Morphology changes in the evolution of liquid two-layer films

We consider two thin layers of immiscible liquids on a heated solid horizontal substrate. The free liquid-liquid and liquid-gas interfaces of such a two-layer (or bilayer) liquid film may be unstable due to effective molecular interactions or the Marangoni effect. Using a long wave approximation we derive coupled evolution equations for the interafce profiles for a general non-isothermal situation allowing for slip at the substrate. Linear and nonlinear analyses are performed for isothermal ultrathin layers below 100 nm thickness under the influence of destabilizing long-range and stabilizing short-range interactions. Flat films may be unstable to varicose, zigzag or mixed modes. During the long-time evolution the nonlinear mode type can change via switching between two different branches of stable stationary solutions or via coarsening along a single such branch.Comment: 14 eps figures and 1 tex fil

Decomposition driven interface evolution for layers of binary mixtures: {II}. Influence of convective transport on linear stability

We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. Thiele, S. Madruga and L. Frastia, Phys. Fluids 19, 122106 (2007)]. To this aim, the linearized bulk equations and boundary equations are solved using continuation techniques for several different cases of energetic bias at the surfaces, corresponding to linear and quadratic solutal Marangoni effects. For purely diffusive transport, an increase in film thickness either exponentially decreases the lateral instability or entirely stabilizes the film. Including convective transport leads to a further destabilization as compared to the purely diffusive case. In some cases the inclusion of convective transport and the related widening of the range of available film configurations (it is then able to change its surface profile) change the stability behavior qualitatively. We furthermore present results regarding the dependence of the instability on several other parameters, namely, the Reynolds number, the Surface tension number and the ratio of the typical velocities of convective and diffusive transport.Comment: Published in Physics of Fluic

Thermal effects in two-phase flow through face seals

When liquid is sealed at high temperature, it flashes inside the seal due to pressure drop and/or viscous heat dissipation. Two-phase seals generally exhibit more erratic behavior than their single phase counterparts. Thermal effects, which are often neglected in single phase seal analyses, play an important role in determining seal behavior under two-phase operation. It is necessary to consider the heat generation due to viscous shear, conduction into the seal rings and convection with the leakage flow. Analytical models developed work reasonably well at the two extremes - for low leakage rates when convection is neglected and for higher leakage rates when conduction is neglected. A preliminary model, known as the Film Coefficient Model, is presented which considers conduction and convection both, and allows continuous boiling over an extended region unlike the previous low-leakage rate model which neglects convection and always forces a discrete boiling interface. Another simplified, semi-analytical model, based on the assumption of isothermal conditions along the seal interafce, has been developed for low leakage rates. The Film Coefficient Model may be used for more accurate and realistic description

Decomposition driven interface evolution for layers of binary mixtures: I. Model derivation and stratified base states

A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on model-H describing the coupled transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological non-equilibrium thermodynamics for a general non-isothermal setting taking into account Soret and Dufour effects and interfacial viscosity for the internal diffuse interface between the two components. Focusing on an isothermal setting the resulting model is compared to literature results and its base states corresponding to homogeneous or vertically stratified flat layers are analysed.Comment: Submitted to Physics of Fluid

Dynamics of face and annular seals with two-phase flow

A detailed study was made of face and annular seals under conditions where boiling, i.e., phase change of the leaking fluid, occurs within the seal. Many seals operate in this mode because of flashing due to pressure drop and/or heat input from frictional heating. Some of the distinctive behavior characteristics of two phase seals are discussed, particularly their axial stability. The main conclusions are that seals with two phase flow may be unstable if improperly balanced. Detailed theoretical analyses of low (laminar) and high (turbulent) leakage seals are presented along with computer codes, parametric studies, and in particular a simplified PC based code that allows for rapid performance prediction: calculations of stiffness coefficients, temperature and pressure distributions, and leakage rates for parallel and coned face seals. A simplified combined computer code for the performance prediction over the laminar and turbulent ranges of a two phase flow is described and documented. The analyses, results, and computer codes are summarized

Experimental study of the stability and flow characteristics of floating liquid columns confined between rotating disks

A low Bond number simulation technique was used to establish the stability limits of cylindrical and conical floating liquid columns under conditions of isorotation, equal counter rotation, rotation of one end only, and parallel axis offset. The conditions for resonance in cylindrical liquid columns perturbed by axial, sinusoidal vibration of one end face are also reported. All tests were carried out under isothermal conditions with water and silicone fluids of various viscosities. A technique for the quantitative measurement of stream velocity within a floating, isothermal, liquid column confined between rotatable disks was developed. In the measurement, small, light scattering particles were used as streamline markers in common arrangement, but the capability of the measurement was extended by use of stereopair photography system to provide quantitative data. Results of velocity measurements made under a few selected conditions, which established the precision and accuracy of the technique, are given. The general qualitative features of the isothermal flow patterns under various conditions of end face rotation resulting from both still photography and motion pictures are presented

Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate

Temporal and spatio-temporal instabilities of binary liquid films flowing down an inclined uniformly heated plate with Soret effect are investigated by using the Chebyshev collocation method to solve the full system of linear stability equations. Seven dimensionless parameters, i.e. the Kapitza, Galileo, Prandtl, Lewis, Soret, Marangoni, and Biot numbers (Ka, G, Pr, L, X, M, B), as well as the inclination angle (beta) are used to control the flow system. In the case of pure spanwise perturbations, thermocapillary S- and P-modes are obtained. It is found that the most dangerous modes are stationary for positive Soret numbers (chi >= 0), and oscillatory for chi 0 and even merges with the long-wave S-mode. In the case of streamwise perturbations, a long-wave surface mode (H-mode) is also obtained. From the neutral curves, it is found that larger Soret numbers make the film flow more unstable as do larger Marangoni numbers. The increase of these parameters leads to the merging of the long-wave H- and S-modes, making the situation long-wave unstable for any Galileo number. It also strongly influences the short-wave P-mode which becomes the most critical for large enough Galileo numbers. Furthermore, from the boundary curves between absolute and convective instabilities (AI/CI) calculated for both the long-wave instability (S- and H-modes) and the short-wave instability (P-mode), it is shown that for small Galileo numbers the AI/CI boundary curves are determined by the long-wave instability, while for large Galileo numbers they are determined by the short-wave instability

Dynamics of a two-dimensional vapor bubble confined between superheated or subcooled parallel plates

The dynamics of a long, two-dimensional vapor bubble confined in the gap between two superheated or subcooled parallel plates is analyzed theoretically. The unsteady expansion and/or contraction of the bubble is driven by mass transfer between the liquid and the vapor. The analysis uses the approach developed by Wilson et al. J. Fluid Mech. 391, 1 1999 for a situation with 'large' gaps and 'small' superheating or subcooling to consider a situation with small gaps and large superheating or subcooling in which the mass transfer from or to the semicircular nose of the bubble is comparable to that from or to the thin liquid films on the plates. In order to permit a semi- analytical treatment the analysis is restricted to low Prandtl number liquids. When both plates are superheated the bubble always expands. In this case there are two possible constant-velocity continuous-film solutions for the expansion of the bubble, namely, an unstable fast mode and a stable slow mode. The evolution of the bubble is calculated numerically for a range of values of the parameters. In particular, these calculations show that eventually the bubble expands either with the constant velocity of the slow mode or exponentially. When both plates are subcooled the bubble always collapses to zero length in a finite time. When one plate is subcooled and the other plate is superheated the situation is rather more complicated. If the magnitude of the subcooling is less than that of the superheating then if the magnitude of the subcooling is greater than a critical value then a variety of complicated behaviors including the possibility of an unexpected 'waiting time' behavior in which the bubble remains almost stationary for a finite period oftime can occur before the bubble eventually collapses to a finite length in an infinite time, whereas if it is less than this critical value then the bubble always expands and eventually does so exponentially. If the magnitude of the subcooling is greater than that of the superheating then the bubble always collapses to zero length in a finite time