It has been shown experimentally that when a drop is deposited at the center of a substrate with an axial temperature gradient (hotter in the center), thermocapillarity effects makes an outward flow ...to appear so that the drop evolves towards a ring whose radius increases with time. Upon reaching a critical radius, the contact line becomes unstable, showing gentle undulations whose amplitudes grow with time. Using the lubrication approximation and adopting appropriate dimensionless variables, a parameter-free differential equation is obtained that governs this type of thermocapillary flow. Numerical solutions of this equation are presented to study the unstable stage. Experimental results are compared with those obtained from the numerical solutions.
We present a new analytical solution for the static shape of a two-dimensional droplet in equilibrium with a surrounding thin film on a solid substrate. The modeling includes the effects of ...capillarity and disjoining−conjoining pressure accounting for intermolecular forces between the solid and the liquid. We derive new analytical solutions for the shape of the droplet, the cross-sectional area, the half-width, and the maximum curvature and inflection points. We study the effects of the size of the droplet on the apparent contact angle. The shape of the droplet in the contact line region is compared with profiles obtained by employing approximations suggested in the literature, and the observed differences are discussed. Finally, we present the time evolution to the steady state to show how the whole profile, including the thin film, evolves to the corresponding stationary configuration.
We study the migration of droplets on a solid surface which is under a uniform temperature gradient. The present article focus on partial wetting fluids which surface tension depends on the squared ...temperature. These type of liquids, called self-rewetting, show a complex dynamics and here we will compare with those liquids of linear dependence in the temperature. Unlike to the latter ones, the droplet width increases with the time.
We report new analytical solutions for the thickness profile of partially wetting two-dimensional droplets. The model includes the effects of capillarity and both short- and long-range molecular ...forces. We analyze the dependence of the maximum thickness, the contact angle, and the cross-sectional area on the height of the nanometric precursor film that surrounds the droplet. We found asymptotic expressions for the thickness profile and for the contact angles for large and small droplets. The results are compared to those obtained previously for polar liquids. The analytical solutions found here are useful to assess the validity of the hypothesis and the semi-analytical solutions proposed in the literature. In addition, these solutions enable the inference of information about the molecular potential from the measured steady profiles.
By means of the lubrication approximation we obtain the full family of static bidimensional profiles of a liquid resting on a substrate under partial-wetting conditions imposed by a ...disjoining-conjoining pressure. We show that for a set of quite general disjoining-conjoining pressure potentials, the free surface can adopt only five nontrivial static patterns; in particular, we find solutions when the height goes to zero which describe satisfactorily the complete free surface for a finite amount of fluid deposited on a substrate. To test the extension of the applicability of our solutions, we compare them with those obtained when the lubrication approximations are not employed and under conditions where the lubrication hypothesis are not strictly valid, and also with axisymmetric solutions. For a given disjoining-conjoining potential, we report a new analytical solution that accounts for all the five possible solutions.
We present here the results of the application of laser induced breakdown spectroscopy (LIBS) to a sample of a solid aluminum–lithium alloy, in which the latter component is at a very low ...concentration and whose proportion should be determined. The samples were placed in a vacuum chamber filled with a controlled xenon atmosphere, and the emission lines of this element were used to determine the electronic density and temperature of the laser generated plasma. Then, by means of a specially designed algorithm, it is possible to quantify the lithium content in the sample. The laser produced aluminum–lithium alloy plasma was generated by a pulsed Nd
+3:YAG laser (50 mJ) the pulse repetition frequency used was varied according to requirement from 1 to 20 Hz. Satisfactory results were obtained for the analytical determination of lithium contents in aluminum–lithium alloys. The lithium concentration was determined in values as low as 300–400 ppm.
Resumen Se ha mostrado experimentalmente que cuando se deposita una gota en el centro de un sustrato con un gradiente axial de temperatura (más caliente en el centro), por efectos termocapilares se ...genera un flujo hacia afuera de modo que la gota evoluciona hacia un anillo cuyo radio crece con el tiempo. Al alcanzar un radio crítico, la línea de contacto se inestabiliza, mostrando suaves ondulaciones cuyas amplitudes crecen con el tiempo. Utilizando la aproximación de lubricación y adoptando adecuadas variables adimensionales, se obtiene una ecuación diferencial libre de parámetros que gobierna este tipo de flujo termocapilar. En este trabajo se presentan soluciones numéricas de dicha ecuación para estudiar en particular la etapa inestable. Se comparan los resultados experimentales con los obtenidos con las soluciones numéricas.
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