Session Q34: Fluid Dynamics - General

Time Transient Effects in Heterogeneous Permselective Systems

The passage of an electric current through a permselective medium (membranes/nanochannels) under an applied electric field is characterized by the formation of ionic concentration gradients which result in regions of depleted and enriched ionic concentration at opposite ends of the medium, i.e. concentration polarization (CP). In this work, we study the time-transient behavior of the concentration and electric potential distributions in a realistic two dimensional and three layered system (i.e. microchannel-permselective medium-microchannel device). We provide an analytical solution for the concentration under the simplifying assumptions of local-electroneutrality, ideal permselectivity and negligible convection while the electric potential is solved numerically. It is shown that time transient effects occur over the diffusive time scale until steady-state is achieved. The numerical steady state solution is compared with previous analytical results and good quantitative behavior is observed.   

Bistability in Inhomogeneity -- Effects of Flow Coherent Structures on the Fate of a Bi-stable Reaction

A numerical study on the mixing process of a chemical reaction model between two stable states adjacent to each other in water is presented. The two stable states are equilibriums and are homogenized by fluid stirring and diffusion, and settle into a single stable state. With all other parameters fixed, we find the dependence of the final state on the reacting speed. Interestingly, with the existence of coherent structures, at a range of intermediate speeds, the final state also depends on the flow topology. The exact dependence on flow topology is explored in detail. For this bistable reaction, the elliptic flow structures help maintain scalar concentration and preserve the small impurity. These results attribute to the fundamental connection between the underlying flow topology and the domain transitions of dynamic biogeochemical processes.   

Convective velocity profiles as a function of applied fields in a magnetic fluid

Natural convection occurs when there is a horizontal temperature gradient across a sample. We have found previously [1] that the convective flow in magnetic fluid responds to applied magnetic fields differently, depending on the relative direction of the gradient of temperature to that of the field. In this work we report the velocity profiles from these flows obtained from optical flow method based on images from temperature-sensitive-paint technique. Results from perturbation fields show the direction change of velocity vectors and crossover from two-dimensional to three-dimensional flow for higher fields. The streamline plots indicate formation of local flow structures that could explain the slowing down of the heat transfer when the temperature gradient is anti-parallel to the field gradient. We will discuss the different responses to the applied magnetic fields for two different sample configurations in terms of relative orientation of the temperature and field gradients. [1] Jun Huang and Weili Luo ``Heat Transfer Through Convection in a Quasi-One-Dimensional Magnetic Fluid.'' Journal of Thermal Analysis and Calorimetry, 113, p449 (2013).   

Manifolds and front propagation barriers in advection-reaction-diffusion systems

We present experiments on the propagation of reaction fronts in laminar, vortex-dominated flows. The fronts are produced by the excitable Belousov-Zhabotinsky chemical reaction. The flows studied are driven by magnetohydrodynamic forcing techniques and are composed of a single vortex, chains or arrays of vortices, or spatially-disordered flows. In all of these cases, one-way barriers appear that either inhibit front propagation or, in some cases, pin the reactions fronts. We analyze this behavior with a recent theory of {\em burning invariant manifolds}\footnote{J. Mahoney, D. Bargteil, M. Kingsbury, K. Mitchell and T. Solomon, Europhys. Lett. {\bf 98}, 44005 (2012).} (BIMs) that are a generalization of the theory of invariant manifolds developed in the past to characterize chaotic mixing and transport of passive impurities. We demonstrate that the BIMs are responsible for the reaction barriers observed experimentally, and we discuss the applicability of this BIM formalism to a range of flows: time-independent, time-periodic and time-aperiodic.   

Tweaks to Turing Patterns, Wavelength Transitions in CDIMA~

Alan Turing predicted that stationary patterns could arise from a uniform steady state in a system through the processes of reaction and diffusion. Beyond the Turing instability, there exist spatially periodic states with different wavelengths. Pattern transitions, including those transitions to patterns of differing wavelengths are of interest in reaction-diffusion systems including ecological systems with patterned biomass prone to desertification. We study pattern transitions in the chlorine dioxide-iodine-malonic acid (CDIMA) system which is the prototypical system for the study of Turing patterns in chemical systems. Additions of selected halides (bromides and chlorides) to the system in its patterned state have led to the observation of up to a five fold increase in wavelength. ~ With the concentration of these halides as bifurcation parameter~we observe that these large wavelength patterns are bistable with the uniform steady state. We explore the pattern wavelength selection of this system.~ Wavelength halving and super lattice structure formation result from transitions between patterns of different wavelengths.~   

Simplistic Approach to Characterize Sloshing Phenomena using CFD Simulation

Liquid sloshing in vessels caused by forced acceleration has been the subject of intense investigations for last several decades both by experiments and numerical simulations. Many studies are done to minimize the sloshing induced forces on the vessel internals and some studies focused on different ways to describe the sloshing patterns. Most of the sloshing characterization methods are done using complex mathematical manipulation and more simplified method may be useful for better practical understanding. In this study, simple/easily understandable methods are explored to describe sloshing phenomenon through Computation Fluid Dynamics (CFD) simulation. Several parameters were varied including liquid level/tank length ratio, wave induced vessel motions, motion frequency, amplitudes in various sea state conditions. Parameters such as hydrodynamic force, pressure, moments, turbulent kinetic energy, height of the free surface, vorticity are used to quantify the sloshing intensity. In addition, visual inspections of sloshing motion are done through gas-liquid/oil-water interface fluctuation, streamlines, vector profiles. An equation connecting independent variables to resultant quantities will be established that will make it easier to describe the sloshing.   

Onset of motion of a particle attached to a wall in a linearly sheared fluid flow

We examine the onset of motion of particle on a bumpy surface which is exposed to a linear shear fluid flow by means of moving a top surface parallel to the bottom surface on which the particle rests with a prescribed shear rate. This system can be considered as a particularly simple limit of a granular bed exposed to a fluid flow, where forces and torques acting on the particles can be clearly determined. The control parameters available to us include the relative size of the particle to the bumps, the relative size of the particle to the gap thickness, and the flow Reynolds number controlled by the density of the particle and the viscosity of the fluid. Further, the degree of exposure of the particle to the fluid flow is measured by means of adding tracer particles to the fluid and measuring the flow field around the particle. By measuring the critical shear rate at onset of motion as a function of control parameters, we estimate the relative magnitude of forces and torques acting due to drag, lift, and gravitational forces on the particle. We contrast the torque balance and force balance conditions obtained using analytical expressions and numerical simulations with those observed in our experiments.   

Kelvin wake pattern and wave resistance at large Froude numbers

Recently, M. Rabaud and F. Moisy provided an analysis of airborne observations of ship wakes [1]. Their conclusion that the angle of the wake was no longer constant when varying the hull Froude number $Fr$ drew the attention of the scientific community, as it was in contradiction with Kelvin's century old theory of ship waves. We perform a mathematical study to understand these surprising observations [2]. Modelling the moving object by a pressure field symmetrical about a point, we analytically show that the angle delimiting the wake region outside which the surface is essentially flat actually remains constant and equal to the Kelvin angle, whereas the angle corresponding to the maximum amplitude of the waves indeed decreases with the Froude number, scaling as $1/Fr$ for large Froude numbers. To correctly reflect the elongated geometry of boats, we extend our calculations to anisotropic objects and show that the angle corresponding to the maximum amplitude of the waves also depends on the aspect ratio $W$ of the object and scales as $\sqrt{W}/Fr$ for large Froude numbers [3]. \\[4pt] [1] M. Rabaud and F. Moisy, PRL 110, 214503.\\[0pt] [2] A. Darmon, M. Benzaquen and E. Raphael, JFM 738, 2014, R3.\\[0pt] [3] M. Benzaquen, A. Darmon and E. Raphael, (accepted in PoF) arXiv:1404.1699.   

Increased swimming efficiency using thickness-varying flexible fins

We use three dimensional computer simulations to probe the hydrodynamics and deformation of oscillating flexible fins with varying thickness. We model the fin as an elastic rectangular plate undergoing a plunging motion at its leading edge. Since we assume that the thickest part of the fin is very small compared to its other length scales, the plate is modeled as infinitely thin. We simulate the thickness gradient by introducing an appropriate mass gradient and stiffness gradient in the plate. We characterize the steady state swimming velocity, input power, and swimming economy as a function of driving frequency and thickness ratio (between the thickest and thinnest parts). Our simulations show that the swimming economy, the ratio between the velocity and input power, is increased when the trailing edge is thinner. These findings help to identify the physical mechanisms that allow fish to have high swimming efficiency.   

Nozzle Spray Delivery Studies for High-Viscosity Shear-Thinning Fluids

Experiments were performed to explore the spray of shear-thinning polymer solutions through various nozzles. High speed images near the nozzle exit, drop size distributions, and spatial mass flux distributions were analyzed with the shear-thinning fluids and deionized water for comparison for seven different nozzles with pressure drops up to 40 psi. The nozzles tested include full cone, hollow cone, and flat fan nozzles. The aim was to identify suitable nozzles that would give droplet sizes in the range of 100-2000 $\mu$m for the shear thinning fluids. It was found in general that the shear-thinning fluids led to formation of ligament like structures whereas sheet perforation was more predominant with deionized water. The spray break up was delayed with the shear-thinning fluids. The spray of the shear-thinning fluids also led to an increase in the median drop size with the extent of increase being dependent on the nozzle type. The spray angle was found to be reduced by around 20$^{\circ}$ at a distance of 12" when compared to that of distilled water. This study lends fundamental insights into spray characteristics for a wide range of spray nozzles with high viscosity shear-thinning solution as compared to spraying deionized water with the same nozzles.   

Designing a Micromixer for Rolling Circle Amplification in Cancer Biomarker Detection

Rolling circle amplification (RCA) is an alternative method to the Polymerase Chain Reaction based amplification for point-of-care (POC) diagnosis. In future personalized cancer diagnostic for POC applications, smaller, faster and cheaper methods are needed instead of costly and time-consuming laboratory tests. Microfluidic chips can perform the detection of cancer biomarkers within less analysis time, and provide for improvement in the sensitivity and specificity required for biochemical analysis as well. Rapid mixing is essential in the chips used in cancer diagnostic. The goal of this study is to design a micromixer for rapid RCA-based analysis and develop the assay time in cancer biomarker detection. By combining assays with micromixers, multi-step bioreactions in microfluidic chips may be achieved with minimal external control. Here, simulation results related to the micromixer are obtained by COMSOL software.   

Travelling Wave Electrophoresis Due To Selective Currents At Electrodes

Abstract Using COMSOL finite element modeling software we simulate a 2D traveling-wave electrophoresis (TWE) device for microfluidic chromatography and electrolyte concentration. A periodic array of four electrodes each produce AC potentials shifted by a quarter-period from one another. This yields an electric wave which travels down the channel. Ions of varying mobilities in solution are carried along with the electric wave or left behind at different rates. We employ a simplified model for asymmetric reactions at the electrodes in order to solve the issue of electric double layer shielding at the electrodes. The selective reactions allow for the formation of diffusion layers of ions which attempt to follow the traveling electric wave. We examine the formation of these diffusion layers and how various system parameters affect motion of various ions through the system. With easy control over the traveling electric wave's frequency and direction one may employ this method for concentrating or separating bands of electrolytes.   

Differences between hydrodynamic and macromolecule induced clusters in microcapillary flow

Recent studies have been shown that despite the large shear rates, the presence of either fibrinogen or the synthetic polymer dextran leads to an enhanced formation of robust clusters of RBC in microcapillaries under flow conditions. The contribution of hydrodynamical interactions and interactions induced by the presence of macromolecules in the cluster formation has not been established. In order to elucidate this mechanism, we compare experimentally in microchannels under flow condition, the pure hydrodynamical cluster formation of RBCs and the cluster formation of RBCs in the presence of macromolecules inducing aggregation. The results reveal strong differences in the cluster morphology. Emphasizing on the case of clusters formed by two cells, the surface to surface interdistances between the cells in the different solutions shows a bimodal distribution. Numerical simulations based on the boundary integral method showed a good agreement with the experimental findings.