Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session KR: Suspensions I |
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Chair: Bruno Eckhardt, Philipps Universitaet Marburg Room: Salt Palace Convention Center 251 F |
Tuesday, November 20, 2007 8:00AM - 8:13AM |
KR.00001: An anisotropic-fluid model for inhomogeneous Stokesian suspensions Joe Goddard A constitutive model is proposed for a suspension of rigid spheres with spatially non-uniform strain rate \textbf{E} and particle concentration $\phi $. As in [1], the model involves a 4$^{th}$ rank viscosity tensor depending on $\phi $ and a 2$^{nd}$ rank structure tensor \textbf{A} determined by a kinematic evolution equations. The particle flux \textbf{j }is a linear function of the spatial gradients in $\phi $, \textbf{E}, {\&} \textbf{A }. In contrast to existing models [2,3], the constitutive equations exhibits Stokesian linearity in \textbf{E}, and all nonlinear suspension-dynamics effects are represented by \textbf{A} and its evolution. An expansion up to third order in \textbf{A} is given, and illustrative calculations are made for oscillatory simple shear based on parameters determined as in [1]. Desirably, the model offers a frame-indifferent description of the effects of streamline curvature on particle flux; and it admits transiently negative particle diffusivities following shear reversal, indicating dominance of Stokesian reversibility over shear-induced memory loss. The main drawback, is the plethora of scalar parameters, and possible simplifications inspired by previous models are discussed briefly. \newline [1] J.~D. Goddard, \textit{J. Fluid. Mech.}, 568:1--17, 2006. \newline [2] G.~P. Krishnan, et al., \textit{J. Fluid Mech.}, 321:371--93, 1996. \newline [3] R.~J. Phillips, et al., \textit{Phys. Fluids A}, 4(1): 30--40, 1992. [Preview Abstract] |
Tuesday, November 20, 2007 8:13AM - 8:26AM |
KR.00002: Formation and Stability of Band Patterns in a Rotating Suspension-Filled Cylinder Gabriel Seiden, Marius Ungarish, Steve Lipson The phenomenon of segregation and pattern formation in the complex system of a rotating horizontal cylinder completely filled with a dilute suspension of non-Brownian particles has been the focus of several recent investigations. Here we present a general dimensionless analysis of the phenomenon, which reveals the importance of the different dimensionless parameters involved, and a detailed account of the mechanism of segregation and formation of axial bands for the case of low viscosity fluids. The question of stability of the band patterns is also addressed. [Preview Abstract] |
Tuesday, November 20, 2007 8:26AM - 8:39AM |
KR.00003: Velocity fluctuations from randomly moving particles at low Re Bruno Eckhardt, Juergen Buehrle We discuss the solution of the time-dependent Stokes equation for particles undergoing random changes in their velocity. Three regimes in the spatial variation of the velocity field and in the second moment of the velocity fluctuations can be distinguished. With increasing distance from the particles, the velocity fluctuations drop off first like $1/r^2$, then like $1/r^4$ and finally like $1/r^6$ for the largest distances. The results will be related to observations on velocity fluctuations in suspensions. [Preview Abstract] |
Tuesday, November 20, 2007 8:39AM - 8:52AM |
KR.00004: Influence of Short-Range Interactions on Wall-Slip in Microgel Pastes Jyoti Seth, Michel Cloitre, Roger Bonnecaze Microgel pastes are complex fluids that behave like elastic solids at rest but flow like viscous fluids when sheared with a stress greater than the yield value. The nature of the yielding transition depends on whether the shearing surface is rough or smooth. In the former, the paste yields at the bulk yield stress $\sigma _{y}$ and exhibits a uniform bulk flow at higher stresses. But when sheared with a smooth wall the paste continues to move and eventually stops at a much lower stress $\sigma _{s}$. The slip mechanism at lower stresses and the physical origin of $\sigma _{s}$ remain two important unsolved issues. In this talk we analyze how the nature of the shearing surface influences wall slip. We present experiments performed with different shearing surfaces and varying paste properties. Two distinct slip behaviors are identified: depending on whether the interaction between the microgel particles and the wall is attractive or repulsive, wall slip can be either suppressed or promoted. We also propose a slip model, which is based on elastohydrodynamic lubrication with possible adhesion or repulsion due to short-range interactions between the microgel and the shearing surface. The onset of slip is determined from a balance between the interaction forces and the elastohydrodynamic lift generated by lubrication. The predicted relationships agree well with the experimental results. [Preview Abstract] |
Tuesday, November 20, 2007 8:52AM - 9:05AM |
KR.00005: Electrokinetic Particle Aggregation and Flow Instabilities in Non-Dilute Colloidal Suspensions Guru Navaneetham, Jonathan Posner An experimental investigation of electrokinetic particle aggregation and flow instabilities of non-dilute colloidal suspensions in microfabricated channels is presented. The addition of charged colloidal particles can alter the solution's conductivity, permittivity as well as the average particle electrophoretic mobility. In this work, a colloid volume fraction gradient is achieved at the intersection of a Y-shaped PDMS microchannel. The solution conductivity and the particle mobility as a function of the particle (500 nm polystyrene) volume fraction are presented. The critical conditions required for particle aggregation and flow instability are given along with a scaling analysis which shows that the flow becomes unstable at a critical electric Rayleigh number for a wide range of applied electric fields and colloid volume fractions. Electrokinetic particle aggregation and instabilities of non-dilute colloidal suspensions may be important for applications such as the electrophoretic deposition of particles to form micropatterned colloidal assemblies, electrorheological devices, and on-chip, electrokinetic manipulation of colloids. [Preview Abstract] |
Tuesday, November 20, 2007 9:05AM - 9:18AM |
KR.00006: Shear Stress Measurements of Non-Spherical Particles in High Shear Rate Flows Erin Koos, Melany L. Hunt, Christopher E. Brennen \noindent The behavior of liquid-solid flows varies greatly depending on fluid viscosity, particle and liquid inertia, and collisions and near-collisions between particles. An initial investigation by Bagnold found two different flow regimes [1]. In an examination of that work, Hunt \emph{et al.} found that Bagnold's experiments were marred by secondary flows in the fluid [2]. The current experiment addresses this rheology further. Shear stress measurements used a coaxial rheometer with a height to gap ratio ($h/b$) of 11.7 and gap to outer radius ratio ($b/r_o$) of 0.166 that was specially designed to minimize effects of secondary flows. Experiments were performed for a range of Reynolds numbers, solid fractions and ratio of particle to fluid densities. With neutrally buoyant particles, the dimensional shear stress exhibits a linear dependence on Reynolds Number: the slope is monotonic but a non-linear function of the solid fraction. Though non-neutrally buoyant particles exhibit a similar linear dependence at higher Reynolds numbers, at lower values the shear stress exhibits a non-linear behavior in which the stress increases with decreasing Reynolds number due to particle settling. \\ \noindent [1] R.A. Bagnold, \emph{Proc. R. Soc. Lond. Ser. A,} \textbf{225}, p.49 (1954). \\ \noindent [2] M.L. Hunt etc., \emph{J. Fluid Mech.,} \textbf{452}, p.1 (2002). [Preview Abstract] |
Tuesday, November 20, 2007 9:18AM - 9:31AM |
KR.00007: Breakdown of local constitutive relations in flows of glassy systems. Annie Colin, Julie Goyon, Guillaume Ovarlez, Armand Ajdari, Lyderic Bocquet Using Particule imaging velocimetry or velocity controlled magnetic resonance imaging, we measure the velocities profiles of a monodisperse emulsion, in various type of flows (shear flow, poiseuille planar flow) and in various type of confinement (wide gap Couette cell or very narrow channel).The velocity profiles cannot be described using a constitutive equation linking the local shear rate to the local shear stress. These experiments point out strong non local effects re- lated to the microscopic mechanisms (T1 events and avalanche process) in charge of the flow. We establish how these cooperativity effects manifest in the rheological behavior and propose a theoretical framework allowing to reproduce all the experimental results. The size of the dynamically correlated regions (typically one to five droplets size) are shown to grow with the concentration and elasticity of the emulsion. [Preview Abstract] |
Tuesday, November 20, 2007 9:31AM - 9:44AM |
KR.00008: Inertial effects on the orientation of fibres in a suspension flow close to a solid surface Allan Carlsson, Fredrik Lundell, L. Daniel S\"oderberg The orientation of fibres suspended in a viscous fluid, flowing over a solid wall, has been studied experimentally. A CCD-camera was mounted underneath the transparent wall, in order to study the fibre orientation in planes parallel to the wall. Experiments were performed on two suspensions with different fibre lengths. In both suspensions the density difference between the fibres and the liquid caused the fibres to slowly sediment, resulting in an accumulation of fibres near the wall. For the shorter fibres there was a peak in the fibre concentration at the wall, while for the longer fibres most fibres were detected at distances from the wall larger than half a fibre length. Another difference was seen in the fibre orientation near the wall. At distances from the wall larger than one fibre length the fibres were oriented in the flow direction in both suspensions. Closer to the wall shorter fibres adapted an orientation close to perpendicular to the flow, a shift in orientation not seen on the longer fibres. A possible explanation for the observed differences could be inertial effects, which is discussed further. [Preview Abstract] |
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