Growth and structure of nematic spherulites under shallow thermal quenches

The growth kinetics, shape, interfacial and internal orientation texture of a submicron nematic spherulite arising during the isotropic-to-nematic liquid crystal phase transformation under shallow thermal quenches is analyzed using theory, scaling, and numerical simulations based on the Landau – de Gennes model (The Physics of Liquid Crystals, 2nd edn. Clarendon, Oxford). The numerical computations from this model yield interfacial cusp formation that relaxes through the nucleation of two disclination lines of topological charge +1/2 and subsequently leads to intra-droplet texturing and a net topological charge within the spherulite of +1. The timing of these events suggests that cusp formation at the interface is intimately associated with the interfacial defect shedding mechanism (J. Chem. Phys. 124:244902, 2006) for shallow quenches. These results are different than predictions for deep quenches (J. Chem. Phys. 124:244902, 2006) where interfacial defect shedding leads to four defects and a net topological charge of +2. A liquid crystal dynamic shape equation is derived from the Landau – de Gennes model to account for the interface shape changes in terms of surface viscosity, the driving forces due to the uniaxial nematic-isotropic free energy difference, capillary forces, and friction forces, and used to semi-quantitatively show that during cusp formation and defect shedding, gradient elasticity, capillary forces and friction play significant roles in decelerating and accelerating the surface. An interfacial eigenvalue analysis shows that during the shallow quench, disclination lines nucleate within the interface itself and then texturize the nematic droplet as they migrate from within the interface to the bulk of the growing nematic droplet. After defect shedding, the spherulite is nearly circular and grows with constant velocity, in agreement with experiments. The results shed new light on intra-spherulite texturing mechanisms in phase ordering under weak driving forces.      

Optimization of shock-wave action on a spherical bubble in an ideal incompressible liquid

The possibility of controlling the oscillations of a spherical gas bubble in an ideal incompressible liquid is subjected to theoretical analysis. Liquid surface tension forces are not taken into account. The optimization process realizing a maximum of the radius amplitude and a maximum of the gas pressure in the bubble for a given impulsive change of pressure at infinity is considered. A shock-resonance bubble oscillation procedure giving stepwise pressure changes at the extrema of the radius is constructed. This problem is of interest in connection with the investigation of cavitation erosion [1] and processes in biological tissues [2–4]. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1988.     

Molecular dynamics simulation of annular flow boiling with the modified Lennard-Jones potential function

Molecular dynamics simulation of annular flow boiling in a nanochannel is numerically investigated. In this research, an annular flow model is developed to predict the superheated flow boiling heat transfer characteristics in a nanochannel. To characterize the forced annular boiling flow in a nanochannel, an external driving force F^?_\textext \overrightarrow {F}_{\text{ext}} ranging from 1 to 12 PN (PN = pico newton) is applied along the flow direction to inlet fluid particles during the simulation. Based on an annular flow model analysis, it is found that saturation condition and superheat degree have great influences on the liquid–vapor interface. Also, the results show that due to the relatively strong influence of the surface tension in small channels, the interface between the liquid film and the vapor core is fairly smooth, and the mean velocity along the stream-wise direction does not change anymore. Also, it is found that the heat flux values depend on the boundary conditions. Finally, the Green–Kubo formula is used to calculate the thermal conductivity of liquid Argon. The simulations predict thermal conductivity of liquid Argon quite well.     

Wave regimes on a nonisothermal film of a viscous liquid flowing down a vertical plane

A thin film flow of a viscous liquid flowing down a vertical wall in the field of the gravity force is studied. The values of temperatures on the solid wall and on the free surface are constant. The viscosity and thermal diffusivity are functions of temperature. An equation that describes the evolution of surface disturbances is derived for small flow rates in the long-wave approximation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 89–97, March–April, 2008.     

Shear response of monodomains of flow-aligning nematic liquid crystals: TIF model comparisons and effect of pre-tilt

This work is the continuation of a previous study [Van Horn BL, Winter HH (2000) Dynamics of shear aligning nematic liquid crystal monodomains. Rheol Acta 39:294–300] on the shear dynamics of monodomains of shear aligning nematic liquid crystals [NLC]. The strain dependence of director orientation has been experimentally investigated for monodomains of a NLC with various initial orientations. Comparison of experimental results to predictions using Ericksen's transversly isotropic fluid [TIF] model supports the validity of the TIF model for systems of low molecular weight NLCs. The TIF model has been used to examine the effect of pre-tilt on the dynamics of flow-aligning NLC monodomains. It is shown that small deviations from planar alignment (no pre-tilt) have a large effect on orientation dynamics.     

Microdroplet absorption by two-layer porous media

Microdroplet absorption by two-layer porous media is studied both theoretically and experimentally. A two-dimensional model for liquid flow from a droplet into a porous medium is presented and veri.ed based on a simultaneous numerical solution of the Euler equations taking into account surface tension forces and the unsteady filtration equation. The effect of the structural parameters of the two-layer porous medium (pore size in the layers, and the thickness and porosity of the layers) on the droplet absorption is analyzed. It is shown that the presence of the second layer can have a significant effect on the droplet absorption rate and the liquid distribution in the medium. The pore size is found to be the main parameter that governs the effect of the second layer. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 121–130, January–February, 2007.     

Thermal explosion during the flow of a viscous liquid

Frank-Kamenetskii has discussed a steady-state formulation of thermal explosions [1]. Bostandzhiyan et al. [2] and Bostandzhiyan and Chernyaeva [3] have shown, for the flow in a cylindrical tube of Newtonian and non-Newtonian liquids having a strong (nonlinear) temperature dependence of the viscosity, that a phenomenon analogous to thermal explosion may occur during the flow of a chemically inert liquid. Bostandzhiyan et al. [4] have also studied Couette flow and the flow between two rotating circular cylinders of a Newtonian liquid having the same temperature dependence for its viscosity. It was shown that, although the heat balance equation reduces to the equations of the steady-state theory of thermal explosion for the corresponding region, hydrodynamic thermal “explosion” was not observed in these cases. This phenomenon was found to be characteristic of only pressurized flows. Below, we study thermal explosions during the Poiseuille flow of a viscous, chemically reactive liquid in an infinite circular cylindrical tube, and during the motion of the liquid between infinite rotating cylinders. The combined effect of chemical and mechanical heat cources are considered. Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, Vol. 9, No. 5, pp. 38–43, 1968     

Mechanism of coagulation of disperse elements in media isolated from external actions

A physical model of the experimentally observed coagulation (the mutual approach) of spherical liquid, solid, and gaseous disperse elements (of diameter of up to1 cm) in polar liquid and viscoelastic thixotropic matrices when the system is completely isolated from the external forces and the gradient temperature and concentration fields is proposed. It is shown that a weak stress-field gradient is formed in a polar liquid or viscoelastic matrix in the presence of interphase at the matrix-spherical disperse element interface, i.e., when the capillary pressure is negative at the convex boundary of the matrix. If the second disperse particle enters into this field, the resulting force acts on it in the direction of the first particle, thus ensuring their coagulation over large time lapses. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 156–161, July–August, 1999.     

Force interaction of a sphere and a viscous liquid in the presence of a wall

The problem of the force interaction of a vibrating sphere and a viscous liquid bounded from outside by a rigid wall at rest is studied under the assumption that the largest displacement of the sphere is small compared to its radius and the radius of the sphere is small compared to the distance between the sphere and the wall surface. The liquid flow and the force exerted by the liquid on the sphere are determined. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol 41, No. 1, pp. 57–62, January–February, 2000.     

Dynamics of explosive boiling of drops at the superheat limit

A physical model for explosive boiling of drops is presented. Loss of stability of the liquid-vapor interface results in occurrence of evaporation fronts. Their propagation in a metastable liquid is determined by the vapor recoil momentum. Detachment of drops from the interface is due to thermocapillary forces. The validity of the model is supported by comparison of calculations with experimental data. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Science, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 83–91, November–December, 1999.     

Stability of small radial oscillations of a spherical layer of liquid

An isothermal spherical layer of a viscoelastic liquid described by the one-parameter Maxwell model is considered. When the model parameter is taken equal to zero, a model of a purely viscous Newtonian fluid is obtained. The stability of the spherical layer of liquid with respect to small radial perturbations of the velocity and pressure is investigated for both types of liquids. Leningrad. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 170–171, September–October, 1988.     

Unsteady gas well operating regimes

A model of a gas well containing liquid is considered, the nature of the steady-state regimes is investigated, and the causes of cyclical output are analyzed. In formulation the problem resembles the oil well gushing problem studied in [1]. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 162–164, November–December, 1986.     

Quasi-steady-state flows in a liquid film in a gas: Comparison of two methods of describing waves

The motion of thin films of a viscous incompressible liquid in a gas under the action of capillary forces is studied. The surface tension depends on the surfactant concentration, and the liquid is nonvolatile. The motion is described by the well-known model of quasi-steady-state viscous film flow. The linear-wave solutions are compared with the solution using the Navier-Stokes equations. Situations are studied where a solution close to the inviscid two-dimensional solutions exists and in the case of long wavelength, the occurrence of sound waves in the film due to the Gibbs surface elasticity is possible. The behavior of the exact solutions near the region of applicability of asymptotic equations is studied, and nonmonotonic dependences of the wave characteristics on wavenumber are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 103–111, May–June, 2007.     

Model problem of instantaneous motion of a three-phase contact line

Hydrodynamic problems of fluid flow with three-phase contact lines (for example, solid body-liquid-gas or solid body and two nonmixing liquids) are of special interest. Much attention has been paid lately to steady and quasisteady flows. Significantly unsteady problems of this kind have almost escaped consideration. In the present paper, we study a model problem of a significantly unsteady motion of a finite volume of an incompressible fluid with a three-phase contact line. The static contact angle is assumed to be right and the initial free surface of the liquid is assumed to be cylindrical. One of the planes instantaneously begins to move toward the other with a constant finite velocity. Flows with high Reynolds numbers and small capillary numbers are considered. Mass forces are ignored in the problem. The basic result is the construction of a formal asymptotic of the solution at small times. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 51–61, July–August, 1999.     

Kinematics of finite-strain elastic-inelastic deformation

Polar decomposition tensors are constructed for slightly disturbed kinematic elastic, inelastic, and thermal strain tensors. Provided that the inelastic and thermal site gradients are pure deformations without rotations, relations are obtained between inelastic small strains and small rotations and between thermal small strains and small rotations which transform an intermediate configuration to a close current configuration. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 165–172, January–February, 2008.     

Equilibrium of a free nonisothermal liquid film

The equilibrium of a free weightless liquid film fixed over a planar contour and acted upon by thermocapillary forces is studied. Trends in the behavior of free liquid films are important for understanding the processes occurring in foams. The equilibrium equations for a nonisothermal weightless free film are derived for the two limiting cases: the temperature of the film is considered a known function of the coordinates; the free surface of the film is thermally insulated. For the plane and axisymmetric cases, the existence conditions for the solutions of the resulting nonlinear boundary-value problems are found and their properties are studied. For the general case, an approximate solution of the equilibrium problem is obtained provided that the analogue of the Marangoni number is small. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 16–29, May–June, 2007.     

Lattice Gas Analysis of Liquid Front in Non-Crimp Fabrics

The liquid flow front during impregnation of non-crimp fabrics is considered. Irregularities in fibre bundle architecture lead to generation of bubbles at this front. The velocity of this interface is highly influenced by capillary forces mainly caused by the small fibres inside the bundles. In order to better understand which shapes the liquid front takes up at different conditions, a lattice gas model has been applied. First, the macroscopic properties of the solved gas in the liquid are discussed. Next, bubble inclusions are analyzed as to liquid–gas interface position and concentrations of minor component in each phase. The capillary effects at the fluid front are studied for systems both with and without gaps between the bundles. The flow in the interior of the fibre bundles is scrutinized, as well, by also considering the viscous stresses. The flow through unidirectional fabrics is considered by a one-dimensional model, which suggests that the liquid front inside bundles and gaps moves with the same speed when the liquid front inside the bundle has to catch up with the liquid front in the gap.     

Gravity-induced spreading of a drop of a viscous fluid over a surface

The unsteady-state nonlinear problem of spreading of a drop of a viscous fluid on the horizontal surface of a solid under the action of gravity and capillary forces is considered for small Reynolds numbers. The method of asymptotic matching is applied to solve the axisymmetrical problem of spreading when the gravity exerts a significant effect on the dynamics of the drop. The flow structure in the drop is determined at large times in the neighborhood of a self-similar solution. The ranges of applicability of the quasiequilibrium model of drop spreading with a dynamic edge angle and a self-similar solution are found. It is shown that the transition from one flow model to another occurs at very large Bond numbers. Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences, Tyumen’ 625000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 59–67, May–June, 1999.     

Effect of Thermal/Gravity Modulation on the Onset of Convection in a Maxwell Fluid Saturated Porous Layer

The effect of thermal/gravity modulation on the onset of convection in a Maxwell fluid saturated porous layer is investigated by a linear stability analysis. Modified Darcy–Maxwell model is used to describe the fluid motion. The regular perturbation method based on the small amplitude of modulation is employed to compute the critical Rayleigh number and the corresponding wavenumber. The stability of the system characterized by a correction Rayleigh number is calculated as a function of the viscoelastic parameter, Darcy–Prandtl number, normalized porosity, and the frequency of modulation. It is found that the low frequency symmetric thermal modulation is destabilizing while moderate and high frequency symmetric modulation is always stabilizing. The asymmetric modulation and lower wall temperature modulations are, in general, stabilizing while the system becomes unstable for large values of Darcy–Prandtl number and for small frequencies. It is shown that in general the gravity modulation produces a stabilizing effect on the onset of convection for moderate and high frequency. The small frequency gravity modulation is found to have destabilizing effect on the stability of the system.     

Mass transport effect on the heat transfer coefficient during boiling of multicomponent mixture

In this work a simplified calculation method taking into account the effect of mass transport on the heat transfer coefficient (HTC) during boiling of multicomponent mixture has been elaborated. The calculation results were compared with own experimental data for ternary system methanol–isopropanol–water and Grigoriev data [1] (acetone–methanol–water). The experiments were performed in different hydrodynamic conditions such as: pool boiling and liquid evaporation at the free surface of the falling film. The experimental data covered wide range of heat fluxes from 6 to 30 kW/m² in the case of liquid evaporation from the falling film and from 30 to 240 kW/m² for pool boiling. The analysis of the results indicates that the mass transfer resistance in the liquid phase caused a significant reduction of experimental value HTC in comparison to so-called ideal HTC.