摘要:

A new three-dimensional boundary-integral algorithm for deformable drops moving in a viscous medium at low Reynolds numbers is developed, which overcomes some familiar difficulties with boundary-integral calculations. The algorithm is used to simulate different modes of interaction between drops or bubbles, primarily for buoyancy-driven motion. The present iterative method for mean curvature calculation is found to be more robust and accurate than contour integration schemes. A novel iterative strategy based on combining biconjugate gradient and simple iterations overcomes the poor convergence of “successive substitutions” for drops in very close approach with extreme viscosity ratio. A substantially new variational method of global mesh stabilization solves the problem of mesh degradation with advantageous, soft stability constraints. A curvatureless boundary-integral formulation is also derived and shown to provide, in principle, a more accurate description of the drop breakup than the conventional formulation. The efficiency of these techniques is demonstrated by numerical examples for two drops in gravity-induced motion with high surface resolutions. The present code successfully simulates mutual approach of slightly deformable drops to extremely small separations, as well as their rotation when in “apparent contact,” thus bridging the gap between finite deformation calculations and a recent asymptotic theory for small capillary numbers. Also provided is a 3D simulation of the experimental phenomenon of enhanced bubble coalescence, discovered by Manga and Stone [J. Fluid Mech.256, 647 (1993);300, 231 (1995)]. For drops of viscosity comparable to that of the surrounding fluid, it is shown in contrast that breakup is a typical result of hydrodynamic interaction in gravity-induced motion for large and even moderate capillary numbers. The code is readily applicable to any type of an ambient flow and may be adapted to more than two drops. © .1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869275

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Oscillations of supported liquid drops are the subject of wide scientific interest, with applications in areas as diverse as liquid–liquid extraction, synthesis of ceramic powders, growing of pure crystals in low gravity, and measurement of dynamic surface tension. In this study, axisymmetric forced oscillations of arbitrary amplitude of a viscous liquid drop of fixed volume which is pendant from or sessile on a rod with a fixed contact line and surrounded by an inviscid ambient gas are induced by moving the rod in the vertical direction sinusoidally in time. This nonlinear free boundary problem is solved by a method of lines using Galerkin/finite element analysis for discretization in space and an implicit, adaptive finite difference technique for discretization in time. The variation of the drop response over a wide range of the governing parameters (Reynolds number Re, gravitational Bond numberG,volume, and forcing frequency and amplitude) is analyzed. The results show that as the forcing frequency is increased, a sequence of oscillation modes is observed, each with its own resonance frequency&ohgr;rn,n=1,2,&ellip;,at which drop response amplitude reaches a local maximum. While resonance frequencies depend strongly on drop size and on forcing amplitude, the effect of Reynolds number on&ohgr;rnis large when Re is small and diminishes when Re is large, in accord with observations for free oscillations. At high Re, a sharp increase in drop deformation can occur for drops forced to oscillate in the vicinity of their resonance frequencies, indicating the incipience of hysteresis. The maximum observed drop deformations increase with Re,G,and forcing amplitude, while the value of the drop deformation as a function of drop size is determined by a balance between the magnitude of the viscous shear stress imposed on the drop liquid by the solid rod relative to the capillary pressure due to surface tension acting on the fluid interface. The effects of viscous dissipation are also seen in the damping of various oscillation modesandin the creation, evolution in time, and disappearance of zones of fluid recirculation within the drop. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869276

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The problem of determining the Nusselt numberN,the nondimensional rate of heat or mass transfer, from an array of cylindrical particles to the surrounding fluid is examined in the limit of small Reynolds numberReand large Peclet numberPe.Nin this limit can be determined from the details of flow in the immediate vicinity of the particles. These are determined accurately using a method of multipole expansions for both ordered and random arrays of cylinders. The results forN/Pe1/3are presented for the complete range of the area fraction of cylinders. The results of numerical simulations for random arrays are compared with those predicted using effective-medium approximations, and a good agreement between the two is found. A simple formula is given for relating the Nusselt number and the Darcy permeability of the arrays. Although the formula is obtained by fitting the results of numerical simulations for arrays of cylindrical particles, it is shown to yield a surprisingly accurate relationship between the two even for the arrays of spherical particles for which several known results exist in the literature suggesting thereby that this relationship may be relatively insensitive to the shape of the particles. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869277

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The rheological behavior of rapidly sheared bubble suspensions is examined through numerical simulations and kinetic theory. The limiting case of spherical bubbles at large Reynolds numberReand small Weber numberWeis examined in detail. Here,Re=&rgr;&ggr;a2/&mgr;andWe=&rgr;&ggr;2a3/s,abeing the bubble radius,&ggr;the imposed shear,sthe interfacial tension, and&mgr;and&rgr;, respectively, the viscosity and density of the liquid. The bubbles are assumed to undergo elastic bounces when they come into contact; coalescence can be prevented in practice by addition of salt or surface-active impurities. The numerical simulations account for the interactions among bubbles which are assumed to be dominated by the potential flow of the liquid caused by the motion of the bubbles and the shear-induced collision of the bubbles. A kinetic theory based on Grad’s moment method is used to predict the distribution function for the bubble velocities and the stress in the suspension. The hydrodynamic interactions are incorporated in this theory only through their influence on the virtual mass and viscous dissipation in the suspension. It is shown that this theory provides reasonable predictions for the bubble-phase pressure and viscosity determined from simulations including the detailed potential flow interactions. A striking result of this study is that the variance of the bubble velocity can become large compared with(&ggr;a)2in the limit of large Reynolds number. This implies that the disperse-phase pressure and viscosity associated with the fluctuating motion of the bubbles is quite significant. To determine whether this prediction is reasonable even in the presence of nonlinear drag forces induced by bubble deformation, we perform simulations in which the bubbles are subject to an empirical drag law and show that the bubble velocity variance can be as large as15&ggr;2a2. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869481

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Hydraulic permeabilities of polymeric membranes and gels are of interest both for calculating fluid flow rates and hindered diffusion coefficients. We have calculated hydraulic permeabilities for monomodal and bimodal, periodic and random fibrous media. Hydrodynamic interactions between fibers are calculated by applying a numerical version of slender body theory to a collection of fibers in a cubic cell many Brinkman screening lengths in dimension. Results for random media are obtained by averaging over many ensembles of fibers. To account for the surrounding medium, the line distribution of point forces along the fiber axes are replicated throughout space by using the Ewald summation technique. Results for periodic media agree with previous theoretical results up to a fiber volume fraction of 50&percent; for parallel flow and 40&percent; for transverse flow. Hydraulic permeabilities calculated for three-dimensional, disordered media with monomodal and bimodal distributions of fiber radius are compared with existing theories and with experimentally determined hydraulic permeabilities for a range of fiber volume fractions. Specific calculations are performed for agarose and collagen/proteoglycan gel systems, which are well described as bimodal fibrous media and are relevant to bioseparations and physiological systems, respectively. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869278

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

In this paper we address the shape of a low-viscosity fluid interface near the breaking point. Experiments show that the shape varies dramatically as a function of fluid viscosity. At low viscosities, the interface develops a region with an extremely sharp slope, with the steepness of the slope diverging with vanishing viscosity. Numerical simulations demonstrate that this tip forms as a result of a convective instability in the fluid; in the absence of viscosity this instability results in a finite time singularity of the interface far before rupture (in which the interfacial curvature diverges). The dynamics before the instability roughly follow the scaling laws consistent with predictions based on dimensional analysis, though these scaling laws are violated at the instability. Since the dynamics after rupture is completely determined by the shape at the breaking point, the time dependences of recoiling do not follow a simple scaling law. In the process of demonstrating these results, we present detailed comparisons between numerical simulations and experimental drop shapes with excellent agreement. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869279

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Pressure (density) and velocity boundary conditions are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and a new method to specify these conditions is proposed. These conditions are constructed in consistency with the wall boundary condition, based on the idea of bounceback of the non-equilibrium distribution. When these conditions are used together with the incompressible LBGK model [J. Stat. Phys.81, 35 (1995)] the simulation results recover the analytical solution of the plane Poiseuille flow driven by a pressure (density) difference. The half-way wall bounceback boundary condition is also used with the pressure (density) inlet/outlet conditions proposed in this paper and in Phys. Fluids8, 2527 (1996) to study 2-D Poiseuille flow and 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback boundary condition is comparable with that of other published boundary conditions and it has better stability behavior. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869307

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A thin annular layer of fluid coating a cylinder is subject to two different instabilities. One, driven by surface tension, is analogous to the Rayleigh instability of a liquid jet. The other is the Rayleigh–Taylor instability, which is driven by gravity. Measurements of the wavelength and growth rate of periodic patterns of droplets which develop as a result of the instability of such a fluid layer are reported for cylinders with radiusrin the range0.0011<r<1.27cm. For smallrthe wavelength and growth rate of the pattern are in agreement with theoretical predictions for the surface-tension-driven instability. For larger, the Rayleigh–Taylor instability is observed. At intermediaterthere is a region of crossover between the two limiting cases. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869280

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

We extend recent works on oscillatory flows over rigid ripples and the instability of sand ripples under such flows, by considering the instability of sand ripples under partially standing surface waves over a finite water depth. The variation of unstable ripples within a wavelength of the standing waves and inferences on the ripple distribution over a sand bar are examined. The steady circulation due to the combined effects of waves and ripples are also discussed. ©1997 American Institute of Physics. 

ISSN:1070-6631    

DOI:10.1063/1.869281

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

We analyze the effect of various thermal boundary conditions on the linear stability of surface-tension-driven flow in an unbounded liquid layer subject to a longitudinal temperature gradient. An original approach is devised to estimate the critical instability parameters. The order of magnitude estimates are used to solve the problem asymptotically for small Prandtl numbers. The instability is shown to be essentially determined by the thermal boundary conditions. For insulating boundaries the critical wavenumber scales askc∼Pr1/2meaning that the most unstable wave is considerably longer than the depth of the layer. When the bottom is well conducting, the critical wavelength is comparable to the depth of the layer. For the case of insulating bottom and non-adiabatic free surface the critical wavenumber depends on the Biot number askc∼Bi1/2.Even a weak thermal coupling between the free surface and the ambient medium such thatBi∼Prcan significantly influence the instability threshold. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869282

出版商:AIP    

年代:1997

数据来源: AIP