Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session G6: Microfluidics: General I |
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Chair: Francois Gallaire, EPFL Room: 24B |
Monday, November 19, 2012 8:00AM - 8:13AM |
G6.00001: Effect of Secondary Flows on convection-dominated dispersion Alessandra Adrover, Elisabetta Veca We investigate the effects of secondary (transverse) flows on ``convection-dominated dispersion'' of pressure driven, open column laminar flow in a conduit with rectangular cross-section. In the convection-controlled dispersion regime (i.e. laminar dispersion in finite-length channel with axial flow at high Peclet numbers) the properties of the dispersion boundary layer and the values of the scaling exponents controlling the dependence of the moment hierarchy on the Peclet number are determined by the local near-wall behavior of the axial velocity. The presence of transverse flows strongly modify the localization properties of the dispersion boundary layer and consequently the moment scaling exponents. Different secondary flows, electrokinetically induced and independent of the primary axial flow, are considered. A complete scaling theory is presented for the dependence of the $n$-th order moment of the outlet chromatogram as a function of the axial Peclet number, the secondary flow's pattern and intensity. [Preview Abstract] |
Monday, November 19, 2012 8:13AM - 8:26AM |
G6.00002: Geometry-Influenced Slippage on a Bubble Mattress in Microfluidics Elif Karatay, Sander Haase, Claas Willem Visser, Chao Sun, Detlef Lohse, Peichun Amy Tsai, Rob Lammertink Hydrodynamic slippage is advantageous for drag reduction and it has been achieved with hydrophobic microstructures. Such substrates can provide soft gas/liquid interfaces with shear-free boundary condition, thereby slippage. The establishment of stable soft-interfaces is crucial for the slippage; however, it has been a challenge. In this study, we design and fabricate hydrophobic microfluidic devices, allowing stable two-phase flow with controllable micro-bubbles at the boundary of the micro-channels. We experimentally and numerically exam the geometric effect of the micro-bubbles on the slippage. The effective slip length is measured for a wide range of protrusion angles, $\theta$, using micro-particle image velocimetry. Our measurements reveal a maximum effective slip length approximately at $\theta$ = 10 degrees. In addition, the experimental results show a decrease in slip length with increasing protrusion angles when $\theta > 10^\circ$. The transverse laminar flow over micro-bubbles has also been numerically studied with finite element methods. The experimental results show a good agreement with the numerical results quantitatively. [Preview Abstract] |
Monday, November 19, 2012 8:26AM - 8:39AM |
G6.00003: Mass transfer through laminar boundary layer in 2-d microchannels with nonuniform cross section: the effect of wall curvature Augusta Pedacchia, Alessandra Adrover We provide an analytical solution for the combined diffusive and convective 2-d mass transport from a surface film (of arbitrary shape at a given uniform concentration) to a pure solvent flowing in creeping flow conditions into a microchannel, delimited by a flat no-slip surface and by the releasing film itself. Such a problem arises in the study of swelling and dissolution of polimeric thin films under the action of a solvent tangential flow simulating the oral thin film dissolution for drug relase towards the buccal mucosa or oral cavity. We present a similarity solution for laminar forced convection mass (or heat) transfer that generalizes the classical boundary layer solution of the Graetz-Nusselt problem (valid for straight channels or pipes) to a solvent flowing in creeping flow conditions into a 2-d channel with cross-section continuously varying along the axial coordinate $x$. Close to the releasing boundary, parametrized by a curvilinear abscissa $s$, both tangential and normal velocity components play a role and their scaling behavior, as a function of wall distance $r$, should be taken into account in order to have an accurate description of the concentration profile in the boundary layer and of the dependence of the Sherwood number on the curvilinear abscissa $s$. [Preview Abstract] |
Monday, November 19, 2012 8:39AM - 8:52AM |
G6.00004: The Effective Slip Length of a Flow of a Fluid in Cassie State along a Structured Surface Clarissa Sch\"onecker, Tobias Baier, Steffen Hardt Microstructured surfaces, like for example superhydrophobic surfaces, can possess a significant apparent slip. This is usually due to a fluid entrapped in the roughness features of the surface. When a second, immiscible fluid flows over such a surface, the presence of the entrapped fluid may lead to a remarkable reduction of drag. So far, the effective slip length of such a flow was only known for a completely dissipation-free fluid being enclosed in the roughness features or for an entrapped fluid which presents a constant local slip length to the outer flow. While the first case completely neglects the viscosity of the enclosed fluid and the geometry of the roughness, the second case lacks the knowledge of the size of the local slip length, besides it being non-constant along a finite interface. We present an analytical expression for the flow field over a surface patterned with rectangular grooves, taking into account dissipation as well as the dimensions of the grooves. This leads to an expression for the effective slip length, which incorporates not only the influence of the viscosity but also provides a direct link between the geometry of the surface structure and the slip length. The results may be of great help for understanding and designing microstructured surfaces. [Preview Abstract] |
Monday, November 19, 2012 8:52AM - 9:05AM |
G6.00005: Studying Droplet dynamics by depth-averaged simulation Mathias Nagel, Fran\c{c}ois Gallaire Droplets in flat micro channels are deformable, avoid obstacles, interact with one another and undergo separation and coealescence. For the simulation of these micro fluidic two-phase flows we propose a depth-averaged model derived from the Stokes equation, the so called Brinkman equation. This equation is solved by the Boundary Element Method, which leads to a meshless numerical algorithm. A flow solver based on the depth-averaged model computes the dynamic evolution of the droplet in the 2D flow plane and retains the dominant effects in the thin/depth-averaged direction. In addition we developed a set of modified boundary conditions that account for 3D effects like film formation, droplet break-up or capillary action on cavities. We present results for droplet breakup in flow focussing devices and interaction between two droplets. In both cases the numerical results show a good agreement with experiments. The reduction from 3D to 2D by depth averaging and 2D to 1D by transformation of the equations to boundary integrals leads to a significant simplification. Yet the model reproduces essentially the physics to describe these confined two-phase flows. [Preview Abstract] |
Monday, November 19, 2012 9:05AM - 9:18AM |
G6.00006: Creeping three-dimensional flow around a immobile penny-shaped cylindrical droplet Francois Gallaire The flow in a shallow microchannel around a stationary flattened cylindrical viscous droplet at low Reynolds number is considered, using matched asymptotic expansions, with the aspect ratio as small parameter. At leading order, the flow is at rest in the center region of the droplet and it is governed by the two-dimensional Hele-Shaw potential flow equations in the exterior. However, close to the interface, a boundary layer has to be introduced in each fluid, in order to fulfill the kinematic and dynamic boundary conditions. As anticipated from simple scaling arguments, the boundary layer thicknesses scale with the channel height. The next order in the boundary-layer expansion shows the appearance of both radial and cross-plane velocity components. The results are compared to numerical solutions of the full 3-D Stokes equations. Marangoni driving along the interface can be included and yields surprising 3-D recirculation patterns. [Preview Abstract] |
Monday, November 19, 2012 9:18AM - 9:31AM |
G6.00007: Taylor-Aris dispersion of droplets (point concentrations) S{\O}ren Vedel, Emil Hovad, Henrik Bruus The effective axial diffusion of solute concentrations advected in channel flows known as Taylor-Aris dispersion is caused by the transverse fluid velocity variations present in any channel flow [1,2]. Using our previously developed general theory [3], we study the dispersion of droplets (point concentrations) in steady and unsteady flows. Since the droplet will eventually fill the entire channel, only the transient phase leading up to complete filling requires investigation. Irrespectable of whether the flow is time-dependent or steady, the transient dispersion exhibits a strong dependence on the initial release position, ``anomalous'' temporal scaling, and surprisingly also shortly exceeds the Taylor-Aris limit. We will show that all these effects, which are unlike the dispersion for transverse uniform initial distributions, are easily understood as being results of variations in the velocity gradient about the release position. This emphasizes that the transient dispersion is caused by the advective stretching of the solute powered by the lateral diffusion, and provides new insight to the underlying mechanisms of Taylor-Aris dispersion for any initial distribution.\\[4pt] [1] Taylor, \textit{Proc. Roy. Soc. Lond. A} \textbf{219}, 186 (1953)\\[0pt] [2] Aris, \textit{Proc. Roy. Soc. Lond. A} \textbf{235}, 67 (1956)\\[0pt] [3] Vedel and Bruus, \textit{J. Fluid Mech.} \textbf{691}, 95 (2012) [Preview Abstract] |
Monday, November 19, 2012 9:31AM - 9:44AM |
G6.00008: Does slippage within a superhydrophobic channel always reduce drag? Anna Lee, Myoung-Woon Moon, Ho-Young Kim It is commonly perceived that super-hydrophobizing channel walls can reduce drag on liquid flowing inside the channel. Here we point out that rough, hydrophobic channels which induce slippage of liquid flows can exert greater drag than hydrophilic channels exhibiting no slippage of liquid. While air pockets formed between liquid and hydrophobic solid structures allow the liquid to slip over themselves, they also reduce the cross-section of the liquid stream. We theoretically set up a criterion for surface structure that determines whether hydrophobizing or hydrophilicizing textured channel walls would be advantageous in reducing drag on liquid flows. On the basis of our theory, we evaluate the efficiency of previously reported superhydrophobic channels in reducing drag as compared to hydrophilic channels. We also experimentally corroborate our theory by measuring the flow rate of water within microchannels of different surface topography and wettability. [Preview Abstract] |
Monday, November 19, 2012 9:44AM - 9:57AM |
G6.00009: Criterion of wetting failure in a Couette flow Peng Gao Wetting failure occurs when the speed of the moving substrate exceeds a threshold, characterized by a critical Capillary number, above which the stationary contact line cannot be sustained. In most experimental and theoretical studies, it is found that the onset of wetting failure is accompanied by a geometry constraint that the apparent contact angle vanishes. In a Couette device, however, it is reported that wetting failure occurs at nonzero apparent contact angles. Using a lubrication theory, we investigate the contact dynamics in a Couette flow. The critical Capillary number is predicted. It is suggested that the criterion of vanishing apparent contact angle still holds if it is well defined. [Preview Abstract] |
Monday, November 19, 2012 9:57AM - 10:10AM |
G6.00010: Probing slip boundaries by bubble fingering Hsien-Hung Wei, Ying-Chih Liao Motivated by experimental efforts on determining slip length, we propose the Bretherton-type bubble fingering as an alternative strategy for probing slip effects. We find that at sufficiently high bubble speeds (but still in the small capillary number regime), the film thickness obeys classical Bretherton's 2/3 law. However, when the bubble speed is below some critical value where the film thickness is comparable to the slip length, a new quadratic law will emerge to govern the behavior of the film thickness below the slip length. The critical bubble speed is also found to be proportional to the 3/2 power of the slip length. In the analogous thermocapillary problem, a bubble in a slip channel can travel much faster than in a no-slip channel, at the speed proportional to the 5/3 power of the slip length. Effects of disjoining pressure and surfactant are also discussed and the results also show strong dependence on the slip length. [Preview Abstract] |
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