On modeling evaporation

We develop a theoretical model for evaporation of a pure liquid drop on a thermally conductive solid substrate. We discuss a variety of effects regarding evaporation regime, the state of the liquid/gas interface and the content of gas phase. Then, we further consider two models: the one resulting from the one-sided non-equilibrium assumption and the other that assumes diffusion-limited regime and equilibrium at the liquid/gas interface. A single governing equation for the evolution of drop thickness is derived for both models. We show that although the model predicts qualitatively different temperature along liquid/gas and liquid/solid interface, the dynamics of the drops is almost the same.      

Dynamics of water evaporation fronts

The evolution and shapes of water evaporation fronts caused by long-wave instability of vertical flows with a phase transition in extended two-dimensional horizontal porous domains are analyzed numerically. The plane surface of the phase transition loses stability when the wave number becomes infinite or zero. In the latter case, the transition to instability is accompanied with reversible bifurcations in a subcritical neighborhood of the instability threshold and by the formation of secondary (not necessarily horizontal homogeneous) flows. An example of motion in a porous medium is considered concerning the instability of a water layer lying above a mixture of air and vapor filling a porous layer under isothermal conditions in the presence of capillary forces acting on the phase transition interface.     

Strong evaporation into a half space

Evaporation of a liquid into a vacuum occupying a half space is investigated on the basis of the one-dimensional BGK model linearized about a drifting Maxwellian distribution. A unique solution is shown to exist if the downstream speed remains subsonic. Exact analysis is used, and numerical results are given.

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Zusammenfassung Auf der Basis eines eindimensionalen BGK-Modells, das über eine driftende Maxwell-Verteilung linearisiert ist, wird die Verdampfung einer Flüssigkeit in ein einen Halbraum ausfüllendes Vakuum untersucht. Es wird gezeigt, daß nur eine einzige Lösung existiert, wenn die Geschwindigkeit im Unterschallbereich bleibt. Exakte Analysis wird verwendet und numerische Resultate angegeben.

     

Mathematical simulation of laser induced melting and evaporation of multilayer materials

Using the laser induced remelting of a three-layer target Al + Ni + Cr as an example, the use of the dynamic adaptation for solving the multifront Stefan problem with explicit tracking of the melting and evaporation fronts is considered. The dynamic adaptation is used to construct quasi-uniform grids in regions with moving boundaries. The characteristic size of those regions may vary by several orders of magnitude in the process of computations. The algorithm used to construct the grids takes into account the varying size of the region and the velocity of the boundary motion, which makes it possible to automatically distribute the grid points without using fitting parameters. The mathematical simulation of the doping process using the melt with respect to the thick substrate and thin doping layers showed the importance of the sequencing of coatings. The computations showed that if the upper exposed layer is chromium, then it can completely evaporate or sublimate by the end of the pulse due to its heat-transfer properties. This can be easily changed if the doping layers are arranged according to the scheme Al + Cr + Ni. Then, the upper exposed layer is nickel, which is not so easily evaporated.     

Inverse problem for the model of evaporation of a binary alloy

Translated from Metody Matematicheskogo Modelirovaniya i Vychislitel'noi Diagnostiki, pp. 10–13, Izd. Moskovskogo Universiteta, Moscow, 1990.     

FREE BOUNDARY PROBLEM ARISING FROM EVAPORATION FROM POROUS MEDIUM

ＦＲＥＥＢＯＵＮＤＡＲＹＰＲＯＢＬＥＭＡＲＩＳＩＮＧＦＲＯＭＥＶＡＰＯＲＡＴＩＯＮＦＲＯＭＰＯＲＯＵＳＭＥＤＩＵＭＹＡＮＧＬＩＰＩＮＧ（杨力平）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔｙ，Ｂｅ...     

Effect of soil capillarity on seepage from a channel with evaporation

The method of Polubarinova-Kochina is applied to solve the seepage problem for a channel with evaporation and capillary soil. The capillary spread of water and the seepage discharge from the channel are investigated as a function of the height of capillary rise and evaporation rate. Results of numerical experiments are presented. The limiting case of flow without evaporation, previously studied by Rizenkampf, is considered.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 40–43, 1986.     

An approximate solution concerning strong evaporation into a half space

Evaporation of a liquid into a vacuum occupying a half space is investigated on the basis of the one-dimensional BGK model linearized about a drifting Maxwellian distribution. TheF _N method is used to deduce accurate numerical results for the perturbations in the density and temperature.

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Zusammenfassung Auf der Basis eines eindimensionalen BGK-Modells, das über eine driftende Maxwell-Verteilung linearisiert ist, wird die Verdampfung einer Flüssigkeit in ein einen Halbraum ausfüllendes Vakuum untersucht. DieF _N-Methode wird verwendet zur Ableitung von genauen numerischen Ergebnissen für die Störungen in Dichte und Temperatur.

     

An abstract approach to evaporation models in rarefied gas dynamics

An efficient algorithm is presented for determining the unique solvability of certain one-dimensional stationary transport problems. The non-existence of stationary evaporation states with supersonic drift velocities for one and three dimensional BGK model is recovered.

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Sommario È presentato un algoritmo efficiente per determinare la solubilità univoca di alcuni probiemi unidimensionali di trasporto stazionario. È ripresa la non esistenza di stati stazionari di evaporazione con velocità di deriva supersoniche per modelli BGK a una e tre dimensioni.

     

Influence of thermal load on the characteristics of a flow with evaporation

The two-layer flows of a liquid and a gas in a horizontal channel are investigated under condition of given gas flow rate. Evaporation on the thermocapillary interface is taken into account. An exact solution is constructed of the Navier–Stokes equations in the Boussinesq approximation, taking into account the Dufour effect in the gas-vapor layer. Within the framework of linear theory, the stability of the obtained solutions and the characteristics of the arising perturbations are studied. The influence is considered of the thickness of the liquid layer and the magnitude of the longitudinal temperature gradient on the structure of the basic flow and perturbations.     

A model for gravity driven flow of a thin liquid-solid solution with evaporation effects

A vertical substrate is coated with a thin film of a solution consisting of a volatile viscous liquid and a solid solute. The liquid film thins under gravity while the volatile component simultaneously evaporates. We develop a model to predict the evolving film thickness and in so doing we develop an approximation for the later stages of the well-known dip-coating process.     

A model for gravity driven flow of a thin liquid-solid solution with evaporation effects

A vertical substrate is coated with a thin film of a solution consisting of a volatile viscous liquid and a solid solute. The liquid film thins under gravity while the volatile component simultaneously evaporates. We develop a model to predict the evolving film thickness and in so doing we develop an approximation for the later stages of the well-known dip-coating process.Received: October 10, 2003; revised: May 4 and July 19, 2004     

Strong evaporation into a half space. II. The three-dimensional BGK model

Evaporation of a liquid into a vacuum occupying a half space is investigated on the basis of the BGK equation for a three-dimensional gas linearized about a drifting Maxwellian distribution. The theory of singular integral equations is used and numerical results are given.

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Zusammenfassung Die Verdampfung einer Flüssigkeit im Vakuum, die den Halbraum füllt, wird untersucht mit Benützung der BGK-Gleichung für ein dreidimensionales Gas, linearisiert in bezug auf eine mitbewegte Maxwell-Verteilung. Es wird die Theorie der singulären Integralgleichungen benützt, und es werden numerische Resultate gegeben.

     

The eigenpairs of a Sylvester–Kac type matrix associated with a simple model for one-dimensional deposition and evaporation

A straightforward model for deposition and evaporation on discrete cells of a finite array of any dimension leads to a matrix equation involving a Sylvester–Kac type matrix. The eigenvalues and eigenvectors of the general matrix are determined for an arbitrary number of cells. A variety of models to which this solution may be applied are discussed.