Macroscopic Transport Phenomena Research Articles

Mesh-Free Simulation of Transport Phenomena in Continuous Castings of Aluminium Alloys

This paper introduces a general numerical scheme for solving convective-diffusive problems that appear in the solution of microscopic and macroscopic transport phenomena in continuous castings and the heat treatment of aluminium alloys. The numerical scheme is based on spatial discretisation that involves pointisation only. The solution is based on diffuse collocation with multi-quadric radial basis functions. The application of the method is demonstrated in a simplified model of a billet DC casting and verified by a comparison with the classical finite volume method.

Macroscopic transport phenomena in native and engineered cartilage tissue

Macroscopic transport phenomena in native and engineered cartilage tissue

Fe-liquid segregation in deforming planetesimals: Coupling Core-Forming compositions with transport phenomena

Abstract The segregation and macroscopic transport phenomena leading ultimately to the formation of metallic cores in planetary silicate mantles is a fundamental yet poorly understood process. Here we report the results of a series of deformation experiments on a sample of partially molten Kernouve H6 chondrite ( T = 900–1050 °C) aimed at determining the siderophile concentrations and associated partition coefficients in both Fe–S–Ni–O quench and Fe–Ni metal as a function of degree of melting, and to provide insight into the melt segregation mechanism(s). The geochemical results show the S content in the segregated Fe-rich liquid metal decreases with increasing degree of melting. As the S content of the liquid metal also strongly affects the partitioning of highly siderophile elements between solid and liquid metal, an increase in porosity (Fe liquid melt fraction) from c. 5% to 30% lowers D SM/LM for HSE by several orders of magnitude. The relationship between melt fraction and porosity is used to compare the migration rate of liquid metal driven by buoyancy pressure gradients with a new theoretical model of melt segregation in a deforming porous medium that takes into account the coupling between volume strain (dilatancy) and shear stress. For buoyancy driven porous flow, highest transport velocities occur at highest porosities, implying the fastest flow velocities will carry Fe-rich liquid metal with low sulfur contents, preferentially enriched in incompatible HSEs. Predicted characteristic timescales of liquid metal transport due to buoyancy effects (diapirism and porous flow) for a c. 100 km-sized planetesimal are contrasted with shear-induced segregation velocities set up in response to external perturbations via impacts, an important process during the final stages of planetary accretion. A novel feature of our analysis is that liquid metal segregated previously into a planetary core by buoyancy instabilities (e.g., porous flow or a raining mechanism), might be drawn locally back into the silicate lower mantle by pressure gradients linked to surface impacts providing a physical mechanism for return flow of siderophile elements across the CMB.

Washing Processes for Disperse Particulate Systems – Process Spectrum and Aspects for the Process Choice

AbstractWashing of disperse solid systems is a widely used and complex operation. Since the washing step is mostly integrated into other process operations, it is subject to numerous demands exceeding by far the primary demands, like a good separation result and a low specific wash liquid demand. Because of the phenomenology and limits of different washing processes it is difficult to choose an appropriate washing process. Additionally, the acting transport mechanisms of some washing processes are not yet sufficiently understood. This work gives a broad overview of the existing washing processes, the numerous parameters, and the demands they have to meet. Based on a categorization of washing processes and the classification of these processes according to their macroscopic transport phenomena, an evaluation scheme has been developed which compares and assesses existing washing processes and shows their individual limits. The present work can be used as a rough guideline for the choice of an appropriate washing process.

Variable sphere molecular model for inverse power law and Lennard-Jones potentials in Monte Carlo simulations

The variable sphere (VS) molecular model for the Monte Carlo simulation of rarefied gas flow is introduced to provide consistency for diffusion and viscosity cross-sections with those of any realistic intermolecular potential. It is then applied to the inverse power law (IPL) and Lennard-Jones (LJ) potentials. The VS model has a much simpler scattering law than either the variable hard sphere (VHS) or variable soft sphere (VSS) models; also, it has almost the same computational efficiency as the VHS and VSS models. A simulation of velocity relaxation in a homogeneous space and two comparative simulations of molecular diffusion in a homogeneous heat-bath gas and normal shock wave structure in a monatomic gas are made to examine VS model validity. The relaxation to a Maxwellian distribution function and equipartition between all degrees of freedom are well established; good agreement is shown in the molecular diffusion and shock wave structure between the VS model and the IPL and LJ potentials. The VS model is combined with the statistical inelastic cross-section (SICS) model and applied to simulation of translational and rotational energy relaxation in a homogeneous space. The VS model shows the relaxation of Maxwellian and Boltzmann distribution functions and equipartition between all degrees of freedom. Comparative calculation between the VS model with the SICS (VS-SICS) model and the VSS model with the SICS (VSS-SICS) model is made for rotational relaxation in a nitrogen normal shock wave. Good agreement is shown in the shock wave structure and rotational energy distribution function between the VS-SICS model and the VSS-SICS model. This study demonstrates that diffusion and viscosity cross-sections, rather than the scattering law of each molecular collision, affect macroscopic transport phenomena.

The role of macroscopic transport phenomena in film microstructure during epitaxial growth

A multiscale integration hybrid algorithm is introduced to describe film microstructure in epitaxial growth under conditions where fluid mechanics and transport phenomena in the adjacent fluid phase are important, such as in chemical vapor deposition at relatively high pressures. This algorithm is demonstrated in a stagnation point flow reactor. It is shown that mass transfer limitations delay the transition from the step flow to the two-dimensional nucleation growth mode, as the substrate temperature decreases, and could possibly eliminate kinetic microroughening. Furthermore, the temporal development of morphological features upon changes in operating conditions is determined by the bulk convective flow.

Lattice-based simulations of chain conformations in semi-crystalline polymers with application to flow-induced crystallization

Polymer fiber processes, such as high-speed spinning of nylon and PET, are highly complex involving a complicated interplay between an evolving internal molecular microstructure, macroscopic transport phenomena, such as fluid mechanics and heat transfer, and also non-equilibrium thermodynamics and kinetics affecting nucleation and subsequent crystal growth. All of the above processes are important in determining the final product's semi-crystalline morphology which is primarily responsible for its mechanical properties. Our approach to attack this problem is a hierarchical one: A macroscopic (continuum) model is developed based on the Hamiltonian formalism of non-equilibrium thermodynamics for flowing systems [Beris and Edwards, Oxford University Press, Oxford, 1994]. This approach allows us to follow the dynamic evolution of several macroscopic (continuum) variables involving both kinematic and structural parameters. To implement this approach successfully, an accurate modeling of the (extended) free energy (Hamiltonian) of the system under consideration and the dissipation therein is necessary. While the later is, at the moment, phenomenological, we are developing a first principles approach for the former based on a microscopic modeling of chain conformations using a lattice model. Lattice models have been used extensively before for the analysis of chain conformations in both purely amorphous and semi-crystalline polymers. We have reinterpreted some of the earlier lattice models by systematically deriving the relevant statistics of polymer chains and by outlining the a priori approximations in those models which are necessary to arrive at closed-form expressions. Although we do make use of such earlier work, we have also extended it through a computer-aided analysis. This analysis has enabled us to generate from first principles free energy surfaces for a system consisting of polymer chains, represented as multiple self- and mutually-avoiding random walks, on a 2-D fully populated semi-crystalline lattice. It is shown that the numerical results for dense semi-crystalline systems can be fitted with low order polynomials that provide closed-form approximations for the configurational entropy in terms of non-equilibrium structural parameters, such as the orientation and stretching of the polymer chains. Finally, chain statistics for bulk amorphous polymers have been validated against their theoretical predictions.

Lateral transport and dynamical behavior of quasi-two-dimensional excitons at high density along a stacking disorder plane in layered BiI 3 crystals

Macroscopic exciton transport phenomena from a small area of an exciting laser spot to outside the spot along a quasi-two-dimensional planar defect in BiI 3, are presented from space-resolved pump-probe absorption, photoluminescence, and four-wave-mixing measurements. At high intensity, the blue shift of the transition energy at the point away from the pump spot is analyzed by the 2-D diffusion. The four-wave-mixing signals are detected with time delays when the two laser beams are spatially separated.

Mixture continuum formulation of convection-conduction energy transport in multiconstituent solid-liquid phase change systems for BEM solution techniques

This paper describes the two nonlinear boundary-domain integral equations for Fourier heat conduction and convection governed energy transport. The equations are compatible with the mixture continuum formulation of an incompressible multiconstituent solid-liquid phase change system. The equations assume the boundary conditions to be functions of thermal field, and thermal conductivity and specific heat to be functions of temperature and species concentrations. The constitutive enthalpy-temperature relation is assumed to be a function of the species concentrations. The integral equations are derived on the basis of time-domain weighting with the fundamental solutions of the Laplace and Fourier equations and are suitable for boundary element discrete approximative method solution techniques. The nonlinearity that appears in thermal conductivity is treated by the Kirchhoff transform and the nonlinearities of specific heat and specific latent heat phase change are both transformed into the nonlinearity of the source term. The presented equations, in connection with a similar integral description for mass, momentum and species conservation, will be used as a basis for the boundary element method computation of macroscopic transport phenomena characteristics for melting and solidification.

A volume-averaged two-phase model for transport phenomena during solidification

A basic model of the transport phenomena occurring during solidification of multicomponent mixtures is presented. The model is based on a two-phase approach, in which each phase is treated separately and interactions between the phases are considered explicitly. The macroscopic transport equations for each phase are derived using the technique of volumetric averaging. The basic forms of the constitutive relations are developed. These relations link the macroscopic transport phenomena to microscopic processes such as microstructure development, interfacial stresses, and interfacial heat and mass transfer. Thermodynamic relations are presented, and it is shown that nonequilibrium effects can be addressed within the framework of the present model. Various simplifications of the model are examined, and future modeling needs are discussed.

Modeling Refractory Material Production by Self-Propagating High Temperature Synthesis (SHS)

ABSTRACTSelf-propagating high temperature synthesis (SHS) can be used to prepare near net refractory shapes which are difficult to produce by other methods. In SHS, green compacts capable of strong exothermal reaction are ignited at one end and transformed into the desired products by a self-propagating reaction. Physical processes involved in SHS include chemical kinetics, macroscopic transport phenomena and phase transformations. This paper describes a simplified mathematical model of the SHS process derived by combining the heat equation with the chemical reaction rate equation. The model equations are solved numerically to obtain representation of the SHS process. Parametric studies have been performed to investigate the relative importance of the physical parameters in the model.

Connection between Macroscopic and Microscopic Transport Phenomena in Solid Conductors

An expression for the rate of production of entropy in a homogeneous solid conductor is obtained and in the process leads to a natural selection of current densities. It is shown that these current densities when written from the microscopic point of view give a system of equations satisfying Onsager's theorem, thus facilitating a comparison between microscopic and macroscopic transport phenomena.