On the lateral migration of a slightly deformed bubble rising near a vertical plane wall

Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated. In particular, our focus is set on a situation with a short clearance $c$ between the bubble interface and the wall. Motivated by the fact that numerically and experimentally measured migration velocities are considerably higher than the velocity estimated by the available analytical solution using the Fax\'{e}n mirror image technique for $a/(a+c)\ll 1$ (here $a$ is the bubble radius), when the clearance parameter $\varepsilon(= c/a)$ is comparable to or smaller than unity, the numerical analysis based on the boundary-fitted finite-difference approach solving the Stokes equation is performed to complement the experiment. The migration velocity is found to be more affected by the high-order deformation modes with decreasing $\varepsilon$. The numerical simulations are compared with a theoretical migration velocity obtained from a lubrication study of a nearly spherical drop, which describes the role of the squeezing flow within the bubble-wall gap. The numerical and lubrication analyses consistently demonstrate that when $\varepsilon\leq 1$, the lubrication effect makes the migration velocity asymptotically $\mu V_{B1}^2/(25\varepsilon \gamma)$ (here, $V_{B1}$, $\mu$, and $\gamma$ denote the rising velocity, the dynamic viscosity of liquid, and the surface tension, respectively).Comment: 24 pages, 9 figures, J. Fluid Mech. (accepted

Lattice Boltzmann Methods for thermal flows: continuum limit and applications to compressible Rayleigh-Taylor systems

We compute the continuum thermo-hydrodynamical limit of a new formulation of lattice kinetic equations for thermal compressible flows, recently proposed in [Sbragaglia et al., J. Fluid Mech. 628 299 (2009)]. We show that the hydrodynamical manifold is given by the correct compressible Fourier- Navier-Stokes equations for a perfect fluid. We validate the numerical algorithm by means of exact results for transition to convection in Rayleigh-B\'enard compressible systems and against direct comparison with finite-difference schemes. The method is stable and reliable up to temperature jumps between top and bottom walls of the order of 50% the averaged bulk temperature. We use this method to study Rayleigh-Taylor instability for compressible stratified flows and we determine the growth of the mixing layer at changing Atwood numbers up to At ~ 0.4. We highlight the role played by the adiabatic gradient in stopping the mixing layer growth in presence of high stratification and we quantify the asymmetric growth rate for spikes and bubbles for two dimensional Rayleigh- Taylor systems with resolution up to Lx \times Lz = 1664 \times 4400 and with Rayleigh numbers up to Ra ~ 2 \times 10^10.Comment: 26 pages, 13 figure

Flow organization in non-Oberbeck-Boussinesq Rayleigh-Benard convection in water

Non-Oberbeck-Boussinesq (NOB) effects on the flow organization in two-dimensional Rayleigh-Benard turbulence are numerically analyzed. The working fluid is water. We focus on the temperature profiles, the center temperature, the Nusselt number, and on the analysis of the velocity field. Several velocity amplitudes (or Reynolds numbers) and several kinetic profiles are introduced and studied; these together describe the various features of the rather complex flow organization. The results are presented both as functions of the Rayleigh number Ra (with Ra up to 10^8) for fixed temperature difference (Delta) between top and bottom plates and as functions of Delta ("non-Oberbeck-Boussinesqness") for fixed Ra with Delta up to 60 K. All results are consistent with the available experimental NOB data for the center temperature Tc and the Nusselt number ratio Nu_{NOB}/Nu_{OB} (the label OB meaning that the Oberbeck-Boussinesq conditions are valid). Beyond Ra ~ 10^6 the flow consists of a large diagonal center convection roll and two smaller rolls in the upper and lower corners. In the NOB case the center convection roll is still characterized by only one velocity scale.Comment: 31 pages, 22 figure

Microbubbly drag reduction in Taylor-Couette flow in the wavy vortex regime

We investigate the effect of microbubbles on Taylor-Couette flow by means of direct numerical simulations. We employ an Eulerian-Lagrangian approach with a gas-fluid coupling based on the point-force approximation. Added mass, drag, lift, and gravity are taken into account in the modeling of the motion of the individual bubble. We find that very dilute suspensions of small non-deformable bubbles (volume void fraction below 1%, zero Weber number and bubble Reynolds number <10) induce a robust statistically steady drag reduction (up to 20%) in the so called wavy vortex flow regime (Re = 600-2500). The Reynolds number dependence of the normalized torque (the so-called Torque Reduction Ratio (TRR) which corresponds to the drag reduction) is consistent with a recent series of experimental measurements performed by Murai et al. (J. Phys. 14, 143 (2005)). Our analysis suggests that the physical mechanism for the torque reduction in this regime is due to the local axial forcing, induced by rising bubbles, that is able to break the highly dissipative Taylor wavy vortices in the system. We finally show that the lift force acting on the bubble is crucial in this process. When neglecting it, the bubbles preferentially accumulate near the inner cylinder and the bulk flow is less efficiently modified.Comment: 21 pages, 13 figures, extended and revised versio

Horizontal Structures of Velocity and Temperature Boundary Layers in 2D Numerical Turbulent Rayleigh-B\'{e}nard Convection

We investigate the structures of the near-plate velocity and temperature profiles at different horizontal positions along the conducting bottom (and top) plate of a Rayleigh-B\'{e}nard convection cell, using two-dimensional (2D) numerical data obtained at the Rayleigh number Ra=10^8 and the Prandtl number Pr=4.4 of an Oberbeck-Boussinesq flow with constant material parameters. The results show that most of the time, and for both velocity and temperature, the instantaneous profiles scaled by the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010) agree well with the classical Prandtl-Blasius laminar boundary layer (BL) profiles. Therefore, when averaging in the dynamical reference frames, which fluctuate with the respective instantaneous kinematic and thermal BL thicknesses, the obtained mean velocity and temperature profiles are also of Prandtl-Blasius type for nearly all horizontal positions. We further show that in certain situations the traditional definitions based on the time-averaged profiles can lead to unphysical BL thicknesses, while the dynamical method also in such cases can provide a well-defined BL thickness for both the kinematic and the thermal BLs.Comment: 16 pages, 16 figure

Nanometer-Resolved Collective Micromeniscus Oscillations through Optical Diffraction

We study the dynamics of periodic arrays of micrometer-sized liquid-gas menisci formed at superhydrophobic surfaces immersed into water. By measuring the intensity of optical diffraction peaks in real time we are able to resolve nanometer scale oscillations of the menisci with sub-microsecond time resolution. Upon driving the system with an ultrasound field at variable frequency we observe a pronounced resonance at a few hundred kHz, depending on the exact geometry. Modeling the system using the unsteady Stokes equation, we find that this low resonance frequency is caused by a collective mode of the acoustically coupled oscillating menisci.Comment: 4 pages, 5 figure

Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent Rayleigh-B\'{e}nard convection

The shape of velocity and temperature profiles near the horizontal conducting plates in turbulent Rayleigh-B\'{e}nard convection are studied numerically and experimentally over the Rayleigh number range $10^8\lesssim Ra\lesssim3\times10^{11}$ and the Prandtl number range $0.7\lesssim Pr\lesssim5.4$. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses.Comment: 10 pages, 6 figure

AJK2011-04001 A FULL EULERIAN FINITE DIFFERENCE METHOD FOR HYPERELASTIC PARTICLES IN FLUID FLOWS

ABSTRACT A full Eulerian finite difference method has been developed for solving a dynamic interaction problem between Newtonian fluid and hyperelastic material. It facilitates to simulate certain classes of problems, such that an initial and neutral configuration of a multi-component geometry converted from voxel-based data is provided on a fixed Cartesian mesh. A solid volume fraction, which has been widely used for multiphase flow simulations, is applied to describing the multicomponent geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for incompressible hyperelastic materials. The present Eulerian approach is confirmed to well reproduce the material deformation in the lid-driven flow and the particle-particle interaction in the Couette flow computed by means of the finite element method. It is applied to a Poiseuille flow containing biconcave neo-Hookean particles. The deformation, the relative position and orientation of a pair of particles are strongly dependent upon the initial configuration. The increase in the apparent viscosity is dependent upon the developed arrangement of the particles. INTRODUCTION Numerical simulations of Fluid-Structure Interaction (FSI) problems would make it possible to predict the effect of a medical treatment and help one decide the treatment strategy in clinical practice. In particular, a blood flow simulation is expected to contribute to assisting the surgical planning of a cardiovascular disease and a brain aneurysm. Recently, there are growing expectations for its applications along with a progress in imaging and computational technologies. It is also expected to contribute to the field of life science, such as in the understanding of the very essence of life and the demonstration of pathological mechanisms. It is of great importance to develop numerical techniques suitable for the characteristics of body tissues, which are flexible and complicated in shape, when attempting to rationalize and to generalize the fluidstructure coupled analyses. The expectations include the further understandings of the micro/mesoscopic behavior of the flexibly deformable Red Blood Cells (RBCs) in plasma useful for evaluating the macroscopic blood rheology, and the thrombosis formation as aggregation of platelets, of which th

Flow reversals in thermally driven turbulence

We analyze the reversals of the large scale flow in Rayleigh-B\'enard convection both through particle image velocimetry flow visualization and direct numerical simulations (DNS) of the underlying Boussinesq equations in a (quasi) two-dimensional, rectangular geometry of aspect ratio 1. For medium Prandtl number there is a diagonal large scale convection roll and two smaller secondary rolls in the two remaining corners diagonally opposing each other. These corner flow rolls play a crucial role for the large scale wind reversal: They grow in kinetic energy and thus also in size thanks to plume detachments from the boundary layers up to the time that they take over the main, large scale diagonal flow, thus leading to reversal. Based on this mechanism we identify a typical time scale for the reversals. We map out the Rayleigh number vs Prandtl number phase space and find that the occurrence of reversals very sensitively depends on these parameters.Comment: 4 pages, 4 figure