B. Guerrier

Drying of a solution in a meniscus: a model coupling the liquid and the gas phases.

A model simulating the drying of a solution in a meniscus in contact with a moving substrate is developed. It takes into account the hydrodynamics in the solution in the framework of the lubrication approximation, the vapor diffusion in the gas phase, and the variation of physical properties during drying. The free surface profile and spatial evaporation flux are not imposed a priori but result from the simulation of the mass transfer in the liquid/gas system (1.5-sided model). Several regimes are observed depending on the substrate velocity. For a large substrate velocity, the classical Landau-Levich regime is obtained. For smaller velocities, a drying front appears that is characterized by a strong concentration gradient and a peak in the evaporation flux. The coupling between the evaporation flux and the meniscus shape in this regime is analyzed. Another regime appears at a very low substrate velocity and seems to be driven by a competition between advection and diffusion. This macroscopic model simulates recent experimental results, namely, the dependence of the deposit thickness on the substrate velocity, which scales as 1/V in the regime dominated by evaporation.

Glass transition induced by solvent desorption for statistical MMA/nBMA copolymers : Influence of copolymer composition

Abstract An experimental study of the glass transition induced by solvent desorption has been performed for a series of Methyl methacrylate (MMA)/n-butyl methacrylate (nBMA) statistical copolymer films. The glass transition temperature of the dry homopolymers, PMMA and PnBMA, are, respectively, about 105 and 7°C above the temperature of the experiment, so that the glass transition domain can be analyzed in detail by varying the solvent concentration and the copolymer composition. A strong coupling was found between drying dynamic and stress relaxation. In particular, the quantitative analysis of the desorption isotherms based on the Leibler–Sekimoto approach led to a bulk modulus K that increases as the proportion of nBMA increases, contrary to the behavior of dry annealed samples.

Drying of colloidal suspensions and polymer solutions near the contact line: deposit thickness at low capillary number.

Drying experiments with a receding contact line have been performed with silica colloidal suspensions and polyacrylamide (PAAm) polymer solutions. The experimental setup allows to control the receding movement of the contact line and the evaporation flux separately. Deposit thickness as a function of these two control parameters has been investigated. The different systems exhibit a similar behavior: in the regime of very low capillary numbers the deposit thickness scaled by the solute volume concentration and the evaporation rate is proportional to the inverse of the contact line velocity. Both the scaling exponent and the constant (which has the dimension of a length) do not depend on the system under study. The observation of this evaporative regime confirms some recent results obtained by Le Berre et al. on a very different system (phospholipidic molecules) and fully supports their interpretation. Following their approach, a simple model based on mass balance accounts for these results. This implies that this regime is dominated by the evaporation and that the deformation of the meniscus induced by viscous forces does not play any significant role. When increasing the velocity, another regime is observed where the thickness does not depend significantly on the velocity.

Analysis of the solvent diffusion in glassy polymer films using a set inversion method

Abstract Within the framework of solvent diffusion in glassy polymers, this paper concerns an experimental study of toluene sorption and desorption in P(MMA/nBMA) copolymer films. Gravimetric experiments (quartz microbalance) are performed in a pressure and temperature controlled chamber. Coupling between solvent diffusion and viscoelastic relaxation is taken into account through the time-dependent solubility model, based on the Fick diffusion equation inside the film and a time variable boundary condition at the film/vapor interface. Viscoelastic relaxation is described by a first order model or by a stretched exponential. In the present paper, a special focus is given on the set inversion method used to analyze the data and to derive well-defined uncertainty intervals upon each determined quantity, taking all the uncertainties on the weight measurements into account. We find that the mutual diffusion coefficient strongly decreases in the glassy state, of about two orders of magnitude for a 0.05 decrease in the solvent weight fraction.

Physical aging of glassy PMMA/toluene films: Influence of drying/swelling history

Gravimetry experiments in a well-controlled environment have been performed to investigate aging for a glassy PMMA/toluene film. The temperature is constant and the control parameter is the solvent vapor pressure above the film (i.e. the activity). Several experimental protocols have been used, starting from a high activity where the film is swollen and rubbery and then aging the film at different activities below the glass transition. Desorption and resorption curves have been compared for the different protocols, in particular in terms of the softening time, i.e. the time needed by the sample to recover an equilibrium state at high activity. Non-trivial behaviors have been observed, especially at small activities (deep quench). A model is proposed, extending the Leibler-Sekimoto approach to take into account the structural relaxation in the glassy state, using the Tool formalism. This model well captures some of the observed phenomena, but fails in describing the specific kinetics observed when aging is followed by a short but deep quench.

Sensitivity of diffusive-convective transition to the initial conditions in a transient Bénard-Marangoni problem

Sensitivity of a transient Benard-Marangoni problem is studied using stochastic models to simulate the uncertainties of thermal initial conditions. Using different assumptions, three probabilistic models are developed and compared. Statistics are performed on flow velocities and temperatures. Transitions are examined with respect to the stochastic models.Copyright

Estimation of the characteristic times of solvent diffusion and polymer relaxation in glassy polymer films by a set inversion method

This study deals with a multiparameter estimation problem with bounded output errors. It concerns the swelling of polymer films in the glassy state by a solvent. Local thermodynamic equilibrium is no more ensured, and the swelling results of two coupled phenomena, the diffusion of solvent on one hand and the change in solubility due to stress relaxation of the entangled polymer chains on the other. The estimation aims to obtain the parameters that characterize these two phenomena from gravimetric experiments. A set inversion analysis is used to perform the estimation: this global estimation method allows us to determine all the sets of parameters that give a mass uptake consistent with the experimental data and bounded errors. It gives interesting information on the coupling between the parameters and is well appropriate to analyze this ill-conditioned problem. A systematic analysis of the estimation performance as a function of the characteristics of the polymer–solvent system and of the experimental setup have been performed.

Some solutions for nonlinear optimal heat transfer problems

A short review of some heat transfer optimal control problems arising in building management for energy conservation is given. These problems are non-linear since both the internal energy source and the time-dependent parameters of the building envelope are control variables. In the singular case, optimal control is shown to be bang-bang and in the non-singular case, the equations of the feedback law are derived. Satisfactory numerical simulations are given that illustrate the two approaches of this practical control problem.

Aging in PMMA/Toluene Films

Experimental results of aging behavior for a polymer solution, when the control parameter is the solvent vapor pressure above the film (i.e. the activity) and the observation is the solvent concentration, are presented. Various aging protocols have been performed and analyzed on the system Polymethylmethacrylate (PMMA)/Toluene.