques through force/torque balance equations in a Lagrangian frame that some of us took in a prior work (Bhalla et al., 2013 [13]). We prove the equivalence of the two approaches for IB methods, thanks to the use of Peskin's delta functions. Both approaches are able to suppress spurious force oscillations and are in excellent agreement, as expected theoretically. Test cases ranging from Stokes to high Reynolds number regimes are considered. We discuss regridding issues for the moving CV method in an adaptive mesh refinement (AMR) context. The proposed moving CV method is not limited to a specific IB method and can also be used, for example, with embedded boundary methods.

We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blob model can provide an accurate representation at low to moderate packing densities of the reactive particles, at a cost not much larger than solving a Poisson equation in the same domain. Unlike multipole expansion methods, our method does not require analytically computed Green's functions, but rather, computes regularized discrete Green's functions on the fly by using a standard grid-based discretization of the Poisson equation. This allows for great flexibility in implementing different boundary conditions, coupling to fluid flow or thermal transport, and the inclusion of other effects such as temporal evolution and even nonlinearities. We develop multigrid-based preconditioners for solving the linear systems that arise when using implicit temporal discretizations or studying steady states. In the diffusion-limited case the resulting linear system is a saddle-point problem, the efficient solution of which remains a challenge for suspensions of many particles. We validate our method by comparing to published results on reaction-diffusion in ordered and disordered suspensions of reactive spheres.

A fundamental issue in locomotion is to understand how muscle forcing produces apparently complex deformation kinematics leading to movement of animals like undulatory swimmers. The question of whether complicated muscle forcing is required to create the observed deformation kinematics is central to the understanding of how animals control movement. In this work, a forced damped oscillation framework is applied to a chain-link model for undulatory swimming to understand how forcing leads to deformation and movement. A unified understanding of swimming, caused by muscle contractions ("active" swimming) or by forces imparted by the surrounding fluid ("passive" swimming), is obtained. We show that the forcing triggers the first few deformation modes of the body, which in turn cause the translational motion. We show that relatively simple forcing patterns can trigger seemingly complex deformation kinematics that lead to movement. For given muscle activation, the forcing frequency relative to the natural frequency of the damped oscillator is important for the emergent deformation characteristics of the body. The proposed approach also leads to a qualitative understanding of optimal deformation kinematics for fast swimming. These results, based on a chain-link model of swimming, are confirmed by fully resolved computational fluid dynamics (CFD) simulations. Prior results from the literature on the optimal value of stiffness for maximum speed are explained.

For nearly a century, researchers have tried to understand the swimming of aquatic animals in terms of a balance between the forward thrust from swimming movements and drag on the body. Prior approaches have failed to provide a separation of these two forces for undulatory swimmers such as lamprey and eels, where most parts of the body are simultaneously generating drag and thrust. We nonetheless show that this separation is possible, and delineate its fundamental basis in undulatory swimmers. Our approach unifies a vast diversity of undulatory aquatic animals (anguilliform, sub-carangiform, gymnotiform, bal-istiform, rajiform) and provides design principles for highly agile bioinspired underwater vehicles. This approach has practical utility within biology as well as engineering. It is a predictive tool for use in understanding the role of the mechanics of movement in the evolutionary emergence of morphological features relating to locomotion. For example, we demonstrate that the drag-thrust separation framework helps to predict the observed height of the ribbon fin of electric knifefish, a diverse group of neotropical fish which are an important model system in sensory neurobiology. We also show how drag-thrust separation leads to models that can predict the swimming velocity of an organism or a robotic vehicle.

Examples of animals evolving similar traits despite the absence of that trait in the last common ancestor, such as the wing and camera-type lens eye in vertebrates and invertebrates, are called cases of convergent evolution. Instances of convergent evolution of locomotory patterns that quantitatively agree with the mechanically optimal solution are very rare. Here, we show that, with respect to a very diverse group of aquatic animals, a mechanically optimal method of swimming with elongated fins has evolved independently at least eight times in both vertebrate and invertebrate swimmers across three different phyla. Specifically, if we take the length of an undulation along an animal's fin during swimming and divide it by the mean amplitude of undulations along the fin length, the result is consistently around twenty. We call this value the optimal specific wavelength (OSW). We show that the OSW maximizes the force generated by the body, which also maximizes swimming speed. We hypothesize a mechanical basis for this optimality and suggest reasons for its repeated emergence through evolution.

Nearly eighty years ago, Gray reported that the drag power experienced by a dolphin was larger than the estimated muscle power - this is termed as Gray's paradox. We provide a fluid mechanical perspective of this paradox. The viewpoint that swimmers necessarily spend muscle energy to overcome drag in the direction of swimming needs revision. For example, in undulatory swimming most of the muscle energy is directly expended to generate lateral undulations of the body, and the drag power is balanced not by the muscle power but by the thrust power. Depending on drag model utilized, the drag power may be greater than muscle power without being paradoxical.

Esophageal transport is a physiological process that mechanically transports an ingested food bolus from the pharynx to the stomach via the esophagus, a multilayered muscular tube. This process involves interactions between the bolus, the esophagus, and the neurally coordinated activation of the esophageal muscles. In this work, we use an immersed boundary (IB) approach to simulate peristaltic transport in the esophagus. The bolus is treated as a viscous fluid that is actively transported by the muscular esophagus, and the esophagus is modeled as an actively contracting, fiber-reinforced tube. Before considering the full model of the esophagus, however, we first consider a standard benchmark problem of flow past a cylinder. Next a simplified version of our model is verified by comparison to an analytic solution to the tube dilation problem. Finally, three different complex models of the multi-layered esophagus, which differ in their activation patterns and the layouts of the mucosal layers, are extensively tested. To our knowledge, these simulations are the first of their kind to incorporate the bolus, the multi-layered esophagus tube, and muscle activation into an integrated model. Consistent with experimental observations, our simulations capture the pressure peak generated by the muscle activation pulse that travels along the bolus tail. These fully resolved simulations provide new insights into roles of the mucosal layers during bolus transport. In addition, the information on pressure and the kinematics of the esophageal wall resulting from the coordination of muscle activation is provided, which may help relate clinical data from manometry and ultrasound images to the underlying esophageal motor function.

Rough surfaces immersed under water remain practically dry if the liquid-solid contact is on roughness peaks, while the roughness valleys are filled with gas. Mechanisms that prevent water from invading the valleys are well studied. However, to remain practically dry under water, additional mechanisms need consideration. This is because trapped gas (e.g. air) in the roughness valleys can dissolve into the water pool, leading to invasion. Additionally, water vapor can also occupy the roughness valleys of immersed surfaces. If water vapor condenses, that too leads to invasion. These effects have not been investigated, and are critically important to maintain surfaces dry under water. In this work, we identify the critical roughness scale, below which it is possible to sustain the vapor phase of water and/or trapped gases in roughness valleys - thus keeping the immersed surface dry. Theoretical predictions are consistent with molecular dynamics simulations and experiments.