Bubbles under stress

We present an experimental and theoretical investigation of a system composed of two soap bubbles strained between two parallel solid surfaces. The two-bubble cluster can be found in several configurations. The existence and stability of each of these states is studied as a function of the distance between the two facing surfaces. The change of this distance can induce a transition from one configuration to another; we observe that most transitions are subcritical, showing that the system is often trapped in states where the minimum of free energy is only local. The hysteretic transitions are responsible for the dissipation of elastic energy. The existence of more than one stable states for given boundaries conditions combined with the absence of thermalization means that the history of the system has to be taken into account and that there is no unique stress-strain relation. In the present system, because of its simplicity, a complete quantitative analysis of these general processes is obtained. The presented results may contribute to a better understanding of the dynamics of more complex systems such as foams or granular materials where similar processes are at work.     

The transition from two-dimensional to three-dimensional foam structures

Small cells in an experimental sample of two-dimensional foam, such as that which is contained between two glass plates, may undergo a transition to a three-dimensional form, becoming detached from one boundary. We present the first detailed observations of this phenomenon, together with computer simulations. The transition is attributed to an instability of the Rayleigh-Plateau type. A theoretical analysis is given which shows that an individual cell is susceptible to this instability only if it has less than six sides. Received 15 October 2001 and Received in final form 14 January 2002     

Transport and sedimentation of solid particles in Bénard hexagonal cells

The motion of particles moving under gravity in the velocity field of a liquid in a Bénard hexagonal cell is studied experimentally and numerically for Stokes flow conditions. We then explain the settlement of particles in the centers of cells to form a regular quincunx. It is found that sedimentation also occurs preferentially along the lines connecting the centers of adjacent cells to form a triangle deposition tessellation. Finally, it is explained why particles occupy the central part of each convective cell while the peripheral part of the cell quickly becomes limpid. Numerical results are in agreement with the experimental observations of Bénard and those of the present study.     

Steady drainage in emulsions: corrections for surface Plateau borders and a model for high aqueous volume fraction

We compare extensive experimental results for the gravity-driven steady drainage of oil-in-water emulsions with two theoretical predictions, both based on the assumption of Poiseuille flow. The first is from standard foam drainage theory, applicable at low aqueous volume fractions, for which a correction is derived to account for the effects of the confinement of the emulsion. The second arises from considering the permeability of a model porous medium consisting of solid sphere packings, applicable at higher aqueous volume fractions. We find quantitative agreement between experiment and the foam drainage theory at low aqueous volume fractions. At higher aqueous volume fractions, the reduced flow rate calculated from the permeability theory approaches the master curve of the experimental data. Our experimental data demonstrates the analogy between the problem of electrical flow and liquid flow through foams and emulsions.     

Bending of charged flexible membranes due to the presence of macroions

We investigate the bending of flexible charged membranes due to the presence of rigid rodlike macroions in the framework of the Debye-Hückel approximation. When the macroions are fixed in space at some distance from the bilayer the membrane bends towards them; we calculate the exact deformation profile. On the other hand a macroion which is adsorbed on the membrane causes a deflection of the bilayer. Finally, we consider swollen lamellar polyanion/charged-lipid complexes where the macroions are intercalated between charged lipid bilayers. We predict the occurrence of a double adsorption (pinching effect) of the macroion for sufficiently flexible membranes. Received: 9 February 1998 / Revised: 9 June 1998 / Accepted: 2 July 1998     

Effects of the rate of evaporation and film thickness on nonuniform drying of film-forming concentrated colloidal suspensions

In this paper, we report on nonuniform distribution of film-forming waterborne colloidal suspensions above the critical concentration _c of the colloidal glass transition during drying. We found that colloidal suspension films dry nonuniformly when the initial rate of evaporation E and/or the initial thickness l₀ are high. We found that a Peclet number Pe, defined as Pe = El₀/D, where D is the diffusion coefficient of the colloids in the diluted suspensions, does not predict uniformity of drying of the concentrated suspensions, contrary to the reported work on drying of diluted suspensions. Since the colloidal particles are crowded and their diffusive motion is restricted in concentrated suspensions, we assumed that above _c water is transported to the drying surface by hydrodynamic flow along the osmotic pressure gradient. The permeability of water through channels between deforming particles is estimated by adapting the theory of foam drainage. We defined a new Peclet number Pe by substituting the transport coefficient of flow (defined as the permeability divided by the viscosity, multiplied by the osmotic pressure gradient) for the diffusion coefficient. This extended Peclet number predicted the nonuniform drying with a criterion of Pe > 1. These results indicate that the mechanism of water transport to the drying surface in concentrated suspensions is water permeation by osmotic pressure, which is faster than mutual diffusion between water and particles --that has been observed in diluted suspensions and discussed by Routh and Russel. The theory fits well the experimental drying curves for various thicknesses and rates of evaporation. The particle distribution in the drying films is also estimated and it is indicated that the latex distribution is nonuniform when Pe > 1.     

Induced bubble shape oscillations and their impact on the rise velocity

When a 2-4 mm diameter bubble rising with constant velocity hits a thin wire, bubble shape oscillations can be induced. As a consequence also the bubble rise velocity strongly oscillates. With the help of a force balance we show that these velocity oscillations are an added-mass effect. Received 9 April 2002 / Received in final form 11 July 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: lohse@tn.utwente.nl     

Aggregation of particles settling in shear-thinning fluids

We have experimentally studied the coaxial settling of three identical non-Brownian spheres in a shear-thinning fluid at small Reynolds numbers. While settling, the particles create corridors of reduced viscosity in their wake and, if they are initially close enough to one another, they can form stable clusters. By analogy with previous results obtained on two-particle interaction in the first part of this work, we show that the particle velocities can be satisfactorily described using a first-order expression and assuming that the reduced viscosity remains constant. We report systematic experiments performed at different initial separation distances between particles and the use of our simple model allows the prediction of the settling behaviour and in particular the conditions for clusters formation. We thus show that particle aggregation can occur even for large initial distances between particles and within times that are small compared to the time scales in Newtonian fluids. Received 10 July 2002 RID="a" ID="a"e-mail: talini@fast.u-psud.fr     

Decorated vertices with 3-edged cells in 2D foams: exact solutions and properties

The energy, area and excess energy of a decorated vertex in a 2D foam are calculated. The general shape of the vertex and its decoration are described analytically by a reference pattern mapped by a parametric Moebius transformation. A single parameter of control allows to describe, in a common framework, different types of decorations, by liquid triangles or 3-sided bubbles, and other non-conventional cells. A solution is proposed to explain the stability threshold in the flower problem.     

Spatio-temporal patterns in the thermoconvection of a planar nematic layer: II. Experiments

We study experimentally the evolution of thermoconvection in a laterally extended planar nematic layer, at zero or weak stabilizing magnetic field. As the applied thermal gradient is increased, a cascade of symmetry breakings occurs, towards structures of increasing spatial complexity, and ultimately towards oscillating states. The patterns are characterized optically, and simple models for the distortion of the vertical (out of plane) component of the director field are proposed. Received: 1st December 1997 / Revised: 25 May 1998 / Accepted: 2 June 1998     

Structural and dynamical properties of aqueous suspensions of NaPSS (HPSS) at very low ionic strength

Results on the structural and dynamical properties of aqueous solutions of NaPSS (HPSS) are reported. Most samples of previous measurements, including our own, are contaminated by the presence of (temporal) aggregates. The emphasis of this paper lies on investigations of well purified samples at very low ionic strength where interacting effects are maximum. As previously reported, this can be achieved by pumping the suspension through ion exchange resin by means of a tube-pump, using filters of pore size. Information has been extracted from static and dynamic light scattering and viscosity measurements. A second maximum is observed in the scattering curves versus wavenumber for the first time. It is discussed on the basis of two current models describing the structure of charged macromolecules. The short time dynamics reflects the measured intensity. Detailed viscosity data in comparison of those of rodlike (TMV), slightly flexible so-called fd virus particles (length 880 nm) are used to confirm the interpretation of the light scattering results. The recently observed maximum in the reduced viscosity could be confirmed. Received: 5 May 1997 / Revised: 1 September 1997 / Accepted: 10 November 1997     

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     

On the use of Galerkin-Eckhaus method to study the nonlinear regime of Marangoni-Bénard instabilities in an evaporating liquid layer

We investigate theoretically Marangoni-Bénard instability in an evaporating liquid layer surmounted by its vapor and an inert gas. A Galerkin-Eckhaus method, based on a slaving principle and an iterative algorithm, and a direct finite element method are used to determine the evaporation rate above the convective threshold. Both methods provide precise quantitative results, even far from the linear stability threshold.     

The interplay between screening properties and colloid anisotropy: Towards a reliable pair potential for disc-like charged particles

The electrostatic potential of a highly charged disc (clay platelet) in an electrolyte is investigated in detail. The corresponding non-linear Poisson-Boltzmann (PB) equation is solved numerically, and we show that the far-field behaviour (relevant for colloidal interactions in dilute suspensions) is exactly that obtained within linearized PB theory, with the surface boundary condition of a uniform potential. The latter linear problem is solved by a new semi-analytical procedure and both the potential amplitude (quantified by an effective charge) and potential anisotropy coincide closely within PB and linearized PB, provided the disc bare charge is high enough. This anisotropy remains at all scales; it is encoded in a function that may vary over several orders of magnitude depending on the azimuthal angle under which the disc is seen. The results allow to construct a pair potential for discs interaction, that is strongly orientation dependent.     

Surface flows of granular mixtures

We present the generalization of the minimal model for surface flows of granular mixtures, proposed by Boutreux and de Gennes [J. Phys. I France 6, 1295 (1996)]. The minimal model was valid for grains differing only in their surface properties. The present model also takes into account differences in the size of the grains. We apply the model to study segregation in two-dimensional silos of mixtures of grains differing in size and/or surface properties. When the difference in size is small, the model predicts that a continuous segregation appears in the static phase during the filling of a silo. When the difference in size is wide, we take into account the segregation of the grains in the rolling phase, and the model predicts complete segregation and stratification in agreement with experimental observations. Received 9 September 1998 and Received in final form 4 November 1998     

Correlation between the viscoelastic properties of a soft crystal and its microstructure

We investigate the rheological properties of a cubic fcc phase of micelles obtained by aggregation of a triblock copolymer (PEO)₁₂₇(PPO)₄₈(PEO)₁₂₇ in water as selective solvent. The resulting soft solid is submitted to a range of stresses varying from 20 to 800Pa in Couette geometry. Creep and flow behaviour can be distinguished and interpreted in terms of structural changes previously observed by SAXS under flow. Contrasting with other systems, no discontinuity in the flow behaviour is associated with the structural changes. The strong shear thinning is interpreted from the scattering data, as resulting from the nucleation of a new structure of hexagonal compact planes parallel to the Couette walls. This creates a lubricating domain in the gap, whose size grows with the applied shear rate. We argue moreover that the very existence of flow (as a steady state opposed to creep) is associated with this so-called layer-sliding structure in a fraction, however small, of the sample. Received on 4 June 1999 and Received in final form 6 September 1999     

Kinematic segregation of granular mixtures in sandpiles

We study the segregation of granular mixtures in two-dimensional silos using a recently proposed set of coupled equations for surface flows of grains. We study the thick flow regime, where the grains are segregated in the rolling phase. We incorporate this dynamical segregation process, called kinematic sieving, free-surface segregation or percolation, into the theoretical formalism and calculate the profiles of the rolling species and the concentration of grains in the bulk in the steady state. Our solution shows the segregation of the mixture with the large grains being found at the bottom of the pile in qualitative agreement with experiments. Received: 6 July 1998 / Revised and Accepted: 13 August 1998     

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     

Electric field light scattering by flexible linear polyelectrolytes in aqueous solution

Electric field light scattering results on aqueous solutions of linear, flexible NaPSS at minimal ionic strength are reported. Samples of molecular weights between 356 kg/mol and 2870 kg/mol were investigated. With increasing field strength the intensity as a function of wavenumber develops a pronounced oscillating behaviour. Besides the well-known first peak a second maximum is observed at the position at which a weak maximum for some samples already occurs at zero field. The overall intensity strongly depends on the frequency of the electric field. The electro-optical effect shows a maximum at 300 kHz. Increasing the particle concentration gives a large increase of the peak maximum, normalized to concentration. If plotted versus scattering angle the relative intensity increase is maximum for samples of medium molecular weight. The results strongly indicate a stretching and alignment of the chains, thus leading to or enlarging the short range order of the chains. Received 9 April 1999 and Received in final form 18 August 1999     

Spatio-temporal patterns in the thermoconvection of a planar nematic layer: I. Weakly nonlinear models

We study theoretically the formation of convection patterns in a laterally extended planar nematic layer heated from below, in the linear and weakly nonlinear regimes. By reformulating the viscous coupling terms of the basic nematohydrodynamic equations, a simple interpretation of the flow effects on the director dynamics can be proposed. A detailed linear analysis of the problem is presented. A systematic method to investigate nonlinear mechanisms is developed, and exemplified by the study of the nonlinear saturation in rolls. The extension of the roll amplitude equation with the envelope formalism is used to characterize the dynamics of the roll modulations near threshold. Coupled envelope equations are shown to describe the structure of the point defects in zig-zags observed experimentally. Finally the bifurcation to the bimodal varicose is studied. The secondary wavevector in the bimodal appears to be selected by a rotation of the director in the horizontal plane. Quantitative predictions concerning the amplitude of this rotation are given. Received: 1st December 1997 / Revised: 25 May 1998 / Accepted: 2 June 1998