Showing papers in "Physics of Fluids in 2006"

Scaling of the velocity fluctuations in turbulent channels up to Reτ=2003

Abstract: A new numerical simulation of a turbulent channel in a large box at Reτ=2003 is described and briefly compared with simulations at lower Reynolds numbers and with experiments. Some of the fluctuation intensities, especially the streamwise velocity, do not scale well in wall units, both near and away from the wall. Spectral analysis traces the near-wall scaling failure to the interaction of the logarithmic layer with the wall. The present statistics can be downloaded from http://torroja.dmt.upm.es/ftp/channels. Further ones will be added to the site as they become available.

Equations of state in a lattice Boltzmann model

Abstract: In this paper we consider the incorporation of various equations of state into the single-component multiphase lattice Boltzmann model. Several cubic equations of state, including the van der Waals, Redlich-Kwong, and Peng-Robinson, as well as a noncubic equation of state (Carnahan-Starling), are incorporated into the lattice Boltzmann model. The details of phase separation in these nonideal single-component systems are presented by comparing the numerical simulation results in terms of density ratios, spurious currents, and temperature ranges. A comparison with a real fluid system, i.e., the properties of saturated water and steam, is also presented.

Effective slip and friction reduction in nanograted superhydrophobic microchannels

Abstract: Enabled by a technology to fabricate well-defined nanogrates over a large area (2×2cm2), we report the effect of such a surface, in both hydrophilic and hydrophobic conditions, on liquid slip and the corresponding friction reduction in microchannels. The grates are designed to be dense (∼230nm pitch) but deep (∼500nm) in order to sustain a large amount of air in the troughs when the grates are hydrophobic, even under pressurized liquid flow conditions (e.g., more than 1bar). A noticeable slip (i.e., slip length of 100–200nm, corresponding to 20%–30% reduction of pressure drop in a ∼3μm high channel) is observed for water flowing parallel over the hydrophobic nanogrates; this is believed to be an “effective” slip generated by the nanostrips of air in the grate troughs under the liquid. The effective slip is clearer and larger in flows parallel to the nanograting patterns than in transverse, suggesting that the nanograted superhydrophobic surfaces would not only reduce friction in liquid flows under pressur...

Microscale tipstreaming in a microfluidic flow focusing device

Abstract: A microfluidic flow-focusing device is used to explore the use of surfactant-mediated tipstreaming to synthesize micrometer-scale and smaller droplets. By controlling the surfactant bulk concentration of a soluble nonionic surfactant in the neighborhood of the critical micelle concentration, along with the capillary number and the ratio of the internal and external flow rates, we observe several distinct modes of droplet breakup. For the most part, droplet breakup in microfluidic devices results in highly monodisperse droplets in the range of tens of micrometers in size. However, we observe a new mode of breakup called “thread formation” that resembles tipstreaming and yields tiny droplets in the range of a few micrometers in size or smaller. In this work, we characterize the growth of the thread and its maximum length as a function of flow variables and surfactant content, and we also characterize the period of droplet breakup as a function of these variables. Our results suggest possible methods for controlling the process. Using a simple flow visualization experiment as the basis, we report on preliminary efforts to model the thread formation process.

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

Abstract: The dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behavior that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localized increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur i...

An experimental study of drop-on-demand drop formation

Abstract: The dynamics of drop-on-demand (DOD) drop formation have been studied experimentally using an imaging system with an interframe time of 1μs and a spatial resolution of 0.81μm∕pixel. Using a piezoelectrical actuated inkjet printhead with the nozzle orifice diameter of 53μm, experiments were conducted over a range of viscosities (1.0–5.0cP) and surface tensions (35–73mN∕m). The effects of the driving signal, which controls the piezoelectric transducer that produces the pressure pulse to drive the liquid from the reservoir through the orifice, have been examined along with those of liquid properties. The main stages of DOD drop formation, including ejection and stretching of liquid, pinch-off of liquid thread from the nozzle exit, contraction of liquid thread, breakup of liquid thread into primary drop and satellites, and recombination of primary drop and satellites, are analyzed based on the experimental results. The breakup time of liquid threads was found to be dependent mainly on the capillary time based...

Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at M=2.25

Abstract: The interaction of a spatially developing adiabatic boundary layer flow at M∞=2.25 and Reθ=3725 with an impinging oblique shock wave (β=33.2°) is analyzed by means of direct numerical simulation of the compressible Navier-Stokes equations. Under the selected flow conditions the incoming boundary layer undergoes mild separation due to the adverse pressure gradient. Coherent structures are shed near the average separation point and the flow field exhibits large-scale low-frequency unsteadiness. The formation of the mixing layer is primarily responsible for the amplification of turbulence, which relaxes to an equilibrium state past the interaction. Complete equilibrium is attained in the inner part of the boundary layer, while in the outer region the relaxation process is incomplete. Far from the interaction zone, turbulence exhibits a universal behavior and it shows similarities with the incompressible case. The interaction of the coherent structures with the incident shock produces acoustic waves that prop...

Steady solutions of the Navier-Stokes equations by selective frequency damping

Abstract: A new method, enabling the computation of steady solutions of the Navier-Stokes equations in globally unstable configurations, is presented. We show that it is possible to reach a steady state by damping the unstable (temporal) frequencies. This is achieved by adding a dissipative relaxation term proportional to the high-frequency content of the velocity fluctuations. Results are presented for cavity-driven boundary-layer separation and a separation bubble induced by an external pressure gradient.

Time evolution and mixing characteristics of hydrogen and ethylene transverse jets in supersonic crossflows

Abstract: We report an experimental investigation that reveals significant differences in the near-flowfield properties of hydrogen and ethylene jets injected into a supersonic crossflow at a similar jet-to-freestream momentum flux ratio. Previously, the momentum flux ratio was found to be the main controlling parameter of the jet’s penetration. Current experiments, however, demonstrate that the transverse penetration of the ethylene jet was altered, penetrating deeper into the freestream than the hydrogen jet even for similar jet-to-freestream momentum flux ratios. Increased penetration depths of ethylene jets were attributed to the significant differences in the development of large-scale coherent structures present in the jet shear layer. In the hydrogen case, the periodically formed eddies persist long distances downstream, while for ethylene injection, these eddies lose their coherence as the jet bends downstream. The large velocity difference between the ethylene jet and the freestream induces enhanced mixing at the jet shear layer as a result of the velocity induced stretching-tilting-tearing mechanism. These new observations became possible by the realization of high velocity and high temperature freestream conditions which could not be achieved in conventional facilities as have been widely used in previous studies. The freestream flow replicates a realistic supersonic combustor environment associated with a hypersonic airbreathing engine flying at Mach 10. The temporal evolution, the penetration, and the convection characteristics of both jets were observed using a fast-framing-rate (up to 100 MHz) camera acquiring eight consecutive schlieren images, while OH planar laser-induced fluorescence was performed to verify the molecular mixing.

Inertial migration of neutrally buoyant particles in a square duct: An investigation of multiple equilibrium positions

Abstract: Inertial migration of neutrally buoyant particles in a square duct has been investigated by numerical simulation in the range of Reynolds numbers from 100 to 1000. Particles migrate to one of a small number of equilibrium positions in the cross-sectional plane, located near a corner or at the center of an edge. In dilute suspensions, trains of particles are formed along the axis of the flow, near the planar equilibrium positions of single particles. At high Reynolds numbers (Re⩾750), we observe particles in an inner region near the center of the duct. We present numerical evidence that closely spaced pairs of particles can migrate to the center at high Reynolds number.

Lagrangian analysis of fluid transport in empirical vortex ring flows

Abstract: In this paper we apply dynamical systems analyses and computational tools to fluid transport in empirically measured vortex ring flows. Measurements of quasisteadily propagating vortex rings generated by a mechanical piston-cylinder apparatus reveal lobe dynamics during entrainment and detrainment that are consistent with previous theoretical and numerical studies. In addition, the vortex ring wake of a free-swimming Aurelia aurita jellyfish is measured and analyzed in the framework of dynamical systems to elucidate similar lobe dynamics in a naturally occurring biological flow. For the mechanically generated rings, a comparison of the net entrainment rate based on the present methods with a previous Eulerian analysis shows good correspondence. However, the current Lagrangian framework is more effective than previous analyses in capturing the transport geometry, especially when the flow becomes more unsteady, as in the case of the free-swimming jellyfish. Extensions of these results to more complex flow geometries is suggested.

Simulating flow of DNA suspension using dissipative particle dynamics

Abstract: We simulate DNA suspension microchannel flows using the dissipative particle dynamics (DPD) method. Two developments make this simulation more realistic. One is to improve the dynamic characteristics of a DPD system by modifying the weighting function of the dissipative force and increasing its cutoff radius, so that the Schmidt number can be increased to a practical level. Another is to set up a wormlike chain model in the DPD framework, according to the measured extension properties of a DNA molecule in uniform flows. This chain model is then used to study flows of a DNA suspension through microchannels. Interesting results on the conformation evolution of DNA molecules passing through the microchannels, including periodic contraction-diffusion microchannels, are reported.

Large eddy simulations of transitional round jets: Influence of the Reynolds number on flow development and energy dissipation

Abstract: Transitional round jets at Mach number M=0.9, with identical initial conditions except for the diameter, yielding Reynolds numbers over the range 1.7×103⩽ReD⩽4×105, are computed by large eddy simulation (LES) using explicit selective/high-order filtering. The effects of the Reynolds number on the jet flows are first presented. As the Reynolds number decreases, the jets develop more slowly upstream from the end of the potential core, but more rapidly downstream. At lower Reynolds numbers, the decay of the centerline velocity and the jet spreading are indeed faster, and the turbulence intensities are higher after the potential core, in agreement with data of the literature. The integral length scales are also significantly larger. The results suggest moreover that the jet self-similar region is reached at shorter axial distances at lower Reynolds numbers. The influence of the Reynolds number on the energy-dissipation mechanisms involved in the LES, namely molecular viscosity and explicit filtering, is secon...

A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces

Abstract: We present a theoretical prediction for the drag reduction rate achieved by superhydrophobic surfaces in a turbulent channel flow. The predicted drag reduction rate is in good agreement with results obtained from direct numerical simulations at Reτ≃180 and 400. The present theory suggests that large drag reduction is possible also at Reynolds numbers of practical interest (Reτ∼105–106) by employing a hydrophobic surface, which induces a slip length on the order of ten wall units or more.

Formation of simple and compound drops in microfluidic devices

Abstract: This work is motivated by the recent experimental development of microfluidic flow-focusing devices that produce highly monodisperse simple or compound drops. Using finite elements with adaptive meshing in a diffuse-interface framework, we simulate the breakup of simple and compound jets in coflowing conditions, and explore the flow regimes that prevail in different parameter ranges. Moreover, we investigate the effects of viscoelasticity on interface rupture and drop pinch-off. The formation of simple drops exhibits a dripping regime at relatively low flow rates and a jetting regime at higher flow rates. In both regimes, drops form because of the combined effects of capillary instability and viscous drag. The drop size increases with the flow rate of the inner fluid and decreases with that of the outer fluid. Viscoelasticity in the drop phase increases the drop size in the dripping regime but decreases it in the jetting regime. The formation of compound drops is a delicate process that takes place in a narrow window of flow and rheological parameters. Encapsulation of the inner drop depends critically on coordination of capillary waves on the inner and outer interfaces.

Experimental Investigations of Elastic Tail Propulsion At Low Reynolds Number

Abstract: A simple way to generate propulsion at low Reynolds number is to periodically oscillate a passive flexible filament. Here we present a macroscopic experimental investigation of such a propulsive mechanism. A robotic swimmer is constructed and both tail shape and propulsive force are measured. Filament characteristics and actuation are varied, and the resulting data are quantitatively compared with existing linear and nonlinear theories.

Laminar flow in a microchannel with superhydrophobic walls exhibiting transverse ribs

Abstract: One approach recently proposed for reducing the frictional resistance to liquid flow in microchannels is the patterning of microribs and cavities on the channel walls. When treated with a hydrophobic coating, the liquid flowing in the microchannel wets only the surfaces of the ribs, and does not penetrate the cavities, provided the pressure is not too high. The net result is a reduction in the surface contact area between channel walls and the flowing liquid. For microribs and cavities that are aligned normal to the channel axis (principal flow direction), these micropatterns form a repeating, periodic structure. This paper presents results of a study exploring the momentum transport in a parallel-plate microchannel with such microengineered walls. The investigation explored the entire laminar flow Reynolds number range and characterized the influence of the vapor cavity depth on the overall flow field. The liquid-vapor interface (meniscus) in the cavity regions is treated as flat in the numerical analysi...

The limits of Navier-Stokes theory and kinetic extensions for describing small-scale gaseous hydrodynamics

Abstract: This paper reviews basic results and recent developments in the field of small-scale gaseous hydrodynamics which has received significant attention in connection with small-scale science and technology. We focus on the modeling challenges arising from the breakdown of the Navier-Stokes description, observed when characteristic lengthscales become of the order of, or smaller than, the molecular mean free path. We discuss both theoretical results and numerical methods development. Examples of the former include the limit of applicability of the Navier-Stokes constitutive laws, the concept of second-order slip and the appropriate form of such a model, and how to reconcile experimental measurements of slipping flows with theory. We also review a number of recently developed theoretical descriptions of canonical nanoscale flows of engineering interest. On the simulation front, we review recent progress in characterizing the accuracy of the prevalent Boltzmann simulation method known as direct simulation Monte Carlo. We also present recent variance reduction ideas which address the prohibitive cost associated with the statistical sampling of macroscopic properties in low-speed flows.

Mechanism of drag reduction by dimples on a sphere

Abstract: In this Letter we present a detailed mechanism of drag reduction by dimples on a sphere such as golf-ball dimples by measuring the streamwise velocity above the dimpled surface. Dimples cause local flow separation and trigger the shear layer instability along the separating shear layer, resulting in the generation of large turbulence intensity. With this increased turbulence, the flow reattaches to the sphere surface with a high momentum near the wall and overcomes a strong adverse pressure gradient formed in the rear sphere surface. As a result, dimples delay the main separation and reduce drag significantly. The present study suggests that generation of a separation bubble, i.e., a closed-loop streamline consisting of separation and reattachment, on a body surface is an important flow-control strategy for drag reduction on a bluff body such as the sphere and cylinder.

A dynamic subgrid-scale eddy viscosity model with a global model coefficient

Abstract: In the present study, a dynamic subgrid-scale eddy viscosity model is proposed for large eddy simulation of turbulent flows in complex geometry. A subgrid-scale eddy viscosity model recently proposed by Vreman [Phys. Fluids 16, 3670 (2004)] which guarantees theoretically zero subgrid-scale dissipation for various laminar shear flows, is considered as a base model. A priori tests with the original Vreman model show that it predicts the correct profile of subgrid-scale dissipation in turbulent channel flow but the optimal model coefficient is far from universal. A dynamic procedure of determining the model coefficient is proposed based on the “global equilibrium” between the subgrid-scale dissipation and the viscous dissipation. An important feature of the proposed procedure is that the model coefficient determined is globally constant in space but varies only in time. A posteriori tests of the proposed dynamic model are conducted through large eddy simulations of forced isotropic turbulence at Reλ=103, tur...

Solitary water wave interactions

Abstract: This article concerns the pairwise nonlinear interaction of solitary waves in the free surface of a body of water lying over a horizontal bottom. Unlike solitary waves in many completely integrable model systems, solitary waves for the full Euler equations do not collide elastically; after interactions, there is a nonzero residual wave that trails the post-collision solitary waves. In this report on new numerical and experimental studies of such solitary wave interactions, we verify that this is the case, both in head-on collisions (the counterpropagating case) and overtaking collisions (the copropagating case), quantifying the degree to which interactions are inelastic. In the situation in which two identical solitary waves undergo a head-on collision, we compare the asymptotic predictions of Su and Mirie [J. Fluid Mech. 98, 509 (1980)] and Byatt-Smith [J. Fluid Mech. 49, 625 (1971)], the wavetank experiments of Maxworthy [J. Fluid Mech. 76, 177 (1976)], and the numerical results of Cooker, Weidman, and Bale [J. Fluid Mech. 342, 141 (1997)] with independent numerical simulations, in which we quantify the phase change, the run-up, and the form of the residual wave and its Fourier signature in both small- and large-amplitude interactions. This updates the prior numerical observations of inelastic interactions in Fenton and Rienecker [J. Fluid Mech. 118, 411 (1982)]. In the case of two nonidentical solitary waves, our precision wavetank experiments are compared with numerical simulations, again observing the run-up, phase lag, and generation of a residual from the interaction. Considering overtaking solitary wave interactions, we compare our experimental observations, numerical simulations, and the asymptotic predictions of Zou and Su [Phys. Fluids 29, 2113 (1986)], and again we quantify the inelastic residual after collisions in the simulations. Geometrically, our numerical simulations of overtaking interactions fit into the three categories of Korteweg-deVries two-soliton solutions defined in Lax [Commun. Pure Appl. Math. 21, 467 (1968)], with, however, a modification in the parameter regime. In all cases we have considered, collisions are seen to be inelastic, although the degree to which interactions depart from elastic is very small. Finally, we give several theoretical results: (i) a relationship between the change in amplitude of solitary waves due to a pairwise collision and the energy carried away from the interaction by the residual component, and (ii) a rigorous estimate of the size of the residual component of pairwise solitary wave collisions. This estimate is consistent with the analytic results of Schneider and Wayne [Commun. Pure Appl. Math. 53, 1475 (2000)], Wright [SIAM J. Math. Anal. 37, 1161 (2005)], and Bona, Colin, and Lannes [Arch. Rat. Mech. Anal. 178, 373 (2005)]. However, in light of our numerical data, both (i) and (ii) indicate a need to reevaluate the asymptotic results in Su and Mirie [J. Fluid Mech. 98, 509 (1980)] and Zou and Su [Phys. Fluids 29, 2113 (1986)].

Subgrid modeling in particle-laden channel flow

Abstract: Direct numerical simulation (DNS) and large-eddy simulation (LES) of particle-laden turbulent channel flow, in which the particles experience a drag force, are investigated for two subgrid models and several Reynolds and Stokes numbers. In this flow, turbophoresis leads to an accumulation of particles near the walls. The objectives of the work are to investigate the accuracy of the subgrid models studied with respect to particle behavior and to explain the observed particle behavior predicted by the different models. The focus is on particle dispersion and mean particle motion in the direction normal to the walls of the channel. For a low Reynolds number, it is shown that the turbophoresis and particle velocity fluctuations are reduced compared to DNS, if the filtered fluid velocity calculated in the LES is used in the particle equation of motion. This is a combined effect of the disregard of the subgrid scales in the fluid velocity and the inadequacy of the subgrid model. Better agreement with DNS is obt...

Wave impact loads: The role of the flip-through

Abstract: The impact of waves upon a vertical, rigid wall during sloshing is analyzed with specific focus on the modes that lead to the generation of a flip-through [M. J. Cooker and D. H. Peregrine, “A model for breaking wave impact pressures,” in Proceedings of the 22nd International Conference on Coastal Engineering (ASCE, Delft, 1990), Vol. 2, pp. 1473–1486]. Experimental data, based on a time-resolved particle image velocimetry technique and on a novel free-surface tracking method [M. Miozzi, “Particle image velocimetry using feature tracking and Delaunay tessellation,” in Proceedings of the 12th International Symposium on Applications of Laser Techniques to Fluid Mechanics (2004)], are used to characterize the details of the flip-through dynamics while wave loads are computed by integrating the experimental pressure distributions. Three different flip-through modes are observed and studied in dependence on the amount and modes of air trapping. No air entrapment characterizes a “mode (a) flip-through,” engulfm...

Spray impact: Rim transverse instability initiating fingering and splash, and description of a secondary spray

Abstract: In this paper, normal spray impact onto a rigid wall, leading to the formation of secondary spray, is considered The mechanism of splash is explained by the bending instability of a rim bounding a free liquid sheet The linear stability analysis of the rim is performed in the framework of the long-wave, quasi-one-dimensional approach The rim instability is caused by the moment of forces associated with the inertia of the liquid entering the rim Next, two components of the drop velocity and their diameter, as well as various flux density vectors (number, volume, mass fluxes) and tensors (momentum flux), are measured using a phase Doppler instrument It is shown that the viscous length scale of drop impact can be used in describing the splash threshold, diameter of secondary droplets, and their velocity Consequently, a closed semi-empirical model for the secondary spray has been proposed and validated using a numerical simulation of spray transport based on an Euler-Lagrange approach

Effect of initial conditions on interaction between a boundary layer and a wall-mounted finite-length-cylinder wake

Abstract: The effects of initial conditions on interaction between a boundary layer over a flat plate and flow around a wall-mounted finite-length cylinder were experimentally investigated. A square cylinder with a characteristic width (d) of 20mm and a length of H=5d was vertically mounted on a horizontal flat plate. Three different boundary layers were investigated, their momentum thickness being 0.07d, 0.13d, and 0.245d, respectively, measured at the cylinder axis in the absence of the cylinder. All the experiments were carried out in a closed-loop water tunnel at a Reynolds numbers of 11 500 based on d and the free-stream velocity U∞. It is found that initial boundary layer conditions have a profound effect on the near wake, including the flow near the cylinder free end that is well beyond the boundary layer. With increasing boundary layer thickness, the base vortex is enhanced, inducing a stronger upwash flow from the cylinder base, which acts to weaken the downwash free-end shear layer and the tip vortex. Con...

Electrospinning of viscoelastic Boger fluids: Modeling and experiments

Abstract: An experimental and theoretical investigation of electrospun Newtonian and viscoelastic jets is presented. In particular, the effect of electrical conductivity and viscoelasticity on the jet profile during the initial stage of electrospinning is examined. In the theoretical study, the fluid is described as a leaky dielectric with charges only on the jet surface and viscoelastic models for polymer solutions such as Oldroyd-B and FENE-P are fully coupled with the fluid momentum equations and Gauss’ law. A theoretical model for the jet is derived using a thin filament approximation, and the resulting differential equations governing electrically charged, stable polymeric jets are solved numerically. Two different experimental systems are considered: Newtonian solutions of glycerol containing trace amounts of lithium chloride salt, and viscoelastic PIB/PB Boger fluid solutions. The experimental jet profiles from electrospinning experiments are compared with the model predictions. Our results reveal that incre...

Unsteady undular bores in fully nonlinear shallow-water theory

Abstract: We consider unsteady undular bores for a pair of coupled equations of Boussinesq-type which contain the familiar fully nonlinear dissipationless shallow-water dynamics and the leading-order fully nonlinear dispersive terms. This system contains one horizontal space dimension and time and can be systematically derived from the full Euler equations for irrotational flows with a free surface using a standard long-wave asymptotic expansion. In this context the system was first derived by Su and Gardner. It coincides with the one-dimensional flat-bottom reduction of the Green-Naghdi system and, additionally, has recently found a number of fluid dynamics applications other than the present context of shallow-water gravity waves. We then use the Whitham modulation theory for a one-phase periodic travelling wave to obtain an asymptotic analytical description of an undular bore in the Su-Gardner system for a full range of “depth” ratios across the bore. The positions of the leading and trailing edges of the undular bore and the amplitude of the leading solitary wave of the bore are found as functions of this “depth ratio.” The formation of a partial undular bore with a rapidly varying finite-amplitude trailing wavefront is predicted for “depth ratios” across the bore exceeding 1.43. The analytical results from the modulation theory are shown to be in excellent agreement with full numerical solutions for the development of an undular bore in the Su-Gardner system.

Dynamics of particle-particle collisions in a viscous liquid

Abstract: When two solid spheres collide in a liquid, the dynamic collision process is slowed by viscous dissipation and the increased pressure in the interparticle gap as compared with dry collisions. This paper investigates liquid-immersed head-on and oblique collisions, which complements previously investigated particle-on-wall immersed collisions. By defining the normal from the line of centers at contact, the experimental findings support the decomposition of an oblique collision into its normal and tangential components of motion. The normal relative particle motion is characterized by an effective coefficient of restitution and a binary Stokes number with a correlation that follows the particle-wall results. The tangential motion is described by a collision model using a normal coefficient of restitution and a friction coefficient that are modified for the liquid effects.

Tip streaming from a liquid drop forming from a tube in a co-flowing outer fluid

Abstract: Dynamics of formation of a drop of an incompressible Newtonian fluid of viscosity μ1 and density ρ1 from the tip of a tube of radius R1 into a co-flowing immiscible, incompressible Newtonian fluid of viscosity μ2 and density ρ2 that is enclosed in a concentric cylindrical tube of radius R2 are investigated under creeping flow conditions. Transient drop shapes, and fluid velocities and pressures, are calculated numerically by solving the governing Stokes equations with the appropriate boundary and initial conditions using the Galerkin/finite element method for spatial discretization and an adaptive finite difference method for time integration. In accord with previous studies, the primary effect of increasing the ratio of the volumetric injection rate Q2 of the outer fluid to that of the inner fluid Q1, Qr≡Q2∕Q1, is shown to be a reduction in the volume of primary drops that are formed. When Qr is small, calculations show that drop formation occurs in a slug flow regime where the primary drops that are...

Selection of the ripple length on a granular bed sheared by a liquid flow

Abstract: The stability of a granular bed sheared by a liquid flow is investigated using an erosion-deposition model for the moving grains. Extending to arbitrary wave number a previous long wave analysis [F. Charru and E. J. Hinch, J. Fluid Mech. 550, 111 (2006)], this study shows that short waves are stabilized by a crest-erosion mechanism that is absent when the local particle flux is assumed to be in equilibrium with the local bed shear stress. The cutoff length associated with this mechanism scales on a deposition length of the particles. This characteristic length is similar, although of a different physical nature, to the inertial length involved in relaxation models of dune dynamics under the wind. Two stabilizing mechanisms cooperate for the most amplified wave number: the new crest-erosion mechanism and the gravity force parallel to the local slope of the inclined bed. The predictions of this model are compared to observations, showing better agreement than previous stability analyses, which strongly unde...