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  • 1.
    Gamero, Rafael
    et al.
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena.
    Picado, Apolinar
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena.
    Luna, Fabio
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena.
    Martínez, Joaquín
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena.
    AN ANALYTICAL SOLUTION OF THE CONVECTIVE DRYING OF A MULTICOMPONENT LIQUID FILM2006In: DRYING 2006 / [ed] I. Farkas, Gödöllo, Hungary: Szent István University Publisher , 2006, p. 516-523Conference paper (Refereed)
    Abstract [en]

    Analytical solutions of the diffusion and conduction equations applied to liquid-side-controlled convective drying of a multicomponent liquid film are developed. Assuming constant physical properties of the liquid, the equations describing interactive mass transfer are decoupled by a similarity transformation and solved simultaneously with conduction equation by the method of variable separation. Variations of physical properties along the process trajectory are taken into account by a stepwise application of the solution in time intervals with averaged coefficients from previous time steps. Despite simplifications, the analytical solution gives a good insight into the selectivity of the drying process and is computationally fast.

  • 2.
    Luna, Fabio
    KTH, Superseded Departments, Chemical Engineering and Technology.
    Drying of Multicomponent Liquid Films2004Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    The convective drying of thin layers of multicomponentliquid mixtures into an inert gas, and the influence ofdifferent process controlling mechanisms on drying selectivityis studied. Drying experiments under gas-phase-controlledconditions are performed by low intensity evaporation, fromfree liquid surfaces, of ternary mixtures without non-volatilesolutes. Liquid-side-controlled experiments are carried out bydrying a multicomponent polymeric solution containing twovolatile components, one non-volatile polymer and an optionalnonvolatile softening substance.

    Mathematical models to describe gas- andliquid-side-controlled drying based on interactive diffusion inboth liquid and gas phases as the main mechanisms for masstransfer are developed. For gas-phase-controlled drying, astability analysis of the ordinary differential equations thatdescribes the evaporation process is performed. Isothermal andnon-isothermal drying processes are considered in batch andcontinuous modes. The mathematical model to describe thecomposition profiles during batch drying of the polymeric film,considering liquid resistance, is solved numerically. Due tothe lack of experimental data, properties for this polymericsystem are estimated by using established methods. Ananalytical solution of the diffusion equation, by assuming anisothermal drying process and a constant matrix ofmulticomponent diffusion coefficients is developed. For thecontinuous case, liquid-side resistance is studied by modellingevaporation of a multicomponent falling liquid film into aninert gas including indirect heating.

    The results of the gas-phase-controlled model are in goodagreement with experimental results. For the polymeric film,the agreement is only qualitative since the model does notaccount for a membrane that develops on the film surface. Thestability analysis permits the prediction of trajectories andfinal state of a liquid mixture in a gas-phase-controlleddrying process. For isothermal evaporation of ternary mixturesinto pure gas, the solutions are trajectories in the phaseplane represented by a triangular diagram of compositions. Thepredicted ternary dynamic azeotropic points are unstable orsaddle. On the other hand, binary azeotropes are stable whenthe combination of the selectivities of the correspondingcomponents is negative. In addition, pure component singularpoints are stable when they are contained within theirrespective isolated negative selectivity zones. Undernon-isothermal conditions, maximum temperature valuescharacterise stable azeotropes. Incremental loading of the gaswith one or more of the components leads to a node-saddlebifurcation, where a saddle azeotrope and a stable azeotropecoalesce and disappear. For continuous drying, the singularpoints are infinite and represent dynamic equilibrium pointswhose stability is mainly dependent on the ratio of inletgas-to-liquid flow rates. As long as the process isgas-phasecontrolled, these results also apply to a porous solidcontaining a liquid mixture.

    In general, liquid-side control makes the drying processless selective but it is difficult to maintain this conditionduring the whole process. Under the influence of its owndynamics, a process starting as liquid-side-controlled tendstowards a gas-phase-controlled process. The presence ofnon-volatile components and indirect heating may delay thisdevelopment. Considering the evolution of the processcontrolling steps and its influence on selectivity, a modelaimed at describing the complete trajectory of a drying orevaporation process must include the coexistence of allrelevant mechanisms.

    Keywords:ternary mixture, falling film, diffusionequation, gas-phase control, liquid-phase control, selectivity,stability analysis, polymeric solution, evaporation, azeotrope,batch drying, continuous drying.

  • 3.
    Luna, Fabio
    et al.
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena.
    Birgersson, Erik E.
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology.
    Martinez, Joaquin
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena.
    Diffusion equation applied to isothermal drying of a multicomponent liquid film2005In: Drying Technology, ISSN 0737-3937, E-ISSN 1532-2300, Vol. 23, no 11-sep, p. 1953-1975Article in journal (Refereed)
    Abstract [en]

    Liquid-side-controlled drying by convection of a multicomponent liquid film is studied. Interactive diffusion in liquid phase is considered the main mechanism for mass transfer. Assuming an isothermal drying process and a constant matrix of multicomponent diffusion coefficients, an analytical solution of the diffusion equation is developed. The equations are decoupled by a similarity transformation and solved by the method of variable separation. The solution is applied to the drying of ternary mixtures, one of them containing a component of negligible volatility. The variation of diffusion coefficients along the process trajectory was taken into account by a piecewise application of the solution in time intervals with averaged coefficients from previous time steps. Despite the simplifications made, the analytical solution gives a god insight into the selectivity of the drying process and is computationally fast. The limitations of the analytical solution and the prospect of applying the solution to the description of a nonisothermal process are discussed. It would introduce an important computational economy since the rigorous treatment of multicomponent drying leads to partial differential equations with variable coefficients, which can only be solved by time-consuming iterative procedures.

  • 4.
    Luna, Fabio
    et al.
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena.
    Martínez, Joaquín
    KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena.
    Isothermal Drying of a Multicomponent Liquid Film2004In: DRYING 2004: IDS 2004 / [ed] M.A. Silva and S.C.S. Rocha, Sao Paulo, Brazil: State University of Campinas , 2004, p. 461-468Conference paper (Refereed)
1 - 4 of 4
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