Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session L25: Microscale Flows: Computations |
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Chair: Francesco Costanzo, Pennsylvania State University Room: E145 |
Monday, November 21, 2016 4:30PM - 4:43PM |
L25.00001: Arbitrary Lagrangian-Eulerian (ALE) formulation for microacoustofluidics Nitesh Nama, Tony Jun Huang, Francesco Costanzo We present an Arbitrary Lagrangian-Eulerian (ALE) formulation for the analysis of acoustic streaming flows. We employ a multiscale approach to separate the flow variables into first-and second-order components which results in two subproblems: a first-order problem, formulated in terms of the fluid displacement at a fast scale and a second-order problem formulated in terms of the Lagrangian flow velocity at a slow time scale. The Lagrangian velocity based formulation of the second-order problem removes the ambiguity concerning the second-order boundary condition at the oscillating walls and circumvents the need to employ the notion of Stokes drift, thereby allowing a direct comparison with the experiments. Moreover, the ALE formulation offers a natural extension to the more complex fluid-structure interaction problems in microacosutofluidic devices. Lastly, we present numerical test cases where the Eulerian flow velocities exhibit several non-physical features that are not observed in the corresponding Lagrangian flow velocities, indicating that a Lagrangian velocity based formulation is much more favorable and readily interpretable. [Preview Abstract] |
Monday, November 21, 2016 4:43PM - 4:56PM |
L25.00002: Autonomously Responsive Pumping by a Bacterial Flagellar Forest: A Mean-field Approach James Martindale, Henry C. Fu The design and fabrication of microscale pumps using magnetically actuated bacterial flagella opens the door for many applications such as the pumping and regulation of chemicals. Here, we discuss simulations for a pump consisting of a regular two-dimensional array of rigid helices. Recent work investigating the flows above a small, finite array by numerically calculating the full dynamics showed that having random phase differences between helices seems essential to produce the flow patterns observed in experiments. We developed a model which allows us to treat random phase differences in an infinite array. Using a mean-field approach we define pumping as the existence of a self-consistent tilt angle of the array. Pumping is then examined numerically as a function of several parameters in the magnetic actuation and helical geometry. We demonstrate how this pumping flow may be mechanically halted by way of magnetic actuation or autonomously halted by the polymorphic transformation of bacterial flagella in response to environmental stimuli. [Preview Abstract] |
Monday, November 21, 2016 4:56PM - 5:09PM |
L25.00003: Directed swimming of nanoscale swimmers in an array of posts with non-circular section: modelling and shape optimization Jiajun Tong, Michael Shelley It has been shown experimentally that swimming of nanoscale rod-like bi-metallic swimmers can be biased and guided by an array of teardrop shaped posts in the solution, giving rise to a statistically directed motion in long time. This could be useful in many applications like concentrating nanoswimmers, or separating them from non-motile particles. We pose a model to study such directed swimming, taking into account the absorption and desorption of the swimmers to the vertical walls of posts. We emphasize the role of varying curvature along the circumference of a single post on the absorption and desorption. In seeking to enhance directed swimming, we apply shape optimization to find how we can design, based on experimental data, better posts which have higher efficiency of transporting swimmers. [Preview Abstract] |
Monday, November 21, 2016 5:09PM - 5:22PM |
L25.00004: Tailoring tails in Taylor dispersion: how boundaries shape chemical delivery in microfluidics: computation and theory Richard M. McLaughlin, Manuchehr Aminian, Francesca Bernardi, Roberto Camassa, Daniel M. Harris We present the results of a combined computational and theoretical study of the dispersion of a passive scalar in laminar shear flow through rectangular and elliptical channels. We show through Monte Carlo simulation and asymptotic analysis that the cross-sectional aspect ratio sets the sign of the average skewness at long times (relative to the Taylor diffusion timescale) which describes the longitudinal asymmetry of the tracer distribution. Universally, thin channels (aspect ratio $\ll 1$) result in negative average skewness, whereas as thick channels (aspect ratio $\sim 1$) result in positive average skewness. Our analysis also allows us to define a ``golden'' aspect ratio which separates thin from thick channels, the value of which is remarkably similar for both the rectangle and the ellipse. Further, by examining the median of the cross-sectionally averaged distribution, we establish that negative skewness correlates with solutes arriving with sharp fronts followed by a tapering tail. Future directions will be discussed. [Preview Abstract] |
Monday, November 21, 2016 5:22PM - 5:35PM |
L25.00005: Dynamic density functional theory for nucleation: Non-classical predictions of mesoscopic nucleation theory Miguel A. Duran-Olivencia, Peter Yatsyshin, James F. Lutsko, Serafim Kalliadasis Classical density functional theory (DFT) for fluids and its dynamic extension (DDFT) provide an appealing mean-field framework for describing equilibrium and dynamics of complex soft matter systems. For a long time, homogeneous nucleation was considered to be outside the limits of applicability of DDFT. However, our recently developed mesoscopic nucleation theory (MeNT) based on fluctuating hydrodynamics, reconciles the inherent randomness of the nucleation process with the deterministic nature of DDFT. It turns out that in the weak-noise limit, the most likely path (MLP) for nucleation to occur is determined by the DDFT equations. We present computations of MLPs for homogeneous and heterogeneous nucleation in colloidal suspensions. For homogeneous nucleation, the MLP obtained is in excellent agreement with the reduced order-parameter description of MeNT, which predicts a multistage nucleation pathway. For heterogeneous nucleation, the presence of impurities in the fluid affects the MLP, but remarkably, the overall qualitative picture of homogeneous nucleation persists. Finally, we highlight the use of DDFT as a simulation tool, which is especially appealing as there are no known applications of MeNT to heterogeneous nucleation. [Preview Abstract] |
Monday, November 21, 2016 5:35PM - 5:48PM |
L25.00006: Steady film flow over 2D topography with air inclusion formed inside the trench. John Tsamopoulos, Stylianos Varchanis, Yannis Dimakopoulos Liquid film flow along an inclined, solid substrate featuring periodic rectangular trenches may either completely wet the trench floor (Wenzel state) or pin on the entrance and exit corners of the trench (Cassie state) or assume any other configuration in between these two extremes. In the intermediate cases a second gas-liquid interface inside the trench is formed, which adheres to the walls of the trench forming two three-phase contact lines, and encloses a different amount of air under different physical conditions. The Galerkin finite element method is used to solve the Navier-Stokes equations in a physical domain, which is adaptively re-meshed. Multiple steady solutions, connected by turning points and transcritical bifurcations as well as isolated solution branches, are revealed by pseudo arc-length continuation. Two possible cases of a single air inclusion inside the trench are examined. The penetration of the liquid inside the trench is enhanced primarily by increasing either the wettability of the substrate or the capillarity or by decreasing the flow rate. Flow hysteresis may occur when the liquid does not penetrate deep enough inside the trench leading to different flow patterns. The interplay of inertia, viscous, gravity and capillary forces along with substrate wettability determines the volume of the air encapsulated in the trench and the extent of free surface deformation. [Preview Abstract] |
Monday, November 21, 2016 5:48PM - 6:01PM |
L25.00007: An ALE Finite Element Approach for Two-Phase Flow with Phase Change Erik Gros, Gustavo Anjos, John Thome In this work, two-phase flow with phase change is investigated through the Finite Element Method (FEM) in the Arbitrary Lagrangian-Eulerian (ALE) framework. The equations are discretized on an unstructured mesh where the interface between the phases is explicitly defined as a sub-set of the mesh. The two-phase interface position is described by a set of interconnected nodes which ensures a sharp representation of the boundary, including the role of the surface tension. The methodology proposed for computing the curvature leads to very accurate results with moderate programming effort and computational costs. Such a methodology can be employed to study accurately many two-phase flow and heat transfer problems in industry such as oil extraction and refinement, design of refrigeration systems, modelling of microfluidic and biological systems and efficient cooling of electronics for computational purposes. The latter is the principal aim of the present research. The numerical results are discussed and compared to analytical solutions and reference results, thereby revealing the capability of the proposed methodology as a platform for the study of two-phase flow with phase change. [Preview Abstract] |
Monday, November 21, 2016 6:01PM - 6:14PM |
L25.00008: Three dimensional simulations of viscous folding in diverging microchannels Bingrui XU, Jalel Chergui, Seungwon Shin, Damir Juric Three dimensional simulations on the viscous folding in diverging microchannels reported by Cubaud and Mason are performed using the parallel code BLUE for multi-phase flows. The more viscous liquid $L_1$ is injected into the channel from the center inlet, and the less viscous liquid $L_2$ from two side inlets. Liquid $L_1$ takes the form of a thin filament due to hydrodynamic focusing in the long channel that leads to the diverging region. The thread then becomes unstable to a folding instability, due to the longitudinal compressive stress applied to it by the diverging flow of liquid $L_2$. We performed a parameter study in which the flow rate ratio, the viscosity ratio, the Reynolds number, and the shape of the channel were varied relative to a reference model. In our simulations, the cross section of the thread produced by focusing is elliptical rather than circular. The initial folding axis can be either parallel or perpendicular to the narrow dimension of the chamber. In the former case, the folding slowly transforms via twisting to perpendicular folding , or it may remain parallel. The direction of folding onset is determined by the velocity profile and the elliptical shape of the thread cross section in the channel that feeds the diverging part of the cell. [Preview Abstract] |
Monday, November 21, 2016 6:14PM - 6:27PM |
L25.00009: Mathematical modelling of Liquid --Liquid extraction in the slug flow regime in a microchannel Sundari Ramji, Dinesh Bhagavatula, Arjun Rakesh, Pushpavanam S Mixing in the slug flow regime in microchannels is enhanced by the presence of internal circulations induced by shear due to wall. This helps improve mass transfer in this flow regime. We exploit the low Re characteristic of the flow and seek a numerical solution to understand the structure of the vortex patterns formed in the two phases in the slug flow regime. We study liquid-liquid extraction in the system to determine the improvement in mass transfer. The system was analyzed for two cases when there is (i) no film surrounding the slug (ii) a thin film surrounding the slug. The 2D governing equations for fluid flow are solved using two approaches: a) a stream function formulation based on finite differences b) primitive variable formulation with the Chebyshev collocation method. The effect of viscosity ratio, slug length and film thickness on the vortex structure were studied. While secondary vortices were induced in the less viscous phase in the case where the thin film is absent, they are always generated in the slug irrespective of the viscosity ratio in the case where the film is present. The species balance equation was then solved numerically using two approaches: a) an Alternating Direction Explicit method and b) the Locally One Dimensional splitting technique. The effect of varying Peclet number from 0 to 10$^{\mathrm{4}}$ on the solute transfer from the slug to the continuous phase was studied. The extraction performance is analyzed in terms of extraction efficiency and mass transfer coefficient. [Preview Abstract] |
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