[Mixing and Deformation of Viscous Fluids]
[Multicomponent, Multiphase Flow in Porous Media]
[Shearing Flow of Polymer Solutions]
[Reactive Mixing and Flow]
The study of multiphase flows has important applications in fluid mixing and reaction, enhanced oil recovery and transport in porous media, as well as in the processing of polymer blends and solutions. However the analysis of these systems by classical continuum formulations presents severe numerical challenges. The model equations have to be solved separately in each phase and the interfacial boundary conditions satisfied by iteration on the unknown position of the interface. The usefulness of molecular dynamics simulations for the study of macroscopic phenomena is limited by the tremendously large ratio of the hydrodynamic scales to the molecular length and time scales. A mesoscale description of the flow provides a good balance between microscopic fidelity and continuum scales.
In the mesoscopic approach for modeling flow and transport phenomena in multiphase systems, the system is characterized by a coarse-grained conserved order parameter that takes characteristic values in the bulk phases and varies continuously in a narrow interfacial region. The free energy of the system is a function not only of the local composition but also includes contributions from gradients in the order parameter field, accounting for interfacial effects. From a computational point of view, the basic idea underlying the method is to replace the dividing surface between the coexisting phases by a transition region of small but finite width, across which the various thermodynamic variables change continuously. Thus the original moving boundary problem is replaced by a system of partial differential equations, with solutions that are continuous throughout the domain but have large variations in the interfacial region. However, what is important from a physical point of view is that this is a thermodynamically consistent formulation, giving the correct fluid behavior at the interface, with the Gibbs-Thomson interfacial conditions being obtained in the limit. This approach allows for the inclusion, in a consistent manner, of interaction with solid walls that gives rise to important phenomena such as wetting and moving contact lines that cannot be easily included in a classical continuum formulation. In addition, coalescence and breakup behavior can be observed without the need for imposition of arbitrary criteria.
For simple geometries and in two dimensions, the model equations can be solved by classical finite-difference or finite-element techniques. However in three-dimensions and for complex geometries, direct numerical integration is prohibitively expensive. For these cases an alternative approach is used. A set of distribution functions representing the mean populations of the particles on a lattice, is allowed to relax to equilibrium according to a Boltzmann equation which is discrete in both space and time. With the proper choice of the equilibrium distribution functions, the appropriate dynamic equations are recovered in the long wavelength limit. Conditions at solid boundaries are relatively easily implemented making them ideal for handling complex geometries, and their local nature makes them highly amenable to massively parallel processing These advantages make possible the study of multiphase flows in irregular three-dimensional geometries.
The deformation and stretching of ``active'' interfaces in externally driven flows of immiscible fluids is characterized by highly convoluted interfaces and large interfacial stretch. We have analyzed the evolution of the interface in driven shear flows using a mesoscopic approach.
We have also used a Green's function approach to study spinodal decomposition and nucleation in unbounded two and three-dimensional creeping flows. We are also analyzing the stratified multiphase flow of polymer melts (coextrusion). These flows can be characterized by large changes in topology --- e.g from a side by side configuration to encapsulation of one phase by the other, which again are difficult to study by classical techniques.
Porous flow problems are generally solved by volume-averaged approaches such as Darcy's laws and its extensions. However, in problems involving multiphase flow and transport there are difficult closure problems, and it is desirable to relate the volume-averaged parameters used at the macroscopic scale to the the microscopic processes occuring at the pore scale. We are carrying out pore-scale studies of immiscible displacement flows in model porous media to calculate volume-averaged quantities.
The coupling of concentration fluctuations to shear for Newtonian fluids leads to apparent decreases in coexistence temperatures. However, for polymeric solutions and blends under shear, enhancement of concentration fluctuations can occur due to their coupling with polymer elastic stresses, leading to significantly enhanced turbidity, without a symmetry breaking transition. This has significant consequences because the same phenomena can be used to explain concentration depletion near solid boundaries, leading to the phenomena of apparent slip at solid walls. Migrstion away from a solid wall can also result from a repulsive potential imposed by the wall which can also be included in our approach.
We are using a cell-dynamic approach for the reaction diffusion equation together with a Boltzmann approach for coupled fluid flow for a computationally efficient approach to the problem of reactive mixing of complex microstructures of segregated reactants undergoing ``fast'' reactions, and stabilization of periodic structures in phase-separated binary mixtures by reaction.
Chella, R., Lasseux, D., and Quintard, M., "Multiphase, Multicomponent Fluid Flow in Homogeneous and Heterogeneous Porous Media, Rev. Inst. Fr. Petr., 53(3), 335-346 (1998).
Chella, R. and Vinals, J, ``Mixing of a two-phase fluid by cavity flow'', Phys. Rev. E 53 , 3832 (1996).
Chella, R., ``Laminar Mixing of Miscible Liquids'', chapter 1 in "Mixing and Compounding of Polymers" (Editors: I. Manas and Z. Tadmor), Progress in Polymer Processing Series, Hanser Publishers, 1995,
Chella, R., Aithal, R. and N. Chandra, ``Evaluation of Fracture Parameters for Composites Subjected to Brittle Shock Using the Boundary Element Method and Sensitivity Analysis Techniques'', Engineering Fracture Mechanics, 44(6), 949-961, 1993.
Chandra, N., Chella, R. and K.L. Chen: Effect of Cracks on the Mechanical Behavior of Materials -- A Finite-Element Approach, Ceramics Transactions, 17, 493-501, 1990. [an error occurred while processing this directive]
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