Note on the instability of capillary jet with thermocapillarity

In this paper, we examine a new basic state of long axisymmetric liquid zone, subjected to axial temperature gradients which induce steady viscous flow driven by thermocapillarity. Axial velocity 1/4S-1/2R(B) of liquid zone connects pulling velocity of single crystal. The stability of liquid zone with pulling velocity 1/4S-1/2R(B) to small axisymmetric disturbance is examined The eigenvalue problems on the stability are derived. A special case (eta = 0) is discussed.

On post-instability processes in adiabatic shear in hot rolled steel

EXPERIMENTS carried out using a split Hopkinson torsional bar have shown that only one shear band develops in specimens of hot rolled steel which break during testing. We observed, however, that in specimens which were not deformed to failure, several fine shear bands appeared. We believe that these formed during the loading cycle before the appearance of the final shear band and were not due to the effect of unloading. So we developed a numerical model to study the evolution of shear banding from several finite amplitude disturbances (FADs) in both temperature and strain rate. This numerical model reveals the detailed processes by which the FADs evolve into a fully developed shear band and suggests that beyond instability, the so-called shear banding process consists of two stages: inhomogeneous shearing and true shear-banding. The latter is characterized by the collapse of the stress and an abrupt increase of the local shear strain rate.

An application of adjoint variational method to the capillary instability in liquid

In this paper, applying the direct variational approach of first-order approximation to the capillary instability problem for the eases of rotating liquid column, toroid and films on both sides of cylinder, we have obtained the necessary and sufficient conditions for motion stability of the "cylindrical coreliquid-liquid-cylindrical shell" systems. The results obtained before are found to be special cases of the present investigation. At the same time, we have explained physical essence of rotating instability and settled a few disputes in previous investigations.

Thermo-plastic instability in simple shear

A theoretical description of thermo-plastic instability in simple shear is presented in a system of equations describing plastic deformation, the first law of thermodynamics and Fourier's heat transfer rule. Both mechanical and thermodynamical parameters influence instability and it is shown that two different modes of instability may exist. One of them is dominated by thermal softening and has a characteristic time and length, connected to each other by thermal diffusion.A criterion combining thermal softening, current stress, density, specific heat, work-hardening, thermal conductivity and current strain rate is obtained and practical implications are discussed.

Oscillatory Instability of Rayleigh-Marangoni-Benard Convection in Two-Layer System

The convective instabilities in two or more superposed layers heated from below were studied extensively by many scientists due to several interfacial phenomena in nature and crystal growth application. Most works of them were performed mainly on the instability behaviors induced only by buoyancy force, especially on the oscillatory behavior at onset of convection (see Gershuni et. Al.(1982), Renardy et. Al. (1985,2000), Rasenat et. Al. (1989), and Colinet et. Al.(1994)) . But the unstable situations of multi-layer liquid convection will become more complicated and interesting while considering at the same time the buoyancy effect combined with thermocapillary effect. This is the case in the gravity reduced field or thin liquid layer where the thermocapillary effect is as important as buoyancy effect. The objective of this study was to investigate theoretically the interaction between Rayleigh-Bénard instability and pure Marangoni instability in a two-layer system, and more attention focus on the oscillatory instability both at the onset of convection and with increasing supercriticality. Oscillatory behavious of Rayleigh-Marangoni-Bénard convective instability (R-M-B instability) and flow patterns are presented in the two-layer system of Silicon Oil (10cSt) over Fluorinert (FC70) for a larger various range of two-layer depth ratios (Hr=Hupper/Hdown) from 0.2 to 5.0. Both linear instability analysis and 2D numerical simulation (A=L/H=10) show that the instability of the system depends strongly on the depth ratio of two-layer liquids. The oscillatory instability regime at the onset of R-M-B convection are found theoretically in different regions of layer thickness ratio for different two-layer depth H=12,6,4,3mm. The neutral stability curve of the system displaces to right while we consider the Marangoni effect at the interface in comparison with the Rayleigh-Bénard instability of the system without the Marangoni effect (Ma=0). The numerical results show different regimes of the developing of convection in the two-layer system for different thickness ratios and some differences at the onset of pure Marangoni convection and the onset of Rayleigh-Bénard convections in two-layer liquids. Both traveling wave and standing wave were detected in the oscillatory instability regime due to the competition between Rayleigh-Bénard instability and Marangoni effect. The mechanism of the standing wave formation in the system is presented numerically in this paper. The oscillating standing wave results in the competition of the intermediate Marangoni cell and the Rayleigh convective rolls. In the two-layer system of 47v2 silicone oil over water, a transition form the steady instability to the oscillatory instability of the Rayleigh-Marangoni-Bénard Convection was found numerically above the onset of convection for ε=0.9 and Hr=0.5. We propose that this oscillatory mechanism is possible to explain the experimental observation of Degen et. Al.(1998). Experimental work in comparison with our theoretical findings on the two-layer Rayleigh-Marangoni-Bénard convection with thinner depth for H<6mm will be carried out in the near future, and more attention will be paid to new oscillatory instability regimes possible in the influence of thermocapillary effects on the competition of two-layer liquids

Numerical Simulation of R-M Instability

In order to capture shock waves and contact discontinuities in the field and easy to program with parallel computation a new algorithm is developed to solve the N-S equations for simulation of R-M instability problems. The method with group velocity control is used to suppress numerical oscillations, and an adaptive non-uniform mesh is used to get fine resolution. Numerical results for cylindrical shock-cylindrical interface interaction with a shock Mach number Ms=1.2 and Atwood number A=0.818, 0.961, 0.980 (the interior density of the interface/outer density p(1)/p(2) = 10, 50, 100, respectively), and for the planar shock-spherical interface interaction with Ms=1.2 and p(1)/p(2) = 14.28are presented. The effect of Atwood number and multi-mode initial perturbation on the R-M instability are studied. Multi-collisions of the reflected shock with the interface is a main reason of nonlinear development of the interface instability and formation of the spike-bubble structures In simulation with double mode perturbation vortex merging and second instability are found. After second instability the small vortex structures near the interface produced. It is important factor for turbulent mixing.

Rayleigh-Marangoni-Bénard Convective Instability

The Rayleigh-Marangoni-Benard convective instability (R-M-B instability) and flow patterns in the two-layer system of silicon oil 10cSt and Fluorinert FC70 liquids are studied theoretically and experimentally. Both linear instability analysis and 2D numerical simulation (A=L/H=10) were performed to study the influence of thermocapillary force on the convective instability of the two-layer system. Time-dependent oscillations arising at the onset of convection were investigated in a larger various range of two-layer depth ratios (Hr=H1/H2) from 0.2 to 5.0 for different total depth less than 12mm. Our results are different from the previous study on the Rayleig-B閚ard instability and show the strong effects of thermocapillary force at the interface on the time-dependent oscillations at the onset of instability convection. Primary experimental results of the critical instability parameters and the convective structure in the R-M-B convection have been obtained by using the digital particle image velocimetry (DPIV) system, and a good agreement in comparison with the results of numerical simulation was obtained.

Influence of Evaporation on Marangoni-Benard Instability

Evaporative convection and instability give rise to both scientific and technological interests. Practically, a number of the industrial applications such as thin-film evaporators, boiling technologies and heat pipes concern with the evaporation process of which through the vapor-liquid interface the heat and mass transfer occur. From a physical viewpoint, one of interesting questions is the mechanisms of convection instability in thin-liquid layers induced by the coupling of evaporation phenomenon and Marangoni effect at the mass exchanged interface. Classical theories, including Rayleigh’s and Pearson’s, have only successfully explained convection in a liquid layer heated from below without evaporation. However these theories are unable to explain the convection in an evaporating thin layer, especially liquid layer is cooled from below. In present paper, a new two-sided model is put forward rather than the one-sided model in previous works. In previous works, the vapor is treated as passive gas and dynamics of vapor has been ignored. In this case, the vapor liquid system can be described by one-sided model. In our two-sided model, the dynamics of vapor should be considered. Linear instability analysis of the Marangoni-Bénard convection in the two-layer system with an evaporation interface is performed. We define a new evaporating Biot number which is different from the Biot number in one-sided model and obtain the curves of critical Marangoni number versus wave number. In our theoretical results, the Biot number and the evaporating velocity play a major role in the stability of the vapor-liquid system.