Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session M14: Microscale Flows: ModelingMicro
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Chair: David Emerson, STFC Daresbury Laboratory Room: 507 |
Tuesday, November 21, 2017 8:00AM - 8:13AM |
M14.00001: Inertial particle manipulation in microscale oscillatory flows Siddhansh Agarwal, Bhargav Rallabandi, David Raju, Sascha Hilgenfeldt Recent work has shown that inertial effects in oscillating flows can be exploited for simultaneous transport and differential displacement of microparticles, enabling size sorting of such particles on extraordinarily short time scales. Generalizing previous theory efforts, we here derive a two-dimensional time-averaged version of the Maxey-Riley equation that includes the effect of an oscillating interface to model particle dynamics in such flows. Separating the steady transport time scale from the oscillatory time scale results in a simple and computationally efficient reduced model that preserves all slow-time features of the full unsteady Maxey-Riley simulations, including inertial particle displacement. Comparison is made not only to full simulations, but also to experiments using oscillating bubbles as the driving interfaces. In this case, the theory predicts either an attraction to or a repulsion from the bubble interface due to inertial effects, so that versatile particle manipulation is possible using differences in particle size, particle/fluid density contrast and streaming strength. We also demonstrate that these predictions are in agreement with experiments. [Preview Abstract] |
Tuesday, November 21, 2017 8:13AM - 8:26AM |
M14.00002: Mathematical modeling of two phase stratified flow in a microchannel with curved interface Rajat Dandekar, Jason R. Picardo, S Pushpavanam Stratified or layered two-phase flows are encountered in several applications of microchannels, such as solvent extraction. Assuming steady, unidirectional creeping flow, it is possible to solve the Stokes equations by the method of eigenfunctions, provided the interface is flat and meets the wall with a 90 degree contact angle. However, in reality the contact angle depends on the pair of liquids and the material of the channel, and differs significantly from 90 degrees in many practical cases. For unidirectional flow, this implies that the interface is a circular arc (of constant curvature). We solve this problem within the framework of eigenfunctions, using the procedure developed by Shankar [Proc.R.Soc.A, 2005, 461, 2121-2133]. We consider two distinct cases: (a) the interface meets the wall with the equilibrium contact angle; (b) the interface is pinned by surface treatment of the walls, so that the flow rates determine the apparent contact angle. We show that the contact angle appreciably affects the velocity profile and the volume fractions of the liquids, while limiting the range of flow rates that can be sustained without the interface touching the top/bottom walls. Non-intuitively, we find that the pressure drop is reduced when the more viscous liquid wets the wall. [Preview Abstract] |
Tuesday, November 21, 2017 8:26AM - 8:39AM |
M14.00003: Hydrodynamic Capture of Particles by Micro-swimmers under Hele-Shaw Flows Grant Mishler, Alan Cheng Hou Tsang, On Shun Pak We explore a hydrodynamic capture mechanism of a driven particle by a micro-swimmer in confined microfluidic environments with an idealized model. The capture is mediated by the hydrodynamic interactions between the micro-swimmer, the driven particle, and the background flow. This capture mechanism relies on the existence of attractive stable equilibrium configurations between the driven particle and the micro-swimmer, which occurs when the background flow is larger than a certain critical threshold. Dynamics and stability of capture and non-capture events will be discussed. This study may have potential applications in the study of capture and delivery of therapeutic payloads by micro-swimmers as well as particle self-assembly under confinements. [Preview Abstract] |
Tuesday, November 21, 2017 8:39AM - 8:52AM |
M14.00004: Brownian Suspensions of Particles with Arbitrary Shape in Totally Confined Domains Brennan Sprinkle, Aleksanda Donev, Neelesh Patankar In past work, we examined the simulation of Brownian motion of passive or active rigid bodies with arbitrary shape in unconfined domains and half space. Here we extend these techniques to fully confined domains, such as narrow channels. The additional constraints of full confinement often admit richer dynamics for active particle suspensions but simulation is substantially more expensive as the solvent must be treated explicitly. To this end, an efficient simulation algorithm will be presented, where generation of the thermal drift in this context will be the primary focus. [Preview Abstract] |
Tuesday, November 21, 2017 8:52AM - 9:05AM |
M14.00005: Scaling arguments for flows induced by oscillating cylinders Tejaswin Parthasarathy, Mattia Gazzola Low and high intensity cylinder oscillations in fluids give rise, respectively, to viscous streaming and Keulegan-Carpenter flows, both well understood. These flow systems have been traditionally characterized via different non-dimensional parameters ($Re$-$Rs$ for streaming flows and $KC$-$\beta$ for the KC flows). Nevertheless, the identical system setups suggest that it might be possible to characterize both flow behaviors through a common set of scaling groups based on fundamental principles. We explore this possibility in an attempt to harmonize these two descriptions by means of physical arguments involving time and length scale separation, and guided by direct numerical simulations. [Preview Abstract] |
Tuesday, November 21, 2017 9:05AM - 9:18AM |
M14.00006: Spontaneous oscillations in microfluidic networks Daniel Case, Jean-Regis Angilella, Adilson Motter Precisely controlling flows within microfluidic systems is often difficult which typically results in systems being heavily reliant on numerous external pumps and computers. Here, I present a simple microfluidic network that exhibits flow rate switching, bistablity, and spontaneous oscillations controlled by a single pressure. That is, by solely changing the driving pressure, it is possible to switch between an oscillating and steady flow state. Such functionality does not rely on external hardware and may even serve as an on-chip memory or timing mechanism. I use an analytic model and rigorous fluid dynamics simulations to show these results. [Preview Abstract] |
Tuesday, November 21, 2017 9:18AM - 9:31AM |
M14.00007: Fully Resolved Simulations of 3D Printing Gretar Tryggvason, Huanxiong xia, Jiacai Lu Numerical simulations of Fused Deposition Modeling (FDM) (or Fused Filament Fabrication) where a filament of hot, viscous polymer is deposited to “print” a three-dimensional object, layer by layer, are presented. A finite volume/front tracking method is used to follow the injection, cooling, solidification and shrinking of the filament. The injection of the hot melt is modeled using a volume source, combined with a nozzle, modeled as an immersed boundary, that follows a prescribed trajectory. The viscosity of the melt depends on the temperature and the shear rate and the polymer becomes immobile as its viscosity increases. As the polymer solidifies, the stress is found by assuming a hyperelastic constitutive equation. The method is described and its accuracy and convergence properties are tested by grid refinement studies for a simple setup involving two short filaments, one on top of the other. The effect of the various injection parameters, such as nozzle velocity and injection velocity are briefly examined and the applicability of the approach to simulate the construction of simple multilayer objects is shown. The role of fully resolved simulations for additive manufacturing and their use for novel processes and as the ``ground truth’’ for reduced order models is discussed. [Preview Abstract] |
Tuesday, November 21, 2017 9:31AM - 9:44AM |
M14.00008: Connecting Ellipses to Rectangles in Passive Scalar Transport Manuchehr Aminian, Francesca Bernardi, Roberto Camassa, Daniel Harris, Richard McLaughlin We study how passive scalar transport in Poiseuille flow is affected by the shape of the pipe cross section. Our previous results have established nontrivial dependence of the skewness of the tracer distribution upon the pipe shape. Previously, we have studied the families of rectangles and ellipses, with the behavior past diffusive timescales primarily depending on aspect ratio, and the type of geometry being secondary. However, at timescales well before the diffusion timescale, the family of ellipses is distinct compared to rectangles. We investigate this phenomenon by studying a collection of exotic cross sections connecting the ellipses and rectangles, using a combination of theoretical and computational tools. [Preview Abstract] |
Tuesday, November 21, 2017 9:44AM - 9:57AM |
M14.00009: Challenges with modeling thermal flows in the slip-flow regime David Emerson, Xiao-Jun Gu The success of the Navier-Stokes-Fourier (NSF) equations has encouraged researchers to develop various velocity-slip and temperature-jump boundary conditions that are deemed suitable for flows that are in a weakly rarefied state. The degree of rarefaction can be estimated through the Knudsen number, Kn, which relates the mean free path of the gas to some characteristic length scale. If the Knudsen number is in the range 0.001 \textless Kn \textless 0.1 the flow is in the \textit{slip flow} regime. The assumption is that the NSF equations remain valid if the boundary conditions are modified to take account of velocity-slip and temperature-jump at the wall. If Kn is in the range 0.1 \textless Kn \textless 10, the flow is in the \textit{transition} regime and the NSF equations are no longer considered reliable. Recent results suggest that using the modified NSF equations for thermal problems in the slip flow regime can produce erroneous answers. This presentation will discuss issues related to thermal problems in the slip flow regime and highlights where researchers need to be very cautious. [Preview Abstract] |
Tuesday, November 21, 2017 9:57AM - 10:10AM |
M14.00010: Generalized slip condition Giuseppe Antonio Zampogna, Jacques Magnaudet, Alessandro Bottaro Using a homogenisation technique, we generalize the well-known Navier slip condition in the form: \begin{equation*}u_i=-{W}_{ij}\partial_j {p} + {E}_{ilk}(\partial_k u_l + \partial_l u_k).\end{equation*} This condition may be applied to any flow over a rough or only partially wetted surface, without any limitation on the flow regime. The macroscopic velocity depends on $W_{ij}$, a ``wettability'' tensor formally analogous to a permeability, and on the tensorial slip length $E_{ijk}$. Components of these tensors are obtained as solutions of microscopic problems arising during the derivation of the above condition. We validated the latter by performing DNS of the flow about a rough sphere under various conditions. This rational framework clarifies the missed analogy between the microscopic characterization of Navier's classical slip length and its applicability to a macroscopic boundary condition. [Preview Abstract] |
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