Self-similar growth of a gas hydrate layer separating gas and liquid

The plane one-dimensional Stefan-type problem of the growth of a layer of solid phase separating a gas and a liquid is studied. A self-similar solution and the necessary conditions of its existence are obtained. A number of estimates of the characteristic rates of growth of the layer and the concentration and temperature gradients in the phases are presented, and the results of calculating the growth of the hydrate layer in a water-methane system at a pressure of 10 MPa and a temperature of 283°K are analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 78–85, September–October, 1992.     

Wave development on a thinning liquid film

Experimental results are presented for the growth of surface waves on a liquid film that thins as it flows under gravity over the surface of an upright circular cone. The characteristics of the mean film are calculated on the assumption of quasi-parallel flow, and the actual mean thickness found to relate very closely to that found on this basis. The development of the film was found to fall into three phases: the entry zone in which the velocity profile of the film becomes established where no waves are visible, a region of wave growth in which amplitude, wave speed, and wave length all grow, and a final region in which amplitude and wave speed decline as the film thins further although wave length continues to grow. An empirical relationship is presented which expresses the wave number at any point on the cone in terms of the flow rate and a parameter based on the local Reynolds and Weber numbers and cone angle. It was found that for a given flow rate the maximum wave amplitude was reached at a value of wave number of 0·048.     

Modelling the wetting of a solid occlusion by a liquid film

We investigate in this work how the presence of an occlusion affects the dynamics of the wetting front of a liquid film draining down a vertical surface. This numerical study is developed in the context of the lubrication approximation. Through a parametric study, we show that depending on the asymptotic film thickness and the fluid properties, there exists a critical substrate contact angle below which separation of the contact line from the occlusion wall is observed which results in the appearance of a dry zone in the wake of the occlusion. In analogy with external aerodynamics, we also show that a sharp corner in the occlusion can induce this contact line separation. Our numerical results also highlight the importance of the occlusion wettability on the morphology of the wetting front suggesting a possible mechanism to control and mitigate the often undesirable fingering instability.     

Self-similar collapse of a circular cavity of a power-law liquid

Using the lubrication approximation we investigate the self-similar axisymmetric flow of a power-law liquid towards a central circular cavity. It is shown that this problem has a self-similar solution of the second kind. The self-similarity exponent is found by solving a non-linear eigenvalue problem arising from the requirement that the integral curve that represents the solution must join the appropriate singular points in the phase plane of the governing equation. The eigenvalues for different values of the rheological index are computed. Numerical integration of the equations allows us to determine the shape of the solution in terms of the physical variables. We make a detailed analysis of the influence of the rheology on the properties of the solutions.     

Dynamic equilibrium shape of a film of viscous or viscoelastic liquid

A theoretical and experimental investigation has been made into the dynamic equilibrium shape of an axisymmetric film of liquid formed when a jet encounters an obstacle. It is shown that the stresses due to elastic deformation of the liquid have a significant influence on films of polymer solutions. The elastic moduli of solutions of polyoxyethylene and polyacrylamide are estimated from experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 9–18, March–April, 1980.     

Lattice Boltzmann study of the interaction between a single solid particle and a thin liquid film

The isothermal single-component multi-phase lattice Boltzmann method(LBM) combined with the particle motion model is used to simulate the detailed process of liquid film rupture induced by a single spherical particle.The entire process of the liquid film rupture can be divided into two stages.In Stage 1,the particle contacts with the liquid film and moves into it due to the interfacial force and finally penetrates the liquid film.Then in Stage 2,the upper and lower liquid surfaces of the thin fi...     

A relation between the jump in temperature across a propagating phase boundary and the stability of solid phases

Unlike the phases of ordinary fluids, solid phases are often found to occur in metastable equilibrium. At constant temperature, a stress-extension test on a bar made of a material which allows the co-existence of two phases will often produce a large hysterysis loop. It is then impossible, by static measurements alone, to determine the values of stress *^* and temperature ^* at which the two phases have the same specific free energy. I show that by a measurement of the jump in temperature across a propagating phase boundary, (^*, ^*) can be determined in several cases of interest.The analysis offers insight into the general behavior of propagating phase boundaries as well as the thermodynamics of solid phases.The discussion is centered around the so-called shape-memory alloys.     

RESEARCH ON METHOD TO CALCULATE VELOCITIES OF SOLID PHASE AND LIQUID PHASE IN DEBRIS FLOW

Velocities of solid phase and liquid phase in debris flow are one key problem to research on impact and abrasion mechanism of banks and control structures under action of debris flow. Debris flow was simplified as two-phase liquid composed of solid phase with the same diameter particles and liquid phase with the same mechanical features. Assume debris flow was one-dimension two-phase liquid moving to one direction, then general equations of velocities of solid phase and liquid phase were founded in two-phase theory. Methods to calculate average pressures, volume forces and surface forces of debris flow control volume were established. Specially, surface forces were ascertained using Bingham's rheology equation of liquid phase and Bagnold's testing results about interaction between particles of solid phase. Proportional coefficient of velocities between liquid phase and solid phase was put forward, meanwhile, divergent coefficient between theoretical velocity and real velocity of solid phase was provided too. To state succinctly before, method to calculate velocities of solid phase and liquid phase was obtained through solution to general equations. The method is suitable for both viscous debris flow and thin debris flow. Additionally, velocities every phase can be identified through analyzing deposits in-situ after occurring of debris flow. It is obvious from engineering case the result in the method is consistent to that in real-time field observation.     

Simultaneous characterization of multiple properties of solid and liquid phases in crystallization processes using NIR

Near infrared spectroscopy (NIR) is now probably the most popular process analytical technology (PAT) for pharmaceutical and some other industries. However, unlike mid-IR, NIR is known to have difficulties in monitoring crystallization or precipitation processes because the existence of solids could cause distortion of the spectra. This phenomenon, seen as unfavorable previously, is however an indication that NIR spectra contain rich information about both solids and liquids, giving the possibility of using the same instrument for multiple property characterization. In this study, transflectance NIR calibration data was obtained using solutions and slurries of varied solution concentration, particle size, solid concentration and temperature. The data was used to build calibration models for prediction of the multiple properties of both phases. Predictive models were developed for this challenging application using an approach that combines genetic algorithm (GA) and support vector machine (SVM). GA is used for wavelength selection and SVM for mode building. The new GA–SVM approach is shown to outperform other methods including GA–PLS (partial least squares) and traditional SVM. NIR is thus successfully applied to monitoring seeded and unseeded cooling crystallization processes of l-glutamic acid.     

Vibrational convection in a saturated porous medium in the absence of thermal equilibrium between the solid and liquid phases

Thermal vibrational convection in a saturated porous medium is theoretically studied on the basis of a thermal nonequilibrium model, in accordance with which the temperatures of the porous medium and the saturating liquid can be different. In the high-frequency vibration approximation the averaged equations of convection are derived. The dependence of the vibration force direction on the interphase heat transfer coefficient and the vibration frequency is established. Vibrational convection in a cylindrical layer is studied. It is shown that, depending on the interphase heat transfer coefficient, the flows of two types differing in the liquid circulation direction can exist.     

Self-similar scattering of evaporation products of a solid wall subjected to variable energy liberation

A system of self-similar equations of motion of the evaporation products (ideal gas) under the effect of variable energy liberation is considered. Conditions are formulated for the existence and uniqueness of a solution of the problem of evaporation and scattering of a material in a vacuum.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 49–54, May–June, 1973.The author is grateful to V. F. Kuropatenko and V. E. Neuvazhaev for aid and interest in the research.     

Thermocapillary instability of a deformable liquid film

The instability of a plane liquid film with a uniform transverse temperature gradient under conditions of weightlessness is considered. The surface tension is assumed to depend linearly on the temperature. On the basis of an exact solution of the neutral perturbation problem for a layer with deformable boundaries, the instability domains, the dispersion curves, and the shape of the perturbations are determined. It is shown that on the interval of low Prandtl numbers both thermocapillary waves with predominantly longitudinal flow and capillary waves, supported by the thermocapillary effect, with intense transverse liquid flow can develop on the film.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 30–36, September–October, 1996.     

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.     

The effect of hydrodynamic coupling on the thinning of a film between a drop and its homophase

The rate of thinning of a film trapped between a drop approaching its homophase according to a model incorporating hydrodynamic coupling is dramatically different from earlier, uncoupled models. Implications for film thinning of microflows analyzed in the preceding paper are here investigated using similar analytical methods to derive a nonautonomous, nonlinear evolution equation for the film thickness which has been solved numerically under a variety of conditions after asymptotic analytical behavior has been extracted. The applied force squeezing the film, together with the initial motion in the three phases, determines the rate of film thinning in a complicated manner through the coupling parameter R = (ρ_Aμ_A/ρ_Bμ_B)^{$\text{1}\text{2}$}. Experimental observations that normal drop circulation enhances thinning, whereas reversed drop circulation can cause thickening, are predicted theoretically for the first time. Films much more viscous than their surroundings are found to thin faster than the converse case, a conclusion at odds with offhand intuition but substantiated experimentally; both classes of systems behave differently, often qualitatively so, from predictions of hydrodynamically decoupled systems, and in particular film thinning rates are generally faster because of less resistance to drainage, although the limit of vanishing R does recover the special case of Reynolds' model. For short times, films are shown analytically to thin more rapidly if there is initially outward film motion and normal drop circulation, but with decreasing effectiveness as R increases, in contrast to the effect of R for intermediate and longer times; if there is initially inward film motion, thickening tendencies are enhanced by reverse drop circulation but with decreasing effectiveness as R increases. These and other detailed conclusions, most predicted theoretically for the first time, are not only in qualitative agreement with experimental observations, they are in quantitative agreement with available data.     

Optical measurement of liquid film thickness and wave velocity in liquid film flows

Two optical techniques are described for measurement of a liquid film's surface. Both techniques make use of the total internal reflection which occurs at a liquid-vapor interface due to the refractive index difference between a liquid and a vapor. The first technique is used for film thickness determination. A video camera records the distance between a light source and the rays which are reflected back from the liquid-vapor interface. This distance can be shown to be linearly proportional to film thickness. The second technique measures surface wave velocities. Two photo sensors, spaced a fixed distance apart, are used to record the time varying intensity of light reflected from the liquid-vapor interface. The velocity is then deduced from the time lag between the two signals.The authors appreciate the support of the Air Conditioning and Refrigeration Center at the University of Illinois at Urbana-Champaign under project 45.     

Advective flow in a rotating liquid film

This paper presents a new exact solution of the Navier–Stokes equations in the Boussinesq approximation that describes thermocapillary advective flow in a slowly rotating horizontal layer of incompressible fluid with free boundaries. Such flow occurs in the case of linear temperature distribution over horizontal coordinates or in the case of heat flux distribution at the layer boundaries. The influence of the Taylor, Marangoni, Grashof, and Biot numbers on the flow and temperature velocity profiles is studied.     

Motion of a liquid bounded by a flexible film

The planar motion of an ideal incompressible liquid bounded by a flexible inextensible film is examined. Some qualitative characteristics of this motion are noted, and the hydrodynamic impact phenomena that can arise are studied.