Microconvection in a Binary System

On the basis of an essentially subsonic-flow approximation, the effect of small density variations of the medium on the development of natural convection in a slightly nonisothermal binary mixture at very small Rayleigh numbers and a constant mean thermodynamic pressure (microconvection) is studied analytically and numerically. Microconvective flows are characterized by a nonsolenoidal velocity field. As compared with microconvection in pure fluid, the presence of an admixture and the thermodiffusion effect result in a number of new interesting opportunities. Attention is mainly focused on essentially unsteady processes (transition processes after two different media are brought into contact and convection in rapidly varying temperature fields), in which the medium volume expansion is very significant. The conditions of onset of monotonic modes of the Rayleigh-Bénard and Bénard-Marangoni long-wave instabilities are also considered.     

A Statistical Model for Short-Wavelength Collective Chain Fluctuations in a Lipid Bilayer under a High External Electric Field

JETP Letters - The influence of a high (~1 V/nm) external electric field on biological soft matter systems has been widely studied for a long time. However, a detailed understanding of the behavior...     

Stability of motion in a planar layer of inhomogeneous ideal incompressible liquid having free boundaries

Research performed with financial support from the Krasnoyarsk Scientific Fund (Project Code 2F0059).     

Nonlinear Electrohydrodynamic Stability of a Poiseuille Two–Layer Flow

The long–wave stability of the Poiseuille two–layer flow of homogeneous viscous dielectrics between plate electrodes under a constant potential difference is studied in an electrohydrodynamic approximation. A linear asymptotic stability analysis shows that surface polarization forces are a destabilizing factor, in addition to viscous stratification. The method of many scales is used to obtain the Kuramoto—Sivashinsky equation governing the weakly nonlinear evolution of the interface between the dielectrics. Within the framework of the approaches used, it is shown that nonlinear interactions limit perturbation growth and the interface does not fail even for a rather large potential difference.     

Bénard-Marangoni Instability of a Two-Layer System with Allowance for Variations in the Interfacial Internal Energy

The effect of variations of the internal surface energy due to local increments in the interfacial area on the conditions of onset of thermocapillary Marangoni instability in a two-layer system of reduced-viscosity fluids is studied. It is shown that in the linear approximation the effect considered leads to stabilization of the development of the monotonic instability mode.     

Subterahertz Longitudinal Phonon Modes Propagating in a Lipid Bilayer Immersed in an Aqueous Medium

The properties of subterahertz longitudinal acoustic phonon modes in the hydrophobic region of a lipid bilayer immersed in a compressible viscous aqueous medium are investigated theoretically. An approximate expression is obtained for the Mandelstam–Brillouin components of the dynamic structure factor of a bilayer. The analysis is based on a generalized hydrodynamic model of the “two-dimensional lipid bilayer + three-dimensional fluid medium” system, as well as on known sharp estimates for the frequencies and lifetimes of long-wavelength longitudinal acoustic phonons in a free hydrated lipid bilayer and in water, obtained from inelastic X-ray scattering experiments and molecular dynamics simulations. It is shown that, for characteristic values of the parameters of the membrane system, subterahertz longitudinal phonon-like excitations in the hydrophobic part of the bilayer are underdamped. In this case, the contribution of the viscous flow of the aqueous medium to the damping of a longitudinal membrane mode is small compared with the contribution of the lipid bilayer. Quantitative estimates of the damping ratio agree well with the experimental results for the vibration mode of the enzyme lysozyme in aqueous solution [1]. It is also shown that a coupling between longitudinal phonon modes of the bilayer and relaxation processes in its fluid environment gives rise to an additional peak in the scattering spectrum, which corresponds to a non-propagating mode.     

Refined dynamic structure factor of a lipid bilayer on scales comparable to its thickness

The structural inhomogeneity of a lipid bilayer is an obstacle to applying the classical Canham–Helfrich model to describe its dynamics on nanometer length scales. In this paper, a refined expression for the free energy of a single-component lipid bilayer is used to describe the dynamics of lipid density fluctuations. In particular, the expression with a term involving the gradient of the area per lipid [8] is used for the free energy per lipid. A refined expression has been derived for the dynamic structure factor of a free lipid bilayer in the hydrodynamic region. It leads to differences in the interpretation and values of the bilayer parameters in comparison with the standard model.     

Nonboussinesq Thermal Convection in Microgravity under Nonuniform Heating

The model of subsonic flows is used to numerically the effect of thermal expansion of a fluid on the formation of naturally convective flows for small Rayleigh numbers (microconvection) and spatially periodic distribution of heat flows on the boundaries of the domain occupied by the fluid.     

Longwave instability of two-layer dielectric fluid flows in a transverse electrostatic field

Some aspects of the problem of the stability and the nature of the secondary regimes of a plane two-layer Poiseuille flow of viscous dielectric fluids between horizontal electrodes with a constant potential difference are considered. A linear analysis shows that the electrostatic field can induce the growth of perturbations with an asymptotically small wavenumber when the dielectric permeabilities of the fluids are different. On the assumption that the perturbation wavelength is large as compared with the thickness of one of the layers and comparable with the thickness of the other in order of magnitude, one of the possible mechanisms of development of finite fluctuations is investigated. Within the framework of this mechanism the initial mathematical mdoel can be reduced to an integrodifferential evolutionary Kuramoto-Sivashinsky-type equation describing the behavior of the fluid interface. The periodic solutions of this equation, which are investigated numerically, are bounded and fairly diverse. Krasnoyarsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 45–55, March–April, 2000.     

Delocalization of Longitudinal Acoustic-Like Excitations in DNA Due to Structural Effects

Terahertz-frequency phonon-like modes in DNA have been widely studied both experimentally and theoretically in recent years. However, current theoretical models turn out to fail to reproduce some basic properties of these modes. Using a generalized hydrodynamics approach and the results of inelastic X-ray scattering measurements, we propose a model to describe structural effects due to wavenumber dependence of the static structure factor in the dynamics of longitudinal acoustic-like excitations in DNA. Our analysis qualitatively suggests that on a length scale corresponding to a wavenumber region between the positions of the maximum and the minimum of the dispersion relation for the excitation frequency, structural effects may induce a tendency of delocalization of the dynamics. This proposal is consistent with the recent experimental observations of delocalized terahertz-frequency DNA phonon-like modes that seem to be relevant to biological function.