An analytical analysis of vesicle tumbling under a shear flow

Vesicles under a shear flow exhibit a tank-treading motion of their membrane, while their long axis points with an angle < 45 degrees with respect to the shear stress if the viscosity contrast between the interior and the exterior is not large enough. Above a certain viscosity contrast, the vesicle undergoes a tumbling bifurcation, a bifurcation which is known for red blood cells. We have recently presented the full numerical analysis of this transition. In this paper, we introduce an analytical model that has the advantage of being both simple enough and capturing the essential features found numerically. The model is based on general considerations and does not resort to the explicit computation of the full hydrodynamic field inside and outside the vesicle.Comment: 19 pages, 9 figures, to be published in Phys. Rev.

Two-component plasma in a gravitational field: Thermodynamics

We revisit the model of the two-component plasma in a gravitational field, which mimics charged colloidal suspensions. We concentrate on the computation of the grand potential of the system. Also, a special sum rule for this model is presented.Comment: 7 pages, LaTeX2

Depletion potentials near geometrically structured substrates

Using the recently developed so-called White Bear version of Rosenfeld's Fundamental Measure Theory we calculate the depletion potentials between a hard-sphere colloidal particle in a solvent of small hard spheres and simple models of geometrically structured substrates: a right-angled wedge or edge. In the wedge geometry, there is a strong attraction beyond the corresponding one near a planar wall that significantly influences the structure of colloidal suspensions in wedges. In accordance with an experimental study, for the edge geometry we find a free energy barrier of the order of several $k_B T$ which repels a big colloidal particle from the edge.Comment: 7 pages, 7 figure

Numerical Solution of Hard-Core Mixtures

We study the equilibrium phase diagram of binary mixtures of hard spheres as well as of parallel hard cubes. A superior cluster algorithm allows us to establish and to access the demixed phase for both systems and to investigate the subtle interplay between short-range depletion and long-range demixing.Comment: 4 pages, 2 figure

The sediment of mixtures of charged colloids: segregation and inhomogeneous electric fields

We theoretically study sedimentation-diffusion equilibrium of dilute binary, ternary, and polydisperse mixtures of colloidal particles with different buoyant masses and/or charges. We focus on the low-salt regime, where the entropy of the screening ions drives spontaneous charge separation and the formation of an inhomogeneous macroscopic electric field. The resulting electric force lifts the colloids against gravity, yielding highly nonbarometric and even nonmonotonic colloidal density profiles. The most profound effect is the phenomenon of segregation into layers of colloids with equal mass-per-charge, including the possibility that heavy colloidal species float onto lighter ones

On the velocity distributions of the one-dimensional inelastic gas

We consider the single-particle velocity distribution of a one-dimensional fluid of inelastic particles. Both the freely evolving (cooling) system and the non-equilibrium stationary state obtained in the presence of random forcing are investigated, and special emphasis is paid to the small inelasticity limit. The results are obtained from analytical arguments applied to the Boltzmann equation along with three complementary numerical techniques (Molecular Dynamics, Direct Monte Carlo Simulation Methods and iterative solutions of integro-differential kinetic equations). For the freely cooling fluid, we investigate in detail the scaling properties of the bimodal velocity distribution emerging close to elasticity and calculate the scaling function associated with the distribution function. In the heated steady state, we find that, depending on the inelasticity, the distribution function may display two different stretched exponential tails at large velocities. The inelasticity dependence of the crossover velocity is determined and it is found that the extremely high velocity tail may not be observable at ``experimentally relevant'' inelasticities.Comment: Latex, 14 pages, 12 eps figure

Statistical mechanics of a colloidal suspension in contact with a fluctuating membrane

Surface effects are generally prevailing in confined colloidal systems. Here we report on dispersed nanoparticles close to a fluid membrane. Exact results regarding the static organization are derived for a dilute solution of non-adhesive colloids. It is shown that thermal fluctuations of the membrane broaden the density profile, but on average colloids are neither accumulated nor depleted near the surface. The radial correlation function is also evaluated, from which we obtain the effective pair-potential between colloids. This entropically-driven interaction shares many similarities with the familiar depletion interaction. It is shown to be always attractive with range controlled by the membrane correlation length. The depth of the potential well is comparable to the thermal energy, but depends only indirectly upon membrane rigidity. Consequenses for stability of the suspension are also discussed

Theory of asymmetric non-additive binary hard-sphere mixtures

We show that the formal procedure of integrating out the degrees of freedom of the small spheres in a binary hard-sphere mixture works equally well for non-additive as it does for additive mixtures. For highly asymmetric mixtures (small size ratios) the resulting effective Hamiltonian of the one-component fluid of big spheres, which consists of an infinite number of many-body interactions, should be accurately approximated by truncating after the term describing the effective pair interaction. Using a density functional treatment developed originally for additive hard-sphere mixtures we determine the zero, one, and two-body contribution to the effective Hamiltonian. We demonstrate that even small degrees of positive or negative non-additivity have significant effect on the shape of the depletion potential. The second virial coefficient $B_2$, corresponding to the effective pair interaction between two big spheres, is found to be a sensitive measure of the effects of non-additivity. The variation of $B_2$ with the density of the small spheres shows significantly different behavior for additive, slightly positive and slightly negative non-additive mixtures. We discuss the possible repercussions of these results for the phase behavior of binary hard-sphere mixtures and suggest that measurements of $B_2$ might provide a means of determining the degree of non-additivity in real colloidal mixtures

Towards a quantitative phase-field model of two-phase solidification

We construct a diffuse-interface model of two-phase solidification that quantitatively reproduces the classic free boundary problem on solid-liquid interfaces in the thin-interface limit. Convergence tests and comparisons with boundary integral simulations of eutectic growth show good accuracy for steady-state lamellae, but the results for limit cycles depend on the interface thickness through the trijunction behavior. This raises the fundamental issue of diffuse multiple-junction dynamics.Comment: 4 pages, 2 figures. Better final discussion. 1 reference adde

Phase behaviour of additive binary mixtures in the limit of infinite asymmetry

We provide an exact mapping between the density functional of a binary mixture and that of the effective one-component fluid in the limit of infinite asymmetry. The fluid of parallel hard cubes is thus mapped onto that of parallel adhesive hard cubes. Its phase behaviour reveals that demixing of a very asymmetric mixture can only occur between a solvent-rich fluid and a permeated large particle solid or between two large particle solids with different packing fractions. Comparing with hard spheres mixtures we conclude that the phase behaviour of very asymmetric hard-particle mixtures can be determined from that of the large component interacting via an adhesive-like potential.Comment: Full rewriting of the paper (also new title). 4 pages, LaTeX, uses revtex, multicol, epsfig, and amstex style files, to appear in Phys. Rev. E (Rapid Comm.