Effect of surface charges on the curvature moduli of a membrane

The modification of the curvature moduli due to surface charges in lipid bilayers is analyzed using the nonlinear Poisson-Boltzmann equation for the relationship between the charge density and surface potential. An expansion in a small parameter ε, which is the ratio of the Debye length and the radius of curvature, is used. At low charge densities, previous results obtained from the Debye-Huckel approximation are recovered. At high charge densities, the corrections to the mean and Gaussian curvature approach constant values. The total energy of curvature for a symmetrically charged membrane becomes negative when the charge density is increased beyond a critical value, indicating that the membrane spontaneously forms vesicles. An asymmetry in the charge densities on the two monolayers that form the bilayer results in a spontaneous curvature, and the radius of curvature could be large compared to the Debye length when the asymmetry is small. The case of adsorbed charges is also considered, where there is a reduction in the chemical energy when a charge is adsorbed on the surface. At low charge density, the mean and Gaussian curvature are equal in magnitude and opposite in sign to that for fixed charges, while at high charge density, the mean and Gaussian curvature approach values identical to that for a surface with fixed charges. Numerical calculations of the change in the curvature moduli with realistic parameter values indicate that these effects are likely to be of importance in the spontaneous formation of vesicles

Electrohydrodynamic instability of a charged membrane

The stability of shape fluctuations of a flat charged membrane immersed in a fluid is analyzed using a linear stability analysis. A displacement of the membrane surface causes a fluctuation in the conterion density at the surface. This in turn causes an additional contribution to the force density in the momentum equation for the fluid, which results in a normal stress at the surface which is opposite in direction to the stress caused by surface tension. This electrohydrodynamic effect destabilizes fluctuations when the surface potential exceeds a critical value

Temperature scaling in a dense vibro-fluidised granular material

The leading order "temperature" of a dense two dimensional granular material fluidised by external vibrations is determined. An asymptotic solution is obtained where the particles are considered to be elastic in the leading approximation. The velocity distribution is a Maxwell-Boltzmann distribution in the leading approximation. The density profile is determined by solving the momentum balance equation in the vertical direction, where the relation between the pressure and density is provided by the virial equation of state. The predictions of the present analysis show good agreement with simulation results at higher densities where theories for a dilute vibrated granular material, with the pressure-density relation provided by the ideal gas law, are in error. The theory also predicts the scaling relations of the total dissipation in the bed reported by McNamara and Luding (PRE v 58, p 813).Comment: ReVTeX (psfrag), 5 pages, 5 figures, Submitted to PR

Stability of wall modes in fluid flow past a flexible surface

The stability of wall modes in fluid flow past a flexible surface is analyzed using asymptotic and numerical methods. The fluid is Newtonian, while two different models are used to represent the flexible wall. In the first model, the flexible wall is modeled as a spring-backed, plate-membrane-type wall, while in the second model the flexible wall is considered to be an incompressible viscoelastic solid of finite thickness. In the limit of high Reynolds number (Re), the vorticity of the wall modes is confined to a region of thickness O(Re-1/3) in the fluid near the wall of the channel. An asymptotic analysis is carried out in the limit of high Reynolds number for Couette flow past a flexible surface, and the results show that wall modes are always stable in this limit if the plate-membrane wall executes motion purely normal to the surface. However, the flow is shown to be unstable in the limit of high Reynolds number when the wall can deform in the tangential direction. The asymptotic results for this case are in good agreement with the numerical solution of the complete governing stability equations. It is further shown using a scaling analysis that the high Reynolds number wall mode instability is independent of the details of the base flow velocity profile within the channel, and is dependent only on the velocity gradient of the base flow at the wall. A similar asymptotic analysis for flow past a viscoelastic medium of finite thickness indicates that the wall modes are unstable in the limit of high Reynolds number, thus showing that the wall mode instability is independent of the wall model used to represent the flexible wall. The asymptotic results for this case are in excellent agreement with a previous numerical study of Srivatsan and Kumaran

Asymptotic analysis of wall modes in a flexible tube revisited

The stability of wall modes in fluid flow through a flexible tube of radius R surrounded by a viscoelastic material in the region R < r < HR is analysed using a combination of asymptotic and numerical methods. The fluid is Newtonian, while the flexible wall is modelled as an incompressible viscoelastic solid. In the limit of high Reynolds number (Re), the vorticity of the wall modes is confined to a region of thickness O(Re -1/3) in the fluid near the wall of the tube. Previous numerical studies on the stability of Hagen-Poiseuille flow in a flexible tube to axisymmetric disturbances have shown that the flow could be unstable in the limit of high Re, while previous high Reynolds number asymptotic analyses have revealed only stable modes. To resolve this discrepancy, the present work re-examines the asymptotic analysis of wall modes in a flexible tube using a new set of scaling assumptions. It is shown that wall modes in Hagen-Poiseuille flow in a flexible tube are indeed unstable in the limit of high Re in the scaling regime Re~Σ¾. Here Σ is a nondimensional parameter characterising the elasticity of the wall, and Σ≡ρGR2/η2, where ρ and η are the density and viscosity of the fluid, and G is the shear modulus of the wall medium. The results from the present asymptotic analysis are in excellent agreement with the previous numerical results. Importantly, the present work shows that the different types of unstable modes at high Reynolds number reported in previous numerical studies are qualitatively the same: they all belong to the class of unstable wall modes predicted in this paper

Darcy-Brinkman free convection about a wedge and a cone subjected to a mixed thermal boundary condition

The Darcy-Brinkman free convection near a wedge and a cone in a porous medium with high porosity has been considered. The surfaces are subjected to a mixed thermal boundary condition characterized by a parameter m; m=0, 1, ∞ correspond to the cases of prescribed temperature, prescribed heat flux and prescribed heat transfer coefficient respectively. It is shown that the solutions for different m are dependent and a transformation group has been found, through which one can get solution for any m provided solution for a particular value of m is known. The effects of Darcy number on skin friction and rate of heat transfer are analyzed

Characterization of the stationary states of a dilute vibrofluidized granular bed

This paper reports two phenomena in an event driven simulation of a dilute vibrofluidized granular material in two dimensions. Both phenomena show inhomogeneity in the horizontal direction. They are convection rolls similar to the Rayleigh-Benard thermal convection in fluids, and a clustering instability, where the bed spontaneously phase separates into coexisting dense and dilute regions. Detailed investigations show that these are different from the known instabilities in a vibrated granular medium. Characterization of these instabilities is carried out with a phase diagram using suitable parameters from the kinetic theory of vibrofluidized beds

Structure and Rheology of the Defect-gel States of Pure and Particle-dispersed Lyotropic Lamellar Phases

We present important new results from light-microscopy and rheometry on a moderately concentrated lyotropic smectic, with and without particulate additives. Shear-treatment aligns the phase rapidly, except for a striking network of oily-streak defects, which anneals out much more slowly. If spherical particles several microns in diameter are dispersed in the lamellar medium, part of the defect network persists under shear-treatment, its nodes anchored on the particles. The sample as prepared has substantial storage and loss moduli, both of which decrease steadily under shear-treatment. Adding particles enhances the moduli and retards their decay under shear. The data for the frequency-dependent storage modulus after various durations of shear-treatment can be scaled to collapse onto a single curve. The elasticity and dissipation in these samples thus arises mainly from the defect network, not directly from the smectic elasticity and hydrodynamics.Comment: 19 pages inclusive of 12 PostScript figures, uses revtex, psfrag and epsfig. Revised version, accepted for publication in Euro. Phys. J. B, with improved images of defect structure and theoretical estimates of network elasticity and scalin