thermocapillary effect

vective instability. When the gas phase is warmer. Bifurcations of the this traveling wave solution lead to multi-hump, traveling waves whose maximal heights will be lower than the. -6 Isothermal case: 2D flow. 1997. -3.2 2D Boundary Layer Equations. With the increase of Ma, the film has a tendency to break up into droplets due to the enhancement of the absolute instability. The limit in which the internal waves are much shorter than the surface wave is considered. Viviani, A. Craster, Richard V. Recent studies of a liquid, film coating the interior surface of a tube by a thin film model, showed that the Marangoni effect enhances the instability, for a thick liquid film to examine the choke phenomenon. -3.7 Scalings: three sets of parameters. The thermocapillary effect, supported by a free surface created as the solid/liquid front progresses, acts driving convection and as an effective mechanism for heat transport.

When this is the case, a qualitatively new behaviour is observed: perturbations of the film interface may evolve into continuous steady patterns that do not rupture. Falling liquid films in narrow tubes: occlusion scenarios - Volume 894 - Georg F. Dietze, G. Lavalle, C. Ruyer-Quil. -1.5 References and further reading. -4.6 Weakly nonlinear models. -4.8 References and further reading. By continuing you agree to the use of cookies. 745 (2014) 682. tube with a porous wall, Phys. To test how the absolute, instability is linked with the choke phenomenon, we considered, arrives at the outlet of the domain, we terminate the numerical, code. The Marangoni effect, enhances the absolute instability. We assume that the mean, (or a typical wavelength) in the axial direction. However, we should be very, careful to apply the present study to the choke phenomenon in, human airways. On ground, natural convection masks the influence of Marangoni flow, which means that quantifying each contribution to the heat transfer rate of the system precisely is not possible. Published by Elsevier Ltd. All rights reserved. temperature fields are compared directly to the experimental Wollaston prism (WP) interferograms for both steady-state and oscillatory convection.
The Bond number. This option allows users to search by Publication, Volume and Page. 10.1017/S0022112085001884 Univ. and These topological differences allow for further classification of the models. Thicker petioles increase the leaf's mechanical stability, but require sizable energy investments

downa uniformly heated vertical cylinder are investigated using a thin film model. -5.2 Relaxing the self-similar assumption. -2.2 Transverse disturbances. of Marangoni convection in a liquid–gas system The numerical simulation as well as the traveling wave, study suggest that the ‘‘absolute instability” is not a good criterion, for the choke phenomenon due to the nonlinear nature of the, choke phenomenon. -3.8 Salient features. -3.1 Boundary layer equations. -11.3 References and further reading. Rayleigh instability: a model for long encapsulated liquid zones, J. Fluid Mech. Marangoni effect exceeds a critical value by a thin liquid film, model. and International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2017.05.030. Generally, a, finite difference method with more than 10, in previous simulations, which is very time-consuming. 123 (2018) 718. Bull. The transverse slippery effect significantly improves the instability while the wavenumber of the perturbation is small, and simultaneously it reduces the cutoff wavenumber. The streamwise slippery effect always impedes the instability of the flow and suppresses the wave height of traveling wave, while the transverse slippery effect has a dual effect on the surface instability. produce greater bending moments on the petiole's cross-section as a result of their greater weights, the bending stresses When, the gas phase is cooler than the liquid phase (, regime” enlarges, indicating an enhancing effect on the ‘‘choke, phenomenon”. Microstructural examination of samples solidified during high-gravity arcs reveals no evidence of convection dampening. Check if you have access via personal or institutional login. -5.1 Averaged two-equation models. Dt ¼ tc À t at ¼ 0:2, a ¼ 3. Our numerical results showed that for various Marangoni number (Ma), breakup of the film mainly occurs in the AI regime. Carpenter, B. In a standard way. Nonlinear study also shows that the coalescence of droplets/ring waves and bound state are weakly dependent on the absolute or convective instability. Thermocapillary effects are then examined in the limiting cases of large and short containers.

In, experimental study, the tube is long and there is an inlet and outlet, would grow or decay as it flows to the downstream. The choke phenomenon can be suppressed by a warm air phase ($Ma<0$). Trevelyan, P. M. J. The Marangoni effect takes place when there is a gradient of surface tension at the interface between two phases – in most situations, a liquid-gas interface. The number of Four-, ier modes is increased as the wave length increases. 603 (2008) 431. The scaling of the lower layer viscosity is such that there is competition between linear damping effects and destabilizing, quadratic viscous effects.

Numerical, simulation shows that the air phase does not choke slightly below. convenience, we follow the studies by Camassa et al. However, if the core-gas phase is. The evolution equation of the interface of the self-rewetting film is established in the framework of a long-wave approximation theory. Linear stability also showed, that the absolute instability is enhanced/suppressed by the cooler/, Traveling wave solutions were sought so as to provide insights, into the choke phenomenon. [11] C. Ruyer-Quil, P. Treveleyan, F. Giorgiutti-Dauphiné. The choke phenomenon, study predicts an upper bound of the critical tube radius, below which the air flow chokes. Therefore, balancing, solution should be matchable to a time-independent outer, convective/absolute instability boundaries predicted by linear stability. The wavelength of the most unstable wave number is not depen-, the domain size increases, the wavelength of the most unstable, mode would remain the same by adjusting the value of, traveling wave solution predicts a critical wavelength, Furthermore, we investigate how the flow patterns in an exper-, imental study can be connected with the absolute/convective, instability and design the following numerical experiments. For large Γ, heat transport can be greatly enhanced by a factor of up to 20, depending on Ma. Sci. -5.4 First-order formulation. the liquid thick-, ness is small) in the isothermal case. We derived an evolution equation for the film thickness using a long-wave approximation. The traveling wave study demonstrated that the choke, phenomenon is promoted by a cold air flow, while it will be sup-, pressed by a warm air flow. The Rayleigh-Plateau instability, indeed, can be suppressed, . Mathematically, the type of, instability is determined by the temporal growth rate at a saddle, point in the complex wave number plane. Therefore, the traveling wave solution, offers a much better criterion of choke phenomenon than the ‘‘ab-, In this paper, we investigated the influence of Marangoni effect, on dynamics of a liquid film flowing down the interior surface of a, vertical tube.

The squares illustrate that the traveling wave solutions do exist for all wavelengths. This work is realized via our own front-tracking finite-difference method with further integration of the energy conservation equation and the surface surfactant transport equation. Results and discussions. Conclusion and the validity of the long-wave model, is the Newtonian stress tensor in the liquid phase, denotes the surface normal which points from the gas, A schematic draw of the system.

The mean thickness of the film is h0. It is well known that the azimuthal component of curvature, the tube radius increases, the flow becomes more stable. 51976160 and 51425603) and the National Key Research Program from Ministry of Science and Technology of China (Grant No. -10.5 References and further reading.

The most prevalent oscillatory mode corresponds to a symmetric up and down fluctuation of the temperature and flow fields associated with an axially traveling wave. As a first approximation, the high-gravity arc is modeled as a centrifuge with a radius of 20,480 ft and angular speed of 0.318 rpm. and -5.6 Second-order formulation -5.7 Reduction of the full second order model. Mathematically, different levels of asymptotic accuracy are found to result in different regularizing properties affecting the long-time behaviour of generic numerical solutions. The domain size considered by the numerical. This paper considers a thick liquid film of mean thickness $h_0$ coating the interior surface of a uniformly heated vertical tube of radius $a$ under the influence of gravity ($h_0$ is not far thinner than the radius $a$). Physiol. instability regime or the convective instability regime, which, shows a strong dependence on the tube radius, film, the choke phenomenon occurs when the dimensionless tube, below which the air flow may be choked. In cases where the surface tension varies with the temperature, the Marangoni effect is referred to as the thermocapillary effect. Recently, liquid falling films on tubes attracted a lot of interest [18][19][20][21][22]. Thiele, U. Fol-, phenomenon, we terminate the computation. -8 Interaction of 3D solitary waves. Experimental study also showed that two different flow patterns, could exist in the exterior flow system: an absolutely unstable flow, film is thin compared with the cylinder’s radius, the instability is. fibers by water sprays, Int. -6.2 Travelling waves.
1999. We per-, (a) shows that the disturbance flows to the down stream, 5, an absolutely unstable flow is observed in, (b). Rayleigh-Plateau instability can be inhibited when the core air phase is warmer than the liquid phase; while the Rayleigh-Plateau instability is enhanced when the air phase is colder than the liquid phase. In The, present study has demonstrated that the Marangoni effect can, enhance the Plateau-Rayleigh mechanism and breathing cold air, could be a factor of winter cough.

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