Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session FC: Microfluidics: Slip Flow |
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Chair: Seth Lichter, Northwestern University Room: Hilton Chicago Grand Ballroom |
Monday, November 21, 2005 8:00AM - 8:13AM |
FC.00001: Modification of no-slip boundary condition by superhydrophobic wall patterning Richard Truesdell, Andrea Mammoli, Peter Vorobieff, Frank van Swol There has been a recent wave of interest in challenging the idea of a ``no-slip'' boundary condition for fluids at a solid surface. We study fluid flow in the vicinity of textured and superhydrophobically coated surfaces. Grooved PDMS (polydimethylsiloxane) surfaces with groove spacing 25$\mu $m are coated with a thin aerogel film creating a superhydrophobic surface. These surfaces are attached to the inner cylinder of a Couette flow apparatus. The apparent viscosity of the fluid situated between the inner and outer rotating cylinder is measured with a viscometer at different strain rates. Apparent reduction in the viscosity would indicate change in the macroscopic boundary condition. We present evidence that, while the actual slip length remains very small, the grooves reduce the fluid-surface contact area, leading to appreciable drag reduction that can be interpreted as ``effective slip.'' The flow physics are further elucidated by micro-PIV imaging of the flow in the immediate vicinity of the textured surface. [Preview Abstract] |
Monday, November 21, 2005 8:13AM - 8:26AM |
FC.00002: Source of Shear Dependent Slip at Liquid/Solid Interfaces Nikolai Priezjev, Sandra Troian Slippage at liquid/solid interfaces can strongly influence transport behavior in micro- and nanoscale systems. Previous molecular dynamics (MD) studies of simple and polymeric fluids subject to planar shear at small Reynolds number have shown that the slip length increases as a power law in the shear rate for moderate to high values. The corresponding boundary condition provides a new generalization of the Navier slip law. In this talk, we examine what physical mechanism is responsible for the shear rate exponent by focusing on the collision events between the fluid particles in the first layer and the adjacent wall particles comprising a crystalline surface. By examining the interfacial frictional force as a function of the fluid sliding velocity, we recover similar behavior as inherent in the generalized slip condition and determine that the dominant frictional response stems from the repulsive part of the Lennard-Jones interaction potential. A reduced kinetic model describing the scattering of a single molecule with a given slip velocity along a crystalline surface helps explain the saturation in the frictional force at large sliding velocities. These results elucidate how different is the slip behavior at liquid/solid interfaces from that observed in rarefied gases. [Preview Abstract] |
Monday, November 21, 2005 8:26AM - 8:39AM |
FC.00003: Slip at the Liquid/Solid Interface: A Dynamical Theory Alexander Roxin, Yaling Liu, Wing-Kam Liu, Seth Lichter Despite numerous experiments and computational studies of slip at the liquid/solid interface, a theory of how, why and when slip occurs has remained elusive. Statistical mechanical theories treat only the limit of small shear rates and determine only average quantities and cannot predict how slip occurs. We develop a theory of the dynamics of liquid molecules adjacent to a solid. Results from the theory agree with molecular-dynamics simulations. The theory shows that slip occurs through several different mechanisms. Individual liquid molecules can hop along the solid surface or the entire layer can slide as a single flexible sheet. Which mechanism occurs depends on the shear rate and the liquid and solid parameters. The theory shows how these parameters can be adjusted in order to enhance or curtail slip. In particular, we show how the surface properties can be tuned to yield slip, even for strongly wetting surfaces. [Preview Abstract] |
Monday, November 21, 2005 8:39AM - 8:52AM |
FC.00004: Slip Dynamics at the Liquid/Solid Interface in MD Simulations Yaling Liu, Seth Lichter, Wing-Kam Liu, Alexander Roxin Determining liquid flows through nanoscale devices requires the proper accounting for slip along the solid boundaries. Using MD simulation, we show how the amount of slip depends on the material properties of the liquid and solid including their energy and size. In agreement with earlier studies, slip length undergoes a drastic increase near a critical value. We analyze the trajectories of individual liquid molecules as they move over the solid surface to reveal the dynamics underlying slip. We observe that below a critical value, localized patches of liquid molecules propagate along the surface: slip is due to the accumulated effect of many such patches. Above a critical value, the entire first layer of liquid slips over the solid. It is found that the liquid structure in the first liquid layer adjacent to the solid plays a crucial role in determining the dynamics. A theory which describes the dynamics of this layer reproduces the main observations. Unlike continuum flows, nanoscale flow properties can be adjusted by modifying the crystal structure of the solid and the relative size of the liquid molecules. [Preview Abstract] |
Monday, November 21, 2005 8:52AM - 9:05AM |
FC.00005: Liquid-Gas Mixtures in Contact with Walls: Molecular Simulations Stephan Markus Dammer, Detlef Lohse We perform molecular dynamics simulations of liquid-gas mixtures in contact to solid walls. We present results concerning Lennard-Jones systems composed of three particle species, namely liquid, foreign gas, and wall particles, which are frozen on a lattice: (i) Close to the wall we observe a layering of the fluid which becomes more pronounced for increasingly hydrophilic walls. (ii) Close to smooth hydrophobic walls we find a two orders of magnitude increase in the number density of gas, which will favor bubble nucleation. (iii) To characterize the walls, we determined the contact angle by simulations of droplets and compare the result to Laplace's estimate of surface energies. [Preview Abstract] |
Monday, November 21, 2005 9:05AM - 9:18AM |
FC.00006: Direct Measurement of Liquid Slip Velocities Using Total Internal Reflection Velocimetry Peter Huang, Jeff Guasto, Kenneth Breuer The possible existence of slip at a liquid/solid interface is experimentally investigated by measuring velocities of suspended tracer particles in a shear flow. Sub-micron fluorescent particles are imaged within 200 nm of a smooth glass surface using Total Internal Reflection Velocimetry. To accurately infer the slip velocity, imaged particles are sorted into different shear layers according to their intensities and a distance-to-surface calibration. Motions of particles in same shear plane are statistically analyzed to determine slip velocities and slip lengths. For an aqueous suspension flowing over a hydrophilic surface, minimal slip is observed with a slight dependence on shear rate ($l^{*}$ = 16 nm at 2000 $s^{-1} $). A larger shear-rate dependent boundary slip is observed over a hydrophobic surface ($l^{*}$ = 72 nm at 2000 $s^{-1}$). This result, in agreement with many recent experiments, rejects some published reports that shear-induced liquid slip length can be as high as one micrometer. Details of the experimental technique, analysis and sources of error, as well as results for non-aqueous liquid slip measurement, are also reported. [Preview Abstract] |
Monday, November 21, 2005 9:18AM - 9:31AM |
FC.00007: Bias in Near-Wall Microscale Velocimetry due to Hindered Brownian Diffusion Reza Sadr, Haifeng Li, Minami Yoda Brownian fluctuations of colloidal tracers used in microscale velocimetry are isotropic in the bulk. In the near-wall region, however, such fluctuations are hindered, and the tracer has a greater probability of diffusing away from (\textit{vs.} towards) the wall. These anisotropic fluctuations can lead to overestimation of near-wall velocities measured using particle-based velocimetry. Hindered Brownian dynamics simulations were used to quantify this error as a function of tracer size, time interval within the image pair, spatial resolution normal to the wall, and fluid properties. The flow velocity based on particle displacements is consistently higher than its actual value for time intervals exceeding a Brownian diffusion timescale. The simulation data were used to generate a probability density function of the distances normal to the wall $z$ sampled by the tracers. A method for rescaling near-wall velocity data using a Gaussian approximation of this PDF is presented, and the implications of this type of bias error on near-wall parameters such as slip length are briefly discussed. [Preview Abstract] |
Monday, November 21, 2005 9:31AM - 9:44AM |
FC.00008: Lattice Boltzmann Simulations of Slip Flow in Microchannels at High Knudsen Numbers Ramesh Agarwal In this paper, we consider the application of Lattice Boltzmann Method (LBM) to flow in micro-fluidic devices, which requires special consideration because of the variation in Knudsen number as the fluid moves along these devices driven by pressure or acceleration. We consider the pressure driven gaseous slip flow with small to moderate rarefaction through a long micro-channel and formulate the problem in LB framework. The accuracy of the LB solution is checked by comparing it with analytical solution with slip boundary condition and the numerical solutions of Navier-Stokes and augmented Burnett equations without and with slip boundary condition. It is shown that the treatment of slip boundary condition has a significant influence on the solution at moderate to high Knudsen numbers. We also consider the influence of magnetic field on the same flow assuming that the gas is conducting. The numerical solution of magnetohydrodynamic (MHD) flows using the LBM, in particular Lattice BGK (LBGK) method, requires the construction of an appropriate particle distribution function which recovers both the continuum MHD flow equations and magnetic induction equations in low Mach number limit. For the test cases considered, the LBGK results agree well with the analytical solutions for velocity and pressure field. As physically expected, the higher value of the magnetic field (higher Hartmann number) flattens the velocity profile in the channel. [Preview Abstract] |
Monday, November 21, 2005 9:44AM - 9:57AM |
FC.00009: The Effects of Geometry and Wetting on Fluid Flow in Microchannels with Superhydrophobic Walls: A Numerical Study Todd Salamon, Wonsuck Lee, Tom Krupenkin, Marc Hodes, Paul Kolodner, Andrew Salinger, Ryan Enright Superhydrophobic surfaces combine roughness and chemical treatment to increase the hydrophobicity of a surface. The enhanced drag reduction (Ou \textit{et al., }2004) exhibited by these surfaces suggests that they may provide an enabling technology for reducing microchannel flow resistance. In this work, a finite element analysis is used to study the fully-developed, three-dimensional laminar flow of a Newtonian fluid in a microchannel with superhydrophobic walls consisting of an array of square posts with uniform post-to-post pitch. The effects of post size, pitch, channel height and wetting on the flow field and corresponding flow enhancement are presented. Examples illustrating insight gained from the simulations include: i) for small values of the post size and pitch relative to the channel height, the axial velocity field away from the superhydrophobic channel walls is well described by the analogous two-dimensional channel flow with Navier's slip law applying at the channel wall and an apparent slip coefficient determined from the calculated flow enhancement; and ii) wetting of the fluid into the post structure dramatically decreases the calculated flow enhancement. [Preview Abstract] |
Monday, November 21, 2005 9:57AM - 10:10AM |
FC.00010: Slip at the liquid-liquid interface Joel Koplik, Jayanth R. Banavar The conventional boundary conditions at the interface between two flowing liquids include the continuity of the velocity field. As in the liquid-solid case, continuity of the tangential component of velocity is not obvious, and we have undertaken molecular dynamics simulations of the Couette and Poiseuille flows of two-layered liquid systems with various molecular structures and interactions. In all cases, the average velocity is found to vary continuously across the interface. However, when the total liquid density in the interfacial region drops significantly compared to the bulk values, the tangential velocity varies very rapidly there, and would appear discontinuous at a coarse or continuum resolution. The value of this apparent slip varies linearly with the shear stress at the interface, with a constant of proportionality depending on the nature of both liquids but not the flow configuration. Thus, a version of the Navier boundary condition appears to apply in this situation. [Preview Abstract] |
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