Waves on the interface between a nematic liquid crystal and an ideal isotropic fluid

The problem of surface wave propagation over the interface between a nematic liquid crystal and an ideal isotropic fluid is considered. For the nematic liquid crystal the Frank-Oseen model with an isotropic viscous stress tensor is used. Anisotropic surface tension is described by the Rapini model. In this formulation, for the problem of harmonic small-amplitude surface wave propagation, in the case of infinite depths of both phases, an analytical solution is obtained. The dispersion relation is derived and its properties are investigated.     

Capillary and gravitational convection in a droplet immersed in a nonuniformly heated liquid

Under the conditions of the Plato technique, the problem of convection in a droplet immersed in a nonuniformly heated liquid is solved analytically. The influence of gravitational convection on the thermocapillary flow is studied. In the linear approximation with respect to the Marangoni and Grashof numbers and their product, the shape of the droplet and the displacement of its center of the mass are obtained.Perm. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 43–51, July–August, 1996.     

Motion of a liquid droplet in a vibrating fluid

The motion of a liquid droplet in a liquid with density different from that of the liquid composing the droplet and subjected to harmonic excitations is investigated. Nonlinear equations are obtained that describe the translational motion of the droplet and its oscillations. It is shown by numerical means that, under the essential resonance conditions, the droplet ascends by a cascade method if the value of the load coefficient is small.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 7, pp. 78–83, July, 1995.     

The flow field induced by an oscillating fluid drop immersed in another fluid

The flow field induced by a translatory oscillating spherical drop immersed in another fluid is considered. It is assumed that the amplitude of the oscillation is small compared with the radius of the drop. We are concerned, for the most part, with the case of a small frequency parameter M. Of particular interest is the steady streaming induced both inside and outside of the drop. The problem has been solved on the basis of the Navier-Stokes equations by the method of matched asymptotic expansions.     

Wave propagation in a transversely isotropic solid cylinder of arbitrary cross-sections immersed in fluid

The wave propagation in an infinite, transversely isotropic solid cylinder of arbitrary cross-section immersed in fluid is studied using the Fourier expansion collocation method, within the framework of the linearized, three-dimensional theory of elasticity. The equations of motion of solid and fluid are respectively formulated using the constitutive equations of a transversely isotropic cylinder and the constitutive equation of an inviscid fluid. Three displacement potential functions are introduced to uncouple the equations of motion along the radial, circumferential and axial directions. The frequency equations of longitudinal and flexural (symmetric and antisymmetric) modes are analyzed numerically for an elliptic and cardioidal cross-sectional transversely isotropic solid cylinder of arbitrary cross-section immersed in fluid. The computed non-dimensional wavenumbers are presented in the form of dispersion curves for the material zinc. The general theory can be used to study any kind of cylinder with proper geometric relations.     

Transition from droplet flow to stream flow in a liquid

The transition from droplet flow to stream flow is examined theoretically for flow of liquid from a vertical capillary and runoff from the edge of an inclined plane under the influence of the force of gravity, and also for spraying of a liquid from a rotating perforated drum and a smooth disk. The formulas proposed agree satisfactorily with experiment.     

Fluid-structure interaction with an application to a body immersed and anchored in a fluid flow

In this paper, an implicit coupling algorithm for fluid–structure interaction problems with under-time steps for the solid is presented. Its implementation on two configurations is achieved by using the CASTEM finite-elements code. First, the free oscillations of a cylinder in an annular fluid domain where its movement is determined by the coupled fluid–solid action is considered in the case of viscous fluid. It should be noted that the implicit coupling algorithm gives the best prediction of the structure oscillations. The under-time steps for the solid are introduced in order to obtain better results. Then, an application whose final objective is to model a floating barrage is studied. The main goal of this application is to predict the displacements of a ring completely immersed and anchored by a cable to the lower boundary of the fluid domain. The finite-element discretization of the Navier–Stokes equations in the ALE formulation is used     

Surface waves in a deformed isotropic hyperelastic material subject to an isotropic internal constraint

An isotropic elastic half-space is prestrained so that two of the principal axes of strain lie in the bounding plane, which itself remains free of traction. The material is subject to an isotropic constraint of arbitrary nature. A surface wave is propagated sinusoidally along the bounding surface in the direction of a principal axis of strain and decays away from the surface. The exact secular equation is derived by a direct method for such a principal surface wave; it is cubic in a quantity whose square is linearly related to the squared wave speed. For the prestrained material, replacing the squared wave speed by zero gives an explicit bifurcation, or stability, criterion. Conditions on the existence and uniqueness of surface waves are given. The bifurcation criterion is derived for specific strain energies in the case of four isotropic constraints: those of incompressibility, Bell, constant area, and Ericksen. In each case investigated, the bifurcation criterion is found to be of a universal nature in that it depends only on the principal stretches, not on the material constants. Some results related to the surface stability of arterial wall mechanics are also presented.     

Automatic liquid crystal thermography for transient heat transfer measurements in hypersonic flow

A technique has been developed to measure surface heat transfer on windtunnel models in hypersonic flow based on the colour response of encapsulated thermochromic liquid crystals. The method supplies results of a superior spatial resolution at experimental uncertainties comparable to traditional methods. The approach is different from other liquid crystal applications in several key areas. It combines the calibration of the liquid crystal coating with the actual mesurement and therefore allows for an efficient experiment. The method is automated in most steps involved. Results are shown for the flow over an axisymmetric compression corner at Mach 5 and compared with surface thermocouple measurements.     

Evaporation of a droplet larger than the Kolmogorov length scale immersed in a relative mean flow

An experimental effort to understand the contribution of turbulence to the evaporation rate of fuel droplets has been performed with particular attention to conditions when the turbulence scale is smaller than the droplet diameter. N-heptane has been chosen as working fluid to give measurable evaporation rates from droplet images over relatively short experiment times. An active turbulence grid wind tunnel is built for the requirements of this experiment. A camera triggered by a pulse generator takes images of the droplets pinned on wires across the tunnel. The results show a small increase in evaporation rate with increasing turbulence intensity, and that mean flow around the droplets has more impact on evaporation than does the turbulence state.     

Motion of a deformed contour in a flow of an ideal incompressible liquid with a constant vorticity

The article gives a solution to the plane problem of the motion of a deformed contour in a flow of an ideal incompressible liquid with a constant vorticity. An explicit expression is obtained for the hydrodynamic force when the velocity of the external flow depends linearly on the coordinates. In the case of a contour of small dimensions, this expression is valid also for an arbitrary external flow.     

Assessment of volume of fluid and immersed boundary methods for droplet computations

The volume of fluid (VOF) and immersed boundary (IB) methods are two popular computational techniques for multi‐fluid dynamics. To help shed light on the performance of both techniques, we present accuracy assessment, which includes interfacial geometry, detailed and global fluid flow characteristics, and computational robustness. The investigation includes the simulations of a droplet under static equilibrium as a limiting test case and a droplet rising due to gravity for Re?1000. Surface tension force models are key issues in both VOF and IB and alternative treatments are examined resulting in improved solution accuracy. A refined curvature model for VOF is also presented. With the newly developed interfacial treatments incorporated, both IB and VOF perform comparably well for the droplet dynamics under different flow parameters and fluid properties. Copyright © 2004 John Wiley & Sons, Ltd.     

Asymptotic analysis of a pulsating flow of viscous fluid in a symmetric deformed channel

The time-periodic flow of a viscous incompressible fluid in a two-dimensional symmetric channel with slightly deformed walls is considered. The solution of the Navier-Stokes equations is constructed by means of the method of matched asymptotic expansions [1] at large characteristic Reynolds numbers. It is shown that in an unsteady flow a region of nonlinear perturbations surrounds the line of zero velocity inside the fluid. The formation and development of such nonlinear zones with respect to time is considered. An alternation of the topological features of the streamline pattern in the nonlinear perturbation zone is discovered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 17–23, July–August, 1987.The author is deeply grateful to V. V. Sychev for his formulation of the problem and his attentive attitude to my work.     

Optical response of a layer of a nematic liquid crystal to an air flow

A liquid crystal coating is used to measure the surface friction created when a flat plate is subjected to an air flow. Surface friction is determined from the optical response of the nematic liquid crystal coating to the flow. The proposed method does not require precise monitoring of the thickness of the coating or the angles of illumination and observation. This makes it possible to eventually progress to panoramic measurements of surface aerodynamic characteristics. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 102–109, July–August, 1998.     

Unsteady two-dimensional rotation of a viscous fluid for steady source flow

We obtain the solution of the Navier-Stokes equations for one class of unsteady axisymmetric two-dimensional rotational flows for the case of a line source or sink of constant intensity in the fluid.     

Effect of particles suspended in a fluid flow on the decay of isotropic turbulence

Dynamic equations have been obtained for the two-point double correlations of the fluctuation velocities of a fluid and the particles suspended in it at low volume concentrations of the solid phase. In the case of uniform isotropic turbulence these equations can be considerably simplified. The final period of decay of isotropic turbulence has been studied in detail. At this stage in the case of high-inertia particles the inhomogeneous-fluid turbulence is similar to the turbulence of a homogeneous fluid (without particles) in the sense that the presence of the particles affects only the fluctuation energy but leaves unchanged the spatial scales of turbulence and the spatial energy spectrum function. The suspended particles lead to exponential damping of the turbulent pulsations.Little theoretical information is available on the hydrodynamics of a suspension of fine particles in a turbulent liquid or gas. Research has been mainly confined to the behavior of the individual particles in a given turbulence field [1]. The problem of the turbulent motion of the mixture as a whole has been examined by Barenblatt [2], who derived the equations of motion of the mixture, using Kolmogorov's hypothesis to close them. Hinze [3] has also attempted to derive equations for turbulent pulsations of the mixture. However, as Murray showed [4], Hinze' s equations contradict Newton' s third law.The effect of suspended particles on the turbulence of a two-phase flow is governed by the noncorrespondence of the local velocities of the particles and the medium. The forces of resistance to the motion of the particles relative to the fluid lead to additional dissipation of fluctuation energy and decay of turbulence [2]. On the other hand, if the averaged velocities of particles and medium do not correspond, the suspended particles may also have a destabilizing effect [5, 6], causing energy transfer from the averaged to the pulsating motion. Below we shall consider the case where the averaged velocities of the two phases coincide, i.e., we shall deal only with the first of the two above-mentioned effects.The authors thank G.I. Barenblatt for his useful advice.     

Transitions in Poiseuille flow of nematic liquid crystal

Recent experiments by Sengupta et al. (Phys. Rev. Lett. 2013) [9] revealed interesting transitions that can occur in flow of nematic liquid crystal under carefully controlled conditions within a long microfluidic channel of width much larger than height, and homeotropic anchoring at the walls. At low flow rates the director field of the nematic adopts a configuration that is dominated by the surface anchoring, being nearly parallel to the channel height direction over most of the cross-section; but at high flow rates there is a transition to a flow-dominated state, where the director configuration at the channel centerline is aligned with the flow (perpendicular to the channel height direction). We analyze simple channel-flow solutions to the Leslie–Ericksen model for nematics. We demonstrate that two solutions exist, at all flow rates, but that there is a transition between the elastic free energies of these solutions: the anchoring-dominated solution has the lowest energy at low flow rates, and the flow-dominated solution has lowest energy at high flow rates.