Three-dimensional viscous steady streaming in a rectangular channel past a cylinder

We consider viscous steady streaming induced by oscillatory flow past a cylinder between two plates, where the cylinder's axis is normal to the plates. While this phenomenon was first studied in the 1930s, it has received renewed interest recently for possible applications in particle manipulations and non-Newtonian flows. The flow is driven at the ends of the channel by the boundary condition which is a series solution of the oscillating flow problem in a rectangular channel in the absence of a cylinder. We use a combination of Fourier series and an asymptotic expansion to study the confinement effects for steady-streaming. The Fourier series in time naturally simplifies to a finite series. In contrast, it is necessary to truncate the Fourier series in z, which is in the direction of the axis of the cylinder, to solve numerically. The successive equations for the Fourier coefficients resulting from the asymptotic expansion are then solved numerically using finite element methods. We use our model to evaluate how steady streaming depends on the domain width and distance from the cylinder to the outer walls, including the possible breaking of the four-fold symmetry due to the domain shape. We utilize the tangential steady-streaming velocity along the radial chord at an angle of pi/4 to analyze our solutions over an extensive range of oscillating frequencies and multiple levels in the z-direction. Finally, higher-order solutions are computed and an asymptotic correction to steady streaming is included.Comment: 25 pages, 14 figure

Two-bead microrheology: Modeling protocols

Microbead rheology maps the fluctuations of beads immersed in soft matter to viscoelastic properties of the surrounding medium. In this paper, we present modeling extensions of the seminal results of Mason & Weitz (1995, Phys. Rev. Lett. 74) for a single bead and of Crocker et al. (2000, Phys. Rev. Lett. 85) and Levine & Lubensky (2000, Phys. Rev. Lett. 85) for two beads. We formulate the linear response analysis for two beads so that the model equations retain: the local diffusive properties of each bead (through the memory kernel of the shell or depletion zone surrounding each bead), and the nonlocal dynamic moduli of the medium separating the beads (through the memory kernel that transmits fluctuations of one bead to the other). We then derive a 3×3 invertible system of equations relating: an isolated bead’s auto-correlations, the auto- and cross-correlations of two coupled beads; and, the shell radius surrounding each bead, the memory kernels of the shell and of the medium between the two beads

A First step towards simulations of tracer motion in a thermally fluctuating viscoelastic fluid.

Many biological fluids, like mucus and cytoplasm, have prominent viscoelastic properties, which lead to the subdiffusive behavior of immersed particles. We propose a viscoelastic generalization of the Landau-Lifschitz Navier-Stokes fluid model for particles that are passively advected by such a medium and develop a simulation techniques based on the theory of stationary Gaussian processes. In contrast to the stochastic immersed boundary method for viscous fluids, which relies on step-by-step simulation techniques exploiting the Markov property, our method is based on the numerical evaluation of the covariance associated with individual fluid modes. The numerical method is spectral, meshless and uses results from the simulations of Generalized Langevin Equations.The implementation presents many practical problems, mostly stemming from the fact that the physical regime of interest corresponds to a situation where the memory kernel has a very slow (power law) decay.Non UBCUnreviewedAuthor affiliation: University of UtahResearche

Small Scale Stochastic Dynamics For Particle Image Velocimetry Applications

Fluid velocities and Brownian effects at nanoscales in the near-wall region of microchannels can be experimentally measured in an image plane parallel to the wall using, for example, evanescent wave illumination technique combined with particle image velocimetry [R. Sadr extit{et al.}, J. Fluid. Mech. 506, 357-367 (2004)]. The depth of field of this technique being difficult to modify, reconstruction of the out-of-plane dependence of the in-plane velocity profile remains extremely challenging. Tracer particles are not only carried by the flow, but they undergo random fluctuation imposed by the proximity of the wall. We study such a system under a particle based stochastic approach (Langevin) and a probabilistic approach (Fokker-Planck). The Langevin description leads to a coupled system of stochastic differential equations. Because the simulated data will be used to test a statistical hypothesis, we pay particular attention to the strong order of convergence of the scheme developing an appropriate Milstein scheme of strong order of convergence 1. Based on the probability density function of mean in-plane displacements, a statistical solution to the problem of the reconstruction of the out-of-plane dependence of the velocity profile is proposed. We developed a maximum likelihood algorithm which determines the most likely values for the velocity profile based on simulated perfect particle position, simulated perfect mean displacements and simulated observed mean displacements. Effects of Brownian motion on the approximation of the mean displacements are briefly discussed. A matched particle is a particle that starts and ends in the same image window after a measurement time. AS soon as the computation and observation domain are not the same, the distribution of the out-of-plane distances sampled by matched particles during the measurement time is not uniform. The combination of a forward and a backward solution of the one dimensional Fokker-Planck equation is used to determine this probability density function. The non-uniformity of the resulting distribution is believed to induce a bias in the determination of slip length and is quantified for relevant experimental parameters.Ph.D.Committee Chair: Peter J. Mucha; Committee Member: Evans M. Harrell; Committee Member: Guillormo Goldsztein; Committee Member: Haomin Zhou; Committee Member: Minami Yod