I. Formation and rise of a bubble stream in a viscous liquid

The continuous emission of gas bubbles from a single ejection orifice immersed in a viscous fluid is considered. We first present a semi empirical model of spherical bubble growth under constant flow conditions to predict the bubble volume at the detachment stage. In a second part, we propose a physical model to describe the rise velocity of in-line interacting bubbles and we derive an expression for the net viscous force acting on the surrounding fluid. Experimental results for air/water-glycerol systems are presented for a wide range of fluid viscosity and compared with theoretical predictions. An imagery technique was used to determine the bubble size and rise velocity. The effects of fluid viscosity, gas flow rate, orifice diameter and liquid depth on the bubble stream dynamic were analyzed. We have further studied the effect of large scale recirculation flow and the influence of a neighbouring bubble stream on the bubble growth and rising velocity. Received: 23 July 1997 / Revised: 16 December 1997 / Accepted: 11 May 1998     

Settling and fluidization of non Brownian hard spheres in a viscous liquid

A mean field approach is used to estimate the energy dissipation during the homogeneous sedimentation or the particulate fluidization of non Brownian hard spheres in a concentrated suspension of infinite extent. Depending on inertial screening and the range of the hydrodynamic interactions, the effective buoyancy force is determined either from the average suspension density in a Stokes flow or from the fluid density in the turbulent flow regime. An energy balance then yields a settling or fluidization law depending on the particle Reynolds number in reasonable agreement with the Richardson and Zaki correlation and recent experimental results for particle settling or fluidization. We further estimate the energy dissipation in the turbulent boundary layers around the particles to precise the Reynolds number dependence of the hindered settling function in the intermediate flow regime. Received 22 February 1999 and Received in final form 14 June 1999     

Uniform foam production by turbulent mixing: new results on free drainage vs. liquid content

An apparatus is described for rapidly producing large quantities of foam via turbulent mixing of gas with a narrow jet of a surfactant solution inside a delivery tube. By controlling relative flow rates, the gas volume fraction in the resulting foam may be easily varied across . Using such foams, we present a comprehensive set of data for free drainage as a systematic function of gas fraction and sample geometry. The qualitative behavior can be understood in terms of simple theoretical considerations, emphasizing the importance of controlling the initial foam conditions. Quantitative features are compared with two approximate versions of the drainage equation, highlighting the crucial role of capillarity for very dry foams and small samples. Received 15 February 1999     

Super lattice formation of an array of volatile wetting droplets

For an ordered array of critical volatile wetting droplets the formation of a super lattice by an Ostwald-ripening-like competition process is considered. The underlying diffusion problem is treated within a quasistatic approximation and to first order in the inverse droplets distance. The approach is rather general but a square lattice and a triangular lattice are studied explicitly. Dispersion relations for the super lattice growth of these arrays are calculated. Received 29 November 1999 and Received in final form 15 February 2000     

Magnetic permeability of a diphasic flow, made of liquid gallium and iron beads

Magnetohydrodynamics studies in laboratory experiments have long been restricted to low magnetic Reynolds number flows, mainly as a result of the very high magnetic diffusivity λ = 1/μσ of common conducting fluids (μ is the fluid's magnetic permeability and σ its electrical conductivity). The best conductivities are found in liquid metals which have a unit magnetic permeability, relative to vacuum. We show experimentally that a suspension of solid particles with a high magnetic permeability in a liquid metal yields an effective medium that has a high electrical conductivity and an enhanced magnetic permeability. The dispersion of the beads results from the turbulent fluid motion. The range of accessible magnetic Reynolds number can be increased by a factor of as much as 4 in our experimental setup. Received 6 March 2000 and Received in final form 13 July 2000     

Probing viscosity of a polymer melt at the nanometre scale with an oscillating nanotip

The Navier-Stokes equation is used to analyze the additional phase delay when an oscillating nanotip touches intermittently an entangled polymer melt. Even when the tip oscillates at frequencies of several hundred kilohertz, it is shown that the inertial contributions are negligible as long as the indentation depth is no more than a few ten nanometers. Consequently, a stationary solution can be used leading to the simple Stokes formula. Two simple geometries of the tip are investigated. A smooth tip apex with a spherical shape and an elongated tip apex that aims at mimicking a single asperity. The tip shape has a drastic influence on the measured viscosity at the local scale. A simple calculation indicates that the viscous force acting against the tip motion may exhibit several different behaviors as a function of the indentation depth. Using the variational principle of least action, we derive the corresponding phase variation of the oscillator as a function of the indentation depth. It is shown that there exist situations for which an absolute value of the local viscosity could be measured. Received 13 April 2001 and Received in final form 1 August 2001     

Surface flows of granular mixtures: II. Segregation with grains of different size

We present the generalization of a theoretical model for segregation of granular mixtures due to surface flows, published in J. Phys. I France 6, 1295 (1996). Our generalized model is valid for grains differing by their size and/or their surface properties; in the present paper, we describe the case of two species with the same surface properties but two different sizes. The rolling stream is assumed to be homogeneous. Exchanges between the grains at rest and the rolling stream are modelized via binary collisions. The model predicts that during the filling of a two-dimensional silo, continuous segregation appears inside the static phase: small (respectively large) grains tend to stop uphill (respectively downhill), although both species remain present everywhere. This fits the observations when the size difference between the species is small. When the size difference is large, a different regime is observed. We argue that in this case, segregation occurs directly inside the rolling stream. Received: 25 February 1998 / Received in final form and Accepted: 6 July 1998     

Vesicle propulsion in haptotaxis: A local model

We study theoretically vesicle locomotion due to haptotaxis. Haptotaxis is referred to motion induced by an adhesion gradient on a substrate. The problem is solved within a local approximation where a Rayleigh-type dissipation is adopted. The dynamical model is akin to the Rousse model for polymers. An invariant formulation is used to solve a dynamical model which includes a kind of dissipation due to bond breaking/restoring with the substrate. For a stationary situation where the vesicle acquires a constant drift velocity, we formulate the propulsion problem in terms of a nonlinear eigenvalue (the a priori unknown drift velocity) one of Barenblat-Zeldovitch type. A counting argument shows that the velocity belongs to a discrete set. For a relatively tense vesicle, we provide an analytical expression for the drift velocity as a function of relevant parameters. We find good agreement with the full numerical solution. Despite the oversimplification of the model it allows the identification of a relevant quantity, namely the adhesion length, which turns out to be crucial also in the nonlocal model in the presence of hydrodynamics, a situation on which we have recently reported (I. Cantat and C. Misbah, Phys. Rev. Lett. 83, 235 (1999)) and which constitutes the subject of a forthcoming extensive study. Received 10 February 2000     

Corrective measures in turbulent pipe flows and extended self-similarity

Significant statistical bias in LDA measurements and how to adequately deal with it is a subtle problem when dealing with turbulent flows. In order to attempt a clarification we have performed measurements on a non-standard “grid experiment” where a clear bias effect is found. We have investigated the effect of several corrective measures and find that best results, in the sense of having the first moment converge to zero, are obtained when using the time between events as statistical weights. The corrected time series have been used to check for extended self-similarity (ESS). Even though no scaling regime is seen for the third moment and the flow certainly is neither isotropic nor homogeneous, perfect ESS scaling based on the absolute third moment is observed up to the twelfth moment, extending into a time domain regime where the Taylor hypothesis of frozen turbulence is obviously violated. Reversing the argument this indicates that the correction scheme needed can be experimentally decided on using the criterion stated above and especially so if ESS is to be expected. Finally we have used the corrected data to quantify the deviations from Gaussian behavior of the velocity difference probability density function for a weakly turbulent flow. Through comparison with results on the Gaussian-Lorentzian distribution we find that the even part of the experimental distribution can be reproduced quite well by a single-parameter family of distributions with second moment equal unity. Received 5 August 1998 and Received in final form 21 December 1998     

Tracer dispersion in power law fluids flow through porous media: Evidence of a cross-over from a logarithmic to a power law behaviour

An analytical model is presented to describe the dispersion of tracers in a power-law fluid flowing through a statistically homogeneous and isotropic porous medium. The model is an extension of Saffman's approach to the case of non-Newtonian fluids. It is shown that an effective viscosity depending on the pressure gradient and on the characteristics of the fluid, must be introduced to satisfy Darcy's law. An analytical expression of the longitudinal dispersivity is given as a function of the Peclet number Pe and of the power-law index n that characterizes the dependence of the viscosity on the shear rate . As the flow velocity increases the dispersivity obeys an asymptotic power law: . This asymptotic regime is achieved at moderate Peclet numbers with strongly non-Newtonian fluids and on the contrary at very large values when n goes to 1 ( for n=0.9). This reflects the cross-over from a scaling behaviour for towards a logarithmic behaviour predicted for Newtonian fluids (n=1). Received: 22 July 1997 / Revised and Accepted: 2 July 1998     

Wigner lattice of ripplopolarons in a multielectron bubble in helium

The properties of ripplonic polarons in a multielectron bubble in liquid helium are investigated on the basis of a path-integral variational method. We find that the two-dimensional electron gas can form deep dimples in the helium surface, or ripplopolarons, to solidify as a Wigner crystal. We derive the experimental conditions of temperature, pressure and number of electrons in the bubble for this phase to be realized. This predicted state is distinct from the usual Wigner lattice of electrons: it melts by dissociation of the ripplopolarons when the electrons shed their localizing dimple as the pressure on the multielectron bubble drops below a critical value. Received 20 February 2003 Published online 11 April 2003 RID="a" ID="a"Also at: TU Eindhoven, Eindhoven, The Netherlands e-mail: devreese@uia.ua.ac.be     

Two-phase flow model for energetic proton beam induced pressure waves in mercury target systems in the planned European Spallation Source

Two-phase flow calculations are presented to investigate the thermo-hydraulical effects of the interaction between 2 ms long 1.3 GeV proton pulses with a closed mercury loop which can be considered as a model system of the target of the planned European Spallation Source (ESS) facility. The two-fluid model consists of six first-order partial differential equations that present one dimensional mass, momentum and energy balances for mercury vapor and liquid phases are capable to describe quick transients like cavitation effects or shock waves. The absorption of the proton beam is represented as instantaneous heat source in the energy balance equations. Densities and internal energies of the mercury liquid-vapor system is calculated from the van der Waals equation, but general method how to obtain such properties using arbitrary equation of state is also presented. A second order accurate high-resolution shock-capturing numerical scheme is applied with different kind of limiters in the numerical calculations. Our analysis show that even 75 degree temperature heat shocks cannot cause considerable cavitation effects in mercury.     

Fingering instability in a water-sand mixture

The temporal evolution of a water-sand interface driven by gravity is experimentally investigated. By means of a Fourier analysis of the evolving interface the growth rates are determined for the different modes appearing in the developing front. To model the observed behavior we apply the idea of the Rayleigh-Taylor instability for two stratified fluids. Carrying out a linear stability analysis we calculate the growth rates from the corresponding dispersion relations for finite and infinite cell sizes. Based on the theoretical results the viscosity of the suspension is estimated to be approximately 100 times higher than that of pure water, in agreement with other experimental findings. Received: 12 December 1997 / Revised: 23 March 1998 / Accepted: 28 April 1998     

Lattice Boltzmann simulation of a binary fluid with different phase viscosities and its application to fingering in two dimensions

A thermodynamically consistent lattice Boltzmann scheme for simulating the flow of a binary fluid is extended to allow the fluid components to have different viscosities. The approach is tested for the shear and Poiseuille flow of layered immiscible fluids and for the dispersion relation and the damping of a capillary wave. We then consider the fingering that results when a fluid is displaced by a less viscous fluid in a two-dimensional channel. The finger widths obtained match the results of Reinelt and Saffman [#!Reinelt85!#], but differ somewhat from those of Halpern and Gaver [#!Halpern94!#] for capillary numbers above 2. A limiting finger width close to 1/2 is obtained for high capillary numbers and high viscosity ratios. Received 25 May 1999 and Received in final form 19 November 1999     

Nuclear spin conversion in CH F induced by an alternating electric field

The nuclear spin conversion in CH₃F molecules subjected to an alternating electric field was investigated experimentally. The conversion rate was found to be almost unaffected by low electric fields ( V/cm) but sharply increased tenfold when the electric field amplitude exceeds the values ( V/cm) sufficiently high to produce crossings of the ortho and para states of the molecule. A theoretical model for the molecular conversion in alternating electric field was developed. The results of the experiment were found to be in a good agreement with the theory. Received 23 July 1999 and Received in final form 7 September 1999     

A Monte-Carlo study of equilibrium polymers in a shear flow

We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear flow on this state is briefly examined. Received 22 October 1998 and Received in final form 12 April 1999     

Orientational diffusivities measured by Rayleigh scattering in a lyotropic calamitic nematic () liquid crystal phase: the backflow problem revisited

Using a light-beating technique we have measured the damping time of thermal fluctuations of the nematic director for the so called cylindrical or calamitic nematic (N_C) phase of the lyotropic system K-laurate/decanol/. By varying the scattering angle in suitable geometries, we have been able to estimate the orientational diffusivities associated to the three pure deformations of splay, twist and bend. A former measurement made in the disk-like N_D phase of the same system yielded a large deviation between the splay and twist diffusivities. The effect was then attributed to induced flows, or backflow, which could be responsible for the reduction of the splay viscosity. In fact, this is the analogous effect, for disks, to the one recognized since long time ago arriving for rod-like molecules in a classical nematic, though in this case it is associated with bend deformations. The analogy comes about thanks to the interchange of the role played by disks and cylinders for, respectively, splay and bend fluctuations.The measurements reported here provide a new test on the applicability of the backflow model to a nematic system composed of micelles, that is, aggregates made of amphiphilic (surfactant) molecules, in its cylindrical-like variant, i.e. the N_C phase. In addition, the comparative study made here with the previous results existing in the literature for the N_D phase, allows us to conjecture on structural issues concerning lyotropic nematics. Received: 29 April 1998 / Revised: 19 August 1998 / Accepted: 31 August 1998