Nonlinear Dynamics of Particles Excited by an Electric Curtain

The use of the electric curtain (EC) has been proposed for manipulation and control of particles in various applications. The EC studied in this paper is called the 2-phase EC, which consists of a series of long parallel electrodes embedded in a thin dielectric surface. The EC is driven by an oscillating electric potential of a sinusoidal form where the phase difference of the electric potential between neighboring electrodes is 180 degrees. We investigate the one- and two-dimensional nonlinear dynamics of a particle in an EC field. The form of the dimensionless equations of motion is codimension two, where the dimensionless control parameters are the interaction amplitude ($A$) and damping coefficient ($\beta$). Our focus on the one-dimensional EC is primarily on a case of fixed $\beta$ and relatively small $A$, which is characteristic of typical experimental conditions. We study the nonlinear behaviors of the one-dimensional EC through the analysis of bifurcations of fixed points. We analyze these bifurcations by using Floquet theory to determine the stability of the limit cycles associated with the fixed points in the Poincar\'e sections. Some of the bifurcations lead to chaotic trajectories where we then determine the strength of chaos in phase space by calculating the largest Lyapunov exponent. In the study of the two-dimensional EC we independently look at bifurcation diagrams of variations in $A$ with fixed $\beta$ and variations in $\beta$ with fixed $A$. Under certain values of $\beta$ and $A$, we find that no stable trajectories above the surface exists; such chaotic trajectories are described by a chaotic attractor, for which the the largest Lyapunov exponent is found. We show the well-known stable oscillations between two electrodes come into existence for variations in $A$ and the transitions between several distinct regimes of stable motion for variations in $\beta$

Mechanics of biofilms formed of bacteria with fimbriae appendages

Gram-negative bacteria, as well as some Gram-positive bacteria, possess hair-like appendages known as fimbriae, which play an important role in adhesion of the bacteria to surfaces or to other bacteria. Unlike the sex pili or flagellum, the fimbriae are quite numerous, with of order 1000 fimbriae appendages per bacterial cell. In this paper, a recently developed hybrid model for bacterial biofilms is used to examine the role of fimbriae tension force on the mechanics of bacterial biofilms. Each bacterial cell is represented in this model by a spherocylindrical particle, which interact with each other through collision, adhesion, lubrication force, and fimbrial force. The bacterial cells absorb water and nutrients and produce extracellular polymeric substance (EPS). The flow of water and EPS, and nutrient diffusion within these substances, is computed using a continuum model that accounts for important effects such as osmotic pressure gradient, drag force on the bacterial cells, and viscous shear. The fimbrial force is modeled using an outer spherocylinder capsule around each cell, which can transmit tensile forces to neighboring cells with which the fimbriae capsule collides. We find that the biofilm structure during the growth process is dominated by a balance between outward drag force on the cells due to the EPS flow away from the bacterial colony and the inward tensile fimbrial force acting on chains of cells connected by adhesive fimbriae appendages. The fimbrial force also introduces a large rotational motion of the cells and disrupts cell alignment caused by viscous torque imposed by the EPS flow. The current paper characterizes the competing effects of EPS drag and fimbrial force using a series of computations with different values of the ratio of EPS to bacterial cell production rate and different numbers of fimbriae per cell

Acoustic streaming, fluid mixing, and particle transport by a Gaussian ultrasound beam in a cylindrical container

A computational study is reported of the acoustic streaming flow field generated by a Gaussian ultrasound beam propagating normally toward the end wall of a cylindrical container. Particular focus is given to examining the effectiveness of the acoustic streaming flow for fluid mixing within the container, for deposition of particles in suspension onto the bottom surface, and for particle suspension from the bottom surface back into the flow field. The flow field is assumed to be axisymmetric with the ultrasound transducer oriented parallel to the cylinder axis and normal to the bottom surface of the container, which we refer to as the impingement surface. Reflection of the sound from the impingement surface and sound absorption within the material at the container bottom are both accounted for in the computation. The computation also accounts for thermal buoyancy force due to ultrasonic heating of the impingement surface, but over the time period considered in the current simulations, the flow is found to be dominated by the acoustic streaming force, with only moderate effect of buoyancy force

An accelerated stochastic vortex structure method for particle collision and agglomeration in homogeneous turbulence

Modeling the response of interacting particles, droplets, or bubbles to subgrid-scale fluctuations in turbulent flows is a long-standing challenge in multiphase flow simulations using the Reynolds-Averaged Navier-Stokes approach. The problem also arises for large-eddy simulation for sufficiently small values of the Kolmogorov-scale particle Stokes number. This paper expands on a recently proposed stochastic vortex structure (SVS) method for modeling of turbulence fluctuations for colliding or otherwise interacting particles. An accelerated version of the SVS method was developed using the fast multipole expansion and local Taylor expansion approach, which reduces computation speed by two orders of magnitude compared to the original SVS method. Detailed comparisons are presented showing close agreement of the energy spectrum and probability density functions of various fields between the SVS computational model, direct numerical simulation (DNS) results, and various theoretical and experimental results found in the literature. Results of the SVS method for particle collision rate and related measures of particle interaction exhibit excellent agreement with DNS predictions for homogeneous turbulent flows. The SVS method was also used with adhesive particles to simulate formation of particle agglomerates with different values of the particle Stokes and adhesion numbers, and various measures of the agglomerate structure are compared to the DNS results

Interaction of unequal anti-parallel vortex tubes

A computational study is reported of the close interaction of nominally anti-parallel vortex tubes with unequal strengths. The computations are performed using a spectral method, with periodic boundary conditions and vortex Reynolds number Re=1500. The vortices are perturbed by a wavelength for which the pair is unstable because of their mutual interaction. The numerical method is tested for the case of equal-strength vortices, which exhibits the classic vortex reconnection phenomenon typifed by bridging between the vortex cores and formation of thin vorticity threads as the bridged sections advect away under their self-induced velocity. Computations for vortices of unequal strengths are reported for cases with small, moderate and large strength differences. The bridges between the vortex structures form loops that twist owing to the unequal vortex strengths. In the thread region, the vortex interaction is controlled by competition between the effects of stretching of the weak vortex as it wraps around the stronger vortex and the core distortion induced on each vortex owing to the straining imposed by the opposing vortex. For cases with large vortex strength difference, the strong vortex remains nearly straight as the weak vortex wraps around it, inducing an interlaced pattern of positive and negative vorticity spirals within the core of the strong vortex. Over long time, the bridge regions form loops that propagate away from the thread region for cases with small strength difference and wrap around the nearly columnar strong vortex for cases with large strength difference

Acoustic streaming and thermal instability of flow generated by ultrasound in a cylindrical container

A vertically orientated ultrasonic transducer contained within a closed cylindrical Pyrex tube was used to study the acoustic streaming flow within a cylindrical container. A particle-image velocimetry (PIV) system incorporating fluorescent 1.5 μm seeding particles suspended in a mixture of diethyl-phthalate and ethanol, whose optical index was matched to that of Pyrex, was used to allow for undistorted PIV imaging within the Pyrex tube. Temperature on the end-wall surface and acoustic pressure within the cylinder were measured for different end-wall materials. Variables considered included acoustic absorption and reflection coefficients, ultrasound intensity, container height, and thermal properties of the end-wall material. It was observed that a quasi-steady flow field driven by acoustic streaming is rapidly established within the container, which is typically dominated by a stationary vortex ring with downward flow along the ring axis. After sufficient time this quasi-stationary flow exhibits a thermal instability causing it to transform into a secondary flow state. Different types of secondary flow states were observed, including cases where the flow along the cylinder axis is oriented upward toward the ultrasound transducer and cases where the axial flow changes directions along the cylinder axis

A stochastic vortex structure method for interacting particles in turbulent shear flows

In a recent study, we have proposed a new synthetic turbulence method based on stochastic vortex structures (SVSs), and we have demonstrated that this method can accurately predict particle transport, collision, and agglomeration in homogeneous, isotropic turbulence in comparison to direct numerical simulation results. The current paper extends the SVS method to non-homogeneous, anisotropic turbulence. The key element of this extension is a new inversion procedure, by which the vortex initial orientation can be set so as to generate a prescribed Reynolds stress field. After validating this inversion procedure for simple problems, we apply the SVS method to the problem of interacting particle transport by a turbulent planar jet. Measures of the turbulent flow and of particle dispersion, clustering, and collision obtained by the new SVS simulations are shown to compare well with direct numerical simulation results. The influence of different numerical parameters, such as number of vortices and vortex lifetime, on the accuracy of the SVS predictions is also examined

Anisotropic Small-Polaron Hopping In W:Bivo4 Single Crystals

DC electrical conductivity, Seebeck and Hall coefficients are measured between 300 and 450 K on single crystals of monoclinic bismuth vanadate that are doped n-type with 0.3% tungsten donors (W:BiVO4). Strongly activated small-polaron hopping is implied by the activation energies of the Arrhenius conductivities (about 300 meV) greatly exceeding the energies characterizing the falls of the Seebeck coefficients' magnitudes with increasing temperature (about 50 meV). Small-polaron hopping is further evidenced by the measured Hall mobility in the ab-plane (10(-1) cm(2) V-1 s(-1) at 300 K) being larger and much less strongly activated than the deduced drift mobility (about 5 x 10(-5) cm(2) V-1 s(-1) at 300 K). The conductivity and n-type Seebeck coefficient is found to be anisotropic with the conductivity larger and the Seebeck coefficient's magnitude smaller and less temperature dependent for motion within the ab-plane than that in the c-direction. These anisotropies are addressed by considering highly anisotropic next-nearest-neighbor (approximate to 5 angstrom) transfers in addition to the somewhat shorter (approximate to 4 angstrom), nearly isotropic nearest-neighbor transfers. (C) 2015 AIP Publishing LLC.U.S. Department of Energy (DOE), DE-FG02-09ER16119Welch Foundation Grant F-1436Hemphill-Gilmore Endowed FellowshipNSF MIRT DMR 1122603Chemical EngineeringTexas Materials InstituteChemistr