A linear stability analysis is performed for a horizontal layer of a binary liquid of which solely the solute evaporates into an inert gas, the latter being assumed to be insoluble in the liquid. In particular, a water-ethanol system in contact with air is considered, with the evaporation of water being neglected (which can be justified for a certain humidity of the air). External constraints on the system are introduced by imposing fixed "ambient" mass fraction and temperature values at a certain effective distance above the free liquid-gas interface. The temperature is the same as at the bottom of the liquid layer, where, besides, a fixed mass fraction of the solute is presumed to be maintained. Proceeding from a (quasi-)stationary reference solution, neutral (monotonic) stability curves are calculated in terms of solutal/thermal Marangoni/Rayleigh numbers as functions of the wavenumber for different values of the ratio of the gas and liquid layer thicknesses. The results are also presented in terms of the critical values of the liquid layer thickness as a function of the thickness of the gas layer. The solutal and thermal Rayleigh and Marangoni effects are compared to one another. For a water-ethanol mixture of 10 wt% ethanol, it appears that the solutal Marangoni effect is by far the most important instability mechanism. Furthermore, its global action can be described within a Pearson-like model, with an appropriately defined Biot number depending on the wavenumber. On the other hand, it is also shown that, if taken into account, water evaporation has only minor quantitative consequences upon the results for this predominant, solutal Marangoni mechanism.

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Thermocapillary convection in three-dimensional rectangular finite containers with rigid lateral walls is studied. The upper surface of the fluid layer is assumed to be flat and non-deformable but is submitted to a temperature-dependent surface tension. The realistic 'no-slip' condition at the sidewalls makes the method of separation of variables inapplicable for the linear problem. A spectral Tau method is used to determine the critical Marangoni number and the convective pattern at the threshold as functions of the aspect ratios of the container. The influence on the critical parameters of a non-vanishing gravity and a non-zero Biot number at the upper surface is also examined. The nonlinear regime for pure Marangoni convection (Ra = 0) and for Pr = lo4, Bi = 0 is studied by reducing the dynamics of the system to the dynamics of the most unstable modes of convection. Owing to the presence of rigid walls, it is shown that the convective pattern above the threshold may be quite different from that predicted by the linear approach. The theoretical predictions of the present study are in very good agreement with the experiments of Koschmieder & Prahl (1990) and agree also with most of Dijkstra's (1995a, 3) numerical results. Important differences with the analysis of Rosenblat, Homsy & Davis (19823) on slippery walls containers are emphasized.

Total stressed blood volume is an important parameter for both doctors and engineers. From a medical point of view, it has been associated with the success or failure of fluid therapy, a primary treatment to manage acute circulatory failure. From an engineering point of view, it dictates the cardiovascular system's behaviour in changing physiological situations. Current methods to determine this parameter involve repeated phases of circulatory arrests followed by fluid administration. In this work, a more straightforward method is developed using data from a preload reduction manoeuvre. A simple six-chamber cardiovascular system model is used and its parameters are adjusted to pig experimental data. The parameter adjustment process has three steps: (1) compute nominal values for all model parameters; (2) determine the five most sensitive parameters; and (3) adjust only these five parameters. Stressed blood volume was selected by the algorithm, which emphasizes the importance of this parameter. The model was able to track experimental trends with a maximal root mean squared error of 29.2 %. Computed stressed blood volume equals 486 ± 117 ml or 15.7 ± 3.6 ml/kg, which matches previous independent experiments on pigs, dogs and humans. The method proposed in this work thus provides a simple way to compute total stressed blood volume from usual hemodynamic data.

We propose a theoretical study of Marangoni driven convection in an evaporating liquid layer surmounted by an inert gas-vapor mixture. After reduction of the full two layer problem to a one-sided model we use a Galerkin-Eckhaus method leading to a finite set of amplitude equations for the weakly nonlinear analysis of the problem. We analyse the stability of the roll, square and hexagonal patterns emerging above the linear stability threshold for a water-air and for an ethanol-air system.