Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems

1990 ◽  
Vol 429 (1877) ◽  
pp. 639-671 ◽  
Keyword(s):  
Solute Transport ◽  
Chemical Reactions ◽  
Coarse Grained ◽  
Solution Technique ◽  
Multiphase System ◽  
Homogeneous Material ◽  
Phase System ◽  
Multiphase Systems ◽  
Phenomenological Coefficients ◽  
Reaction Processes

Convective-diffusive transport of a chemically reactive solute is studied analytically for a general model of a multiphase system composed of ordered or disordered particles of arbitrary shapes and sizes. Use of spatially periodic boundary conditions permits analysis of particulate multiphase systems of effectively infinite size. Solute transport occurs in both the continuous and discontinuous bulk phases, as well as within and across the interfacial phase boundaries separating them. Additionally, the solute is allowed to undergo generally inhomogeneous first-order irreversible chemical reactions occurring in both the continuous and discontinuous volumetric phases, as well as within the interfacial surface phase. Our object is that of globally describing the solute transport and reaction processes at a macro- or Darcy-scale level, wherein the resulting, coarse-grained particulate system is viewed as a continuum possessing homogeneous material transport and reactive properties. At this level the asymptotic long-time solute macrotransport process is shown to be governed by three Darcy-scale phenomenological coefficients: the mean solute velocity vector ͞U *, dispersivity dyadic ͞D *, and apparent volumetric reactivity coefficient ͞K *. A variant of a Taylor-Aris method-of-moments scheme (Brenner & Adler 1982), modified to include solute disappearance via chemical reactions, is used to express these three macroscale phenomenological coefficients in terms of the given microscale phenomenological data and geometry. The general solution technique, illustrated here for a simple, ordered geometrical realization of a two-phase system, reveals the competitive influences of the respective volumetric/surface-excess transport and reaction processes, as well as the solute adsorptivity, upon the three macroscale transport coefficients.

The chemical potential in thermodynamic systems under non-hydrostatic stresses

1968 ◽  
Vol 307 (1488) ◽  
pp. 1-13 ◽  
Keyword(s):  
Thermodynamic Equilibrium ◽  
Chemical Potential ◽  
Normal Component ◽  
Fluid Pressure ◽  
Multiphase System ◽  
Phase System ◽  
Hydrostatic Stresses ◽  
Discontinuous Displacement ◽  
Multi Phase ◽  
Work Done

It is proved that a chemical potential μ v = u v – Ts v + pv v may be introduced for every chemical component v which may be considered a possible component everywhere in a multiphase system in thermodynamic equilibrium under non-hydrostatic stresses, where —3 p is the trace of the stress tensor. It is a condition of equilibrium that μ v has the same value throughout such a system and it is shown that in a virtual infinitesimal variation d U = T d S + d W + Ʃ v μ v d N v , where U, S are the total energy and entropy of the multi-phase system, and d W is the total mechanical work done on the system. At an interface between phases where a discontinuous displacement is permitted, it is shown also that μ v = u v - Ts v + P n v v , for both phases in contact at the interface, P n being the normal component of the pressure at the interface. In a system in which each phase is under a uniform stress and is connected to at least one other phase by such an interface, all phases at equilibrium must thus have the same value of p , and the normal component of the pressure at every such interface must also be p . An important example of this latter result is that of a fluid-solid system, for which, if p is the fluid pressure, the solid must be under an equal hydrostatic pressure p together with a shear stress whose principal directions are perpendicular to the normal of the interface, this new result representing a considerable restriction on the possible stress in a solid at chemical equilibrium with the fluid. The chemical potential is not assumed to exist but is introduced as an undetermined multiplier in the application of the Gibbs condition of thermodynamic equilibrium, and all its important properties are deduced. The same method may be applied more simply in hydrostatic cases.

scholarly journals Reaction–diffusion basis of retroviral infectivity

2016 ◽  
Vol 374 (2080) ◽  
pp. 20160148 ◽  
Author(s):  
S. Kashif Sadiq
Keyword(s):  
Chemical Reactions ◽  
Membrane Surface ◽  
Reaction Diffusion ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Multiscale Approach ◽  
The Matrix ◽  
Membrane Bound ◽  
Spatio Temporal ◽  
Dynamics Simulations

Retrovirus particle (virion) infectivity requires diffusion and clustering of multiple transmembrane envelope proteins (Env 3 ) on the virion exterior, yet is triggered by protease-dependent degradation of a partially occluding, membrane-bound Gag polyprotein lattice on the virion interior. The physical mechanism underlying such coupling is unclear and only indirectly accessible via experiment. Modelling stands to provide insight but the required spatio-temporal range far exceeds current accessibility by all-atom or even coarse-grained molecular dynamics simulations. Nor do such approaches account for chemical reactions, while conversely, reaction kinetics approaches handle neither diffusion nor clustering. Here, a recently developed multiscale approach is considered that applies an ultra-coarse-graining scheme to treat entire proteins at near-single particle resolution, but which also couples chemical reactions with diffusion and interactions. A model is developed of Env 3 molecules embedded in a truncated Gag lattice composed of membrane-bound matrix proteins linked to capsid subunits, with freely diffusing protease molecules. Simulations suggest that in the presence of Gag but in the absence of lateral lattice-forming interactions, Env 3 diffuses comparably to Gag-absent Env 3 . Initial immobility of Env 3 is conferred through lateral caging by matrix trimers vertically coupled to the underlying hexameric capsid layer. Gag cleavage by protease vertically decouples the matrix and capsid layers, induces both matrix and Env 3 diffusion, and permits Env 3 clustering. Spreading across the entire membrane surface reduces crowding, in turn, enhancing the effect and promoting infectivity. This article is part of the themed issue ‘Multiscale modelling at the physics–chemistry–biology interface’.

scholarly journals Morphological changes of amphiphilic molecular assemblies induced by chemical reactions

Soft Matter ◽  
2015 ◽  
Vol 11 (7) ◽  
pp. 1403-1411 ◽  
Author(s):  
Koh M. Nakagawa ◽  
Hiroshi Noguchi
Keyword(s):  
Chemical Reactions ◽  
Morphological Changes ◽  
Molecular Simulations ◽  
Coarse Grained ◽  
Molecular Assemblies ◽  
Shape Transformations

Shape transformations of amphiphilic molecular assemblies induced by chemical reactions are studied using coarse-grained molecular simulations.

Multiphase approximation for small-angle scattering

2009 ◽  
Vol 43 (1) ◽  
pp. 8-11 ◽  
Author(s):  
Dragomir Tatchev
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
Multiphase System ◽  
Contrast Variation ◽  
Two Phase ◽  
Angle Scattering ◽  
Multiphase Systems ◽  
Phase Systems ◽  
The Difference ◽  
Two Phases

The two-phase approximation in small-angle scattering is well known and is still the dominant approach to data analysis. The intensity scattered at small angles is proportional to the second power of the difference between the scattering densities of the two phases. Nevertheless, scattering contrast variation techniques are widely used, and they are obviously suitable for multiphase systems or systems with gradually varying scattering density, since if no parasitic scattering contributions are present the scattering contrast variation would only change a proportionality coefficient. It is shown here that the scattered intensity at small angles of a multiphase system can be represented as a sum of the scattering of two-phase systems and terms describing interference between all pairs of phases. Extracting two-phase scattering patterns from multiphase samples by contrast variation is possible. These two-phase patterns can be treated with the usual small-angle scattering formalism. The case of gradually varying scattering density is also discussed.

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