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  • 1.
    Gustavsson, Katarina
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Oppelstrup, Jesper
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Numerical 2D models of consolidation of dense flocculated suspensions2001In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 41, no 2-3, p. 189-201Article in journal (Refereed)
    Abstract [en]

    A mathematical 2D model for a consolidation process of a highly concentrated, flocculated suspension is developed. The suspension is treated as a mixture of a fluid and solid particles by an Eulerian two-phase fluid model. The suspension is characterized by constitutive relations correlating the stresses, interaction forces, and inter-particle forces to concentration and velocity gradients. This results in three empirical material functions: a permeability, a non-Newtonian viscosity and a non-reversible particle interaction pressure. Parameters in the models are fitted to experimental data. A simulation program using finite difference methods both in time and space is applied to one and two dimensional test cases. The effect of different viscosity models as well as the effect of shear on consolidation rate is studied. The results show that a shear thinning viscosity model yields a higher consolidation rate compared to a model that only depends on the volume fraction. It is also concluded that the size of the viscosity influences the time scale of the process and that the expected effect of shear on the process is not weil reproduced with any of the models.

  • 2. Hamalainen, J.
    et al.
    Lindström, Stefan B.
    KTH, School of Chemical Science and Engineering (CHE), Fibre and Polymer Technology, Fibre Technology.
    Hamalainen, T.
    Niskanen, H.
    Papermaking fibre-suspension flow simulations at multiple scales2011In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 71, no 1, p. 55-79Article in journal (Refereed)
    Abstract [en]

    Papermaking flows are extremely challenging for modelling and simulation, if one accepts their full complexity. A wide range of particles, including fibres, fibre fragments (fines) and fillers (non-organic particles), flow and interact with each other in a non-dilute suspension, a complex geometry and at a high flow rate. Different simulation approaches are reviewed from particle-level simulations, through meso-scale simulations to the full flow geometry of the papermaking line. Their application to papermaking and potential to provide fundamental understanding as well as direct process-optimization support are discussed.

  • 3.
    Vynnycky, Michael
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Casting of Metals. University of Limerick, Ireland.
    An asymptotic model for the primary drying stage of vial lyophilization2016In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 96, no 1, p. 175-200Article in journal (Refereed)
    Abstract [en]

    Asymptotic methods are employed to analyse a commonly used one-dimensional transient model for coupled heat and mass transfer in the primary drying stage of freeze-drying (lyophilization) in a vial. Mathematically, the problem constitutes a two-phase moving boundary problem, in which one of the phases is a frozen porous matrix that undergoes sublimation, and the other is a low-pressure binary gaseous mixture. Nondimensionalization yields a model with 19 dimensionless parameters, but a systematic separation of timescales leads to a reduced model consisting of just a second-order differential equation with two initial conditions for the location of a sublimation front; the temperature and gas partial pressures can be found a posteriori. The results of this asymptotic model are compared with those of earlier experimental and theoretical work. Most significantly, the current model would be a computationally efficient tool for predicting the onset of secondary drying.

  • 4.
    Vynnycky, Michael
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Casting of Metals. University of Limerick, Ireland .
    Gordon, A. D.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Casting of Metals. University of Limerick, Ireland .
    Non-isothermal hydrophobicity-dependent two-phase flow in the porous cathode gas diffusion layer of a polymer electrolyte fuel cell2015In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 92, no 1, p. 123-146Article in journal (Refereed)
    Abstract [en]

    In this paper, we extend a recent one-dimensional isothermal steady-state generalized Darcy model for two-phase flow in the porous cathode gas diffusion layer of a polymer electrolyte fuel cell, so as to include the effect of heat transfer. As for the isothermal case, we arrive at either a fixed- or free-boundary problem, depending on the main problem parameters: inlet temperature (), inlet water saturation (), inlet relative humidity (RH), porous medium hydrophobicity and cathode overpotential (). The inclusion of heat transfer is found to limit the range of values of and RH over which two-phase flow can occur, as compared to that predicted by the isothermal model. The ensuing non-isothermal two-phase flow model equations are then computed numerically, with particular care being required for the treatment of an integrably singular inter-phase mass transfer term.

  • 5.
    Vynnycky, Michael
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. Univ Limerick, Dept Math & Stat, Limerick V94 T9PX, Ireland.
    Lacaze, J.
    Univ Toulouse, CIRIMAT, 4 Allee Emile Monso CS44362, F-31030 Toulouse 4, France..
    On the modelling of joint formation in dissolutive brazing processes2019In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 116, no 1, p. 73-99Article in journal (Refereed)
    Abstract [en]

    In this paper, earlier dissolutive wetting models describing the dynamics of an axisymmetric alloy drop spreading on pure metal substrate are extended to describe reactive wetting and subsequent joint formation in brazing processes. A two-dimensional time-dependent problem is formulated, and the model equations are nondimensionalized, revealing the possibilities for asymptotic model reduction. Whilst the numerical solution of the time-dependent problem, which contains two moving contact lines and would not in general be amenable to lubrication theory, is relegated to future work, the steady-state problem is analyzed in detail. The analysis offers an arguably more transparent alternative to an earlier energy minimization approach for finding the location of the meniscus, which ultimately constitutes the joint. The results of the present model are found to compare favourably to those of earlier experimental and theoretical work.

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