Thermodynamics of sustaining gases in the roughness of submerged superhydrophobic surfaces

Rough surfaces submerged in a liquid can remain almost dry if the liquid does not fully wet the roughness and gases are sustained in roughness grooves. Such partially dry surfaces can help reduce drag or enhance boiling. Gases sustained in roughness grooves would be composed of air and the vapor phase of the liquid itself. The thermodynamics of sustaining vapor was considered in a prior work [Patankar, Soft Matter, 2010, 6:1613]. Here, the thermodynamics of sustaining gases (e.g. air) is considered. Governing equations are presented along with a solution methodology to determine a critical condition to sustain gases. The critical roughness scale to sustain gases is estimated for different degrees of saturation of gases dissolved in the liquid. It is shown that roughness spacings of less than a micron are essential to sustain gases on surfaces submerged in water at atmospheric pressure. This is consistent with prior empirical data.Comment: 15 pages, 6 figure

Separability of drag and thrust in undulatory animals and machines

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 fishes 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.Comment: 41 pages, 13 figures, 4 table

Quasiequilibrium lattice Boltzmann models with tunable bulk viscosity for enhancing stability

Taking advantage of a closed-form generalized Maxwell distribution function [ P. Asinari and I. V. Karlin Phys. Rev. E 79 036703 (2009)] and splitting the relaxation to the equilibrium in two steps, an entropic quasiequilibrium (EQE) kinetic model is proposed for the simulation of low Mach number flows, which enjoys both the H theorem and a free-tunable parameter for controlling the bulk viscosity in such a way as to enhance numerical stability in the incompressible flow limit. Moreover, the proposed model admits a simplification based on a proper expansion in the low Mach number limit (LQE model). The lattice Boltzmann implementation of both the EQE and LQE is as simple as that of the standard lattice Bhatnagar-Gross-Krook (LBGK) method, and practical details are reported. Extensive numerical testing with the lid driven cavity flow in two dimensions is presented in order to verify the enhancement of the stability region. The proposed models achieve the same accuracy as the LBGK method with much rougher meshes, leading to an effective computational speed-up of almost three times for EQE and of more than four times for the LQE. Three-dimensional extension of EQE and LQE is also discussed

Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially

A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies

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 equation in a Lagrangian frame that some of us took in a prior work (Bhalla et al., J Comp Phys, 2013). 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

Screening effects in flow through rough channels

A surprising similarity is found between the distribution of hydrodynamic stress on the wall of an irregular channel and the distribution of flux from a purely Laplacian field on the same geometry. This finding is a direct outcome from numerical simulations of the Navier-Stokes equations for flow at low Reynolds numbers in two-dimensional channels with rough walls presenting either deterministic or random self-similar geometries. For high Reynolds numbers, when inertial effects become relevant, the distribution of wall stresses on deterministic and random fractal rough channels becomes substantially dependent on the microscopic details of the walls geometry. In addition, we find that, while the permeability of the random channel follows the usual decrease with Reynolds, our results indicate an unexpected permeability increase for the deterministic case, i.e., ``the rougher the better''. We show that this complex behavior is closely related with the presence and relative intensity of recirculation zones in the reentrant regions of the rough channel.Comment: 4 pages, 5 figure

A fully resolved active musculo-mechanical model for esophageal transport

Esophageal transport is a physiological process that mechanically transports an ingested food bolus from the pharynx to the stomach via the esophagus, a multi-layered 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, which is modeled as an actively contracting, fiber-reinforced tube. A simplified version of our model is verified by comparison to an analytic solution to the tube dilation problem. Three different complex models of the multi-layered esophagus, which differ in their activation patterns and the layouts of the mucosal layers, are then 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 due to the coordination of muscle activation is provided, which may help relate clinical data from manometry and ultrasound images to the underlying esophageal motor function