Session G37: General Fluid Dynamics I

Colloidal band assembly from different suspended particles

Particle visualizations, mainly based on evanescent-wave illumination, have shown that sulfate- and carboxylate-terminated polystyrene particles in a dilute suspension flowing through a microchannel assemble into near-wall bands when the flow is driven by a dc electric field and a pressure gradient along the channel axis applied in opposite directions. In these bands, the colloidal particles (of radius $a\approx 250-500$ nm) are concentrated in a liquid state in regions with a cross-sectional dimension of a few $\mu \mbox{m}$ and an axial extent comparable to the channel length of $O$(1 cm). In many cases, the particles first assemble into many closely spaced, fairly unstable bands before achieving a fairly stable ``steady-state'' configuration with fewer bands. Results at a given channel location for the timescales of particle assembly as well as the characteristics of the bands are presented for a range of particle and suspension properties including the particle volume fraction $\varphi_{\infty } ,\,\;a\mbox{,\thinspace }$ and particle zeta-potential $\zeta_{\mbox{p}} $ and flow properties such as the electric field magnitude $\left| E \right|$ and near-wall shear rate $\dot{{\gamma }}$. The band characteristics appear to scale with the electric field ``offset,'' or $\left| E \right|-\left| {E_{\mbox{min}} } \right|$ where $\left| {E_{\mbox{min}} } \right|$ is the minimum electric field magnitude at a given $\dot{{\gamma }}$ required for band formation.   

Colloidal band assembly in different microchannels

Over the last few years, we have shown that polystyrene colloidal particles in a dilute suspension flowing through a microchannel assemble into near-wall bands in combined steady Poiseuille and electroosmotic (EO) ``counterflow'' driven by a pressure gradient and dc electric field, respectively, in opposite directions. The bands of concentrated particles have a cross-sectional dimension of a few $\mu \mbox{m}$ and an axial extent of $O$(1 cm) and a cross-stream spacing of $O$(10 $\mu \mbox{m})$. This type of colloidal assembly has been demonstrated for a variety of particle radii, zeta-potentials, and concentrations, and the flow characteristics required for band assembly, as well as the characteristics of the bands once formed, depend strongly upon these suspension and particle properties. More recently, we have started investigating how band assembly is affected by channel properties. Results are presented at different streamwise ($x)$ locations in different channel geometries for fused-silica and polydimethyl siloxane(PDMS)-fused silica channels with their different wall zeta-potentials $\zeta_{\mbox{w}} $ . The effect of suspending liquid properties including electrolyte composition and ionic strength is also discussed.   

Observations of the initial stages of colloidal band formation

A number of studies have shown that particles suspended in a conducting fluid near a wall are subject to wall-normal repulsive ``lift'' forces, even in the absence of interparticle interactions, in a flowing suspension. Evanescent-wave visualizations have shown that colloidal particles in a dilute (volume fractions \textless 0.4{\%}) suspension are instead \textit{attracted} to the wall when the suspension is driven through $\sim 30\mbox{\thinspace }\mu \mbox{m}$ deep channels by a pressure gradient and an electric field when the resulting combined Poiseuille and electroosmotic (EO) flow are in opposite direction, $i.e.$, ``counterflow,'' although the particles and channel walls both have negative zeta-potentials. Above a minimum ``threshold'' electric field magnitude $\left| {E_{\mbox{min}} } \right|$, the particles assemble into dense ``bands'' with cross-sectional dimensions of a few $\mu \mbox{m}$ and length comparable to that of the channel ($i.e.$, a few cm). The results suggest that the threshold field $\left| {E_{\mbox{min}} } \right|$ is large enough so that there is a region of ``reverse'' flow, along the direction of the EO flow, near the wall. Visualization of a large segment of the channel (\textgreater 300 hydraulic diameters) at frame rates as great as 1 kHz is used to determine banding maps for a variety of dilute colloidal suspensions and to investigate the initial stages of band formation over a wide range of flow conditions.   

Exploration of Piezoelectric Bimorph Deflection in Synthetic Jet Actuators

The design of piezoelectric bimorphs for synthetic jet actuators could be improved by greater understanding of the deflection of the bimorphs; both their mode shapes and the resulting volume change inside the actuator. The velocity performance of synthetic jet actuators is dependent on this volume change and the associated internal pressure changes. Knowledge of these could aid in refining the geometry of the cavity to improve efficiency. Phase-locked jet velocities and maps of displacement of the surface of the bimorph were compared between actuators of varying diameter. Results from a bimorph of alternate stiffness were also compared. Bimorphs with higher stiffness exhibited a more desirable (0,1) mode shape, which produced a high volume change inside of the actuator cavity. Those with lower stiffness allowed for greater displacement of the surface, initially increasing the volume change, but exhibited higher mode shapes at certain frequency ranges. These higher node shapes sharply reduced the volume change and negatively impacted the velocity of the jet at those frequencies. Adjustments to the distribution of stiffness along the radius of the bimorph could prevent this and allow for improved deflection without the risk of reaching higher modes.   

Direct numerical simulation of axisymmetric laminar low-density jets

The stability of submerged laminar axisymmetric low-density jets has been investigated experimentally (Kyle \& Sreenivasan 1993, Hallberg \& Strykowski 2006) and with linear analysis (Jendoubi \& Strykowski 1994, Coenen \& Sevilla 2012, Coenen et al. 2017). These jets become globally unstable when the Reynolds number is larger than a certain critical value which depends on the density ratio and on the velocity profile at the injector outlet. In this work, Direct Numerical Simulations using FreeFEM$++$ (Hecht 2012) with P1 elements for pressure and P2 for velocity and density are performed to complement the above mentioned studies. Density and velocity fields are analyzed at long time showing the unforced space-time evolution of nonlinear disturbances propagating along the jet. Using the Stuart-Landau model to fit the numerical results for the self-excited oscillations we have computed a neutral stability curve that shows good agreement with experiments and stability theory.   

Cell-Averaged discretization for incompressible Navier-Stokes with embedded boundaries and locally refined Cartesian meshes: a high-order finite volume approach

We present a consistent cell-averaged discretization for incompressible Navier-Stokes equations on complex domains using embedded boundaries. The embedded boundary is allowed to freely cut the locally-refined background Cartesian grid. Implicit-function representation is used for the embedded boundary, which allows us to convert the required geometric moments in the Taylor series expansion (upto arbitrary order) of polynomials into an algebraic problem in lower dimensions. The computed geometric moments are then used to construct stencils for various operators like the Laplacian, divergence, gradient, etc., by solving a least-squares system locally. We also construct the inter-level data-transfer operators like prolongation and restriction for multi grid solvers using the same least-squares system approach. This allows us to retain high-order of accuracy near coarse-fine interface and near embedded boundaries. Canonical problems like Taylor-Green vortex flow and flow past bluff bodies will be presented to demonstrate the proposed method.   

Solutions to the linearized Navier-Stokes equations for channel flow via the WKB approximation

Progress on determining semi-analytical solutions to the linearized Navier-Stokes equations for incompressible channel flow, laminar and turbulent, is reported. Use of the WKB approximation yields, e.g., solutions to initial-value problem for the inviscid Orr-Sommerfeld equation in terms of the Bessel functions $J_{+1/3}, J_{-1/3}, J_1,$ and $Y_1$ and their modified counterparts for any given wave speed $c = \omega/k_x$ and $k_{\perp}, (k_{\perp}^2 = k_x^2 + k_z^2)$. Of particular note to be discussed is a sequence $i = 1, 2,. . .$ of homogeneous inviscid solutions with complex $k_{\perp i}$ for each speed $c$, ($0 < c \leq U_{max}$), in the downstream direction. These solutions for the velocity component normal to the wall $v$ are localized in the plane parallel to the wall. In addition, for limited range of negative $c $, $( - c* \leq c \leq 0)$, we have found upstream-traveling homogeneous solutions with real $k_{\perp}(c)$. In both cases the solutions for $v$ serve as a source for corresponding solutions to the inviscid Squire equation for the vorticity component normal to the wall $\omega_y$.   

Mixing in turbulent channel flow with Lagrangian computations

Turbulent mixing has been studied because of its importance in transport processes in both nature and engineering [1]. The effects of convection dominate over molecular diffusion, but effects of molecular diffusion are not negligible at molecular scales, and are significant in reacting flows. Several studies have been devoted to molecular mixing in homogeneous, isotropic turbulence. In this study, the effect of anisotropic turbulence, along with that of molecular diffusion, on passive scalar mixing is explored. Simulation of a turbulent channel flow is conducted by direct numerical simulation, followed by Lagrangian tracking of the motion of passive scalars with different Schmidt numbers (Sc) in the flow field. The friction Re is 300 and the Sc ranges from 0.7 to 2,400. Mass markers are released from instantaneous and continuous line sources, located at the center region of the channel to the wall. The combined effects of mean velocity difference, molecular diffusion and near-wall coherent structures lead to the observation of different concentrations of particles at different heights, downstream from the source. Mixing efficiency is quantified by measuring both the intensity and the area of the channel where mixing happens. While results with instantaneous sources demonstrate the physics of mixing, using continuous sources reveals how to control the timing and spatial distribution of the mixing. References 1. Dimotakis, P.E. Annu. Rev. Fluid Mech. 37, 329, 2005 2. Nguyen, Q., Papavassiliou, D.V. Phys. Fluids, 28(12), 125103, 2016 3. Nguyen, Q., Srinivasan, C., Papavassiliou, D.V. Phys Rev E, 91, 033019, 2015   

Flow effects on the formation of nanoparticle aggregates in packed beds

Aggregation of nanoparticles in porous media may give rise to pore clogging and sedimentation, which are undesirable phenomena in stable dispersing systems. In addition, deposited/settled aggregates might serve as secondary collectors for further attachment of suspended nanoparticles. In this work, the transient mean size of nanoparticle systems, propagating in packed beds is numerically explored. Primary nanoparticles can interact with each other to form aggregates with a known aggregation probability. The velocity fields in the packed-sphere beds are generated by using the lattice Boltzmann method for single phase flow. In conjunction with that, a Lagrangian framework [1, 2] is employed to track the positions of the nanoparticles at every simulation step. We explore the change of the transient mean size under different hydrodynamic conditions (pore velocity, primary particle size, particle concentration, aggregation probability). An empirical correlation, predicting the final mean size of aggregates under given hydrodynamic conditions, is also obtained. References 1. R. S. Voronov, S. VanGordon, V. I. Sikavitsas, D. V. Papavassiliou, Int. J. Num. Methods Fluids, 67, 501-517, 2011 2. N.H. Pham, D.P. Swatske, J.H. Harwell, B-J Shiau, D.V. Papavassiliou, Int. J. Heat {\&} Mass Transf. 72, 319-328, 2014   

Energy harvesting from the interaction of a Lamb dipole with a flexible cantilever

Energy harvesting from interactions of coherent flow structures with flexible solid structures can be used for powering miniature electronic devices. Although effective, the fundamental mechanism of such an energy extraction process has not been fully understood. Therefore, this study aims to provide more physical insights into this problem. The coherent flow structure is represented by a Lamb dipole, and the solid structure is assumed as a two-dimensional flexible cantilever. The cantilever is placed along the propagation direction of the dipole, with its fixed end initially towards or away from the dipole and its lateral distance from the dipole center varied. As the dipole passes through the cantilever, the latter can extract energy from the former through effective interactions. Such a two-dimensional fluid-structure interaction problem is numerically studied at a low Reynolds number of 200 using a lattice Boltzmann method (LBM) based numerical framework. The simulation results reveal that the flexible cantilever with a moderate stiffness is more beneficial to the energy harvesting, and it can scavenge more energy from the ambient vortices when its fixed end is initially away from the dipole with a relatively small lateral distance.