Macroscopic coefficients proper

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

Macroscopic experiments such as core flooding have been used to obtain relative permeabilities, dispersion coefficients, and other variables relevant to reservoir flow. However, they cannot reveal details of how immiscible phases interact on the pore level. Instead visual experiments have been used to elucidate microscopic flow mechanisms. The latter approach is taken here with experiments using a novel flow cell and state-of-the-art video equipment. The pore level phenomena observed provide a basis for the proper modeling of two-phase flow through porous media at high capillary numbers. 

Determination of the coefficients based on understanding of the membrane microstructure and modelling of the interaction between the membrane and the two transported species, i.e. hydronium and water, would be better. Most desirable would be a proper mathematical transition from an exact microscopic description of the interaction of membrane, hydronium and water, towards a macroscopic model. Such information and description being currently unavailable, we have to rely on guidance from knowledge on the membrane morphology to devise assumptions on the functional dependence of the coefficients on temperature and water content. 

Diffusion. The translational diffusion coefficient D is the most commonly measured transport property of polymer solutions, but as there are several distinct types of diffusion, care must be taken to interpret D properly. For c < c, Brownian motion of isolated chains in a homogeneous solvent defines the dilute solution diffusion coefficient Dq. As c increases toward c and above, chain-chain interactions modify the friction felt during chain motion. Under these conditions, the tracer- or self-diffusion coefficient Dtr is measured by tracking the path of a single chain in a macroscopically imiform mixture of chains and solvent. To distinguish the test chain from neighbors so that its path can be identified, the chain... 

The proper representation of macroscopic transport properties, particularly the heat transfer coefficient, is a major problem in the predictive modeling of spinning and other free-surface processing flows. Heat transfer coefficients are typically obtained from experiments on nondeforming wires, and the extension to a deforming surface with a variable cross section is not obvious. Data obtained on real spinlines require either infrared or intrusive contact temperatme... 

It should be noted that the radiotracer and pulsed field gradient NMR techniques measure the self-diffusion coefficient of water, Ds, rather than the Fickian or interdiffusion coefficient of water through the polymer membrane, D, and some correction is required, because it is the Fickian water diffusion coefficient that is the proper transport property to use in macroscopic studies of water diffusion [17]. The relationship is ... 

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