Models microstructured fluids

In all but the most basic cases of very dilute systems, with microstructural elements such as rigid particles whose properties can be described simply, the development of a theory in a continuum context to describe the dynamical interactions between structure and flow must involve some degree of modeling. For some systems, such as polymeric solutions, we require modeling to describe both polymer-solvent and polymer-polymer interactions, whereas for suspensions or emulsions we may have an exact basis for describing particle-fluid interactions but require modeling via averaging to describe particle-particle interactions. In any case, the successful development of useful theories of microstructured fluids clearly requires experimental input and a comparison between experimental data and model... 

At its most satisfying level, a statistical thermodynamic theory would begin by specifying realistic interaction potentials for the molecular components of a complex mixture and from these potentials the thermodynamic functions and phase behavior would be predicted without further approximation. For the next decade or so, there is little hope to accomplish such a theory for microstructured fluids. However, predictive theories can be obtained with the aid of elemental structures models. Also, lattice models... 

James Wei Thermodynamics in service to oil and gas and commodity chemicals is a very successful model. It s a mature technology on the S curve. The problem is to know the material properties in very great detail so we can optimize each percent improvement in efficiency, which represents a lot of money. Early in his lecture, Keith mentioned new materials and speciality chemicals. In these applications, we re going into a different mode, and a different type of a commitment is needed. For instance, many biotechnology products and some of the microstructured fluids and solids are produced in very small volume, they have a short product cycle, and we cannot be assured that the same product will still be produced ten years from now. It s important to get these specialty chemical products on the market speedily. Because they are produced in very small volume, we cannot afford large amounts of time or research money. Let s say that one percent of the sales volume is a reasonable research dollar. Instead of methane,... 

Problem 2-23. Constitutive Equations. As a model of a nonpolar microstructured fluid, consider the material to be described by a single unit vector p. Construct the most general relation between the stress tensor T and the rate-of-strain tensor e that is linear in e and depends on p. Note when e = 0, the stress is not necessarily isotropic. 

The major component of the synovial fluid, that is, hyaluronan, has two main functions namely lubricant and shock impulse damping [25]. Furthermore, hyaluronic acid is a major component of the extracellular matrix of the connective tissue. This kind of polymer should exhibit viscoelastic properties that directly depend on its microstructure and external parameters such as shear rate, stress and temperature. Knowledge of dependence of model synovial fluid viscosity on the shear rate, stress and temperature is very useful for biomedical applications, for example, in treatment of joint diseases. 

Pearson,. I.R.A., 1994. Report on University of Wales Institute of Non-Newtonian Fluid Mechanics Mini Symposium on Continuum and Microstructural Modelling in Computational Rheology. /. Non-Newtonian Fluid Mech. 55, 203 -205. 

As noted before, thin film lubrication (TFL) is a transition lubrication state between the elastohydrodynamic lubrication (EHL) and the boundary lubrication (BL). It is widely accepted that in addition to piezo-viscous effect and solid elastic deformation, EHL is featured with viscous fluid films and it is based upon a continuum mechanism. Boundary lubrication, however, featured with adsorption films, is either due to physisorption or chemisorption, and it is based on surface physical/chemical properties [14]. It will be of great importance to bridge the gap between EHL and BL regarding the work mechanism and study methods, by considering TFL as a specihc lubrication state. In TFL modeling, the microstructure of the fluids and the surface effects are two major factors to be taken into consideration. 

When the length scale approaches molecular dimensions, the inner spinning" of molecules will contribute to the lubrication performance. It should be borne in mind that it is not considered in the conventional theory of lubrication. The continuum fluid theories with microstructure were studied in the early 1960s by Stokes [22]. Two concepts were introduced couple stress and microstructure. The notion of couple stress stems from the assumption that the mechanical interaction between two parts of one body is composed of a force distribution and a moment distribution. And the microstructure is a kinematic one. The velocity field is no longer sufficient to determine the kinematic parameters the spin tensor and vorticity will appear. One simplified model of polar fluids is the micropolar theory, which assumes that the fluid particles are rigid and randomly ordered in viscous media. Thus, the viscous action, the effect of couple stress, and... 

TFL is an important sub-discipline of nano tribology. TFL in an ultra-thin clearance exists extensively in micro/nano components, integrated circuit (IC), micro-electromechanical system (MEMS), computer hard disks, etc. The impressive developments of these techniques present a challenge to develop a theory of TFL with an ordered structure at nano scale. In TFL modeling, two factors to be addressed are the microstructure of the fluids and the surface effects due to the very small clearance between two solid walls in relative motion [40]. 

The issues of selection of the spatial wavelength and the deterministic character of the fine scale features of the microstructure are closely related to similar questions in nonlinear transitions in a host of other physical systems, such as macroscopic models of immiscible displacement in porous media - - the Hele Shaw Problem (15) - and flow transitions in fluid mechanical systems (16). 

The simulations of fluid flow and heat transfer in such microstructured geometries were carried out with an FVM solver. Air with an inlet temperature of 100 °C was considered as a fluid, and the channel walls were modeled as isothermal with a temperature of 0 °C. The streamline pattern is characterized by recirculation zones which develop behind the fins at comparatively high Reynolds numbers. The results of the heat transfer simulations are summarized in Figure 2.34, which shows the Nusselt number as a fimction of Reynolds number. For... 

The major difficulty in predicting the viscosity of these systems is due to the interplay between hydrodynamics, the colloid pair interaction energy and the particle microstructure. Whilst predictions for atomic fluids exist for the contribution of the microstructural properties of the system to the rheology, they obviously will not take account of the role of the solvent medium in colloidal systems. Many of these models depend upon the notion that the applied shear field distorts the local microstructure. The mathematical consequence of this is that they rely on the rate of change of the pair distribution function with distance over longer length scales than is the case for the shear modulus. Thus... 

Turbulent mass transfer near a wall can be represented by various physical models. In one such model the turbulent flow is assumed to be composed of a succession of short, steady, laminar motions along a plate. The length scale of the laminar path is denoted by x0 and the velocity of the liquid element just arrived at the wall by u0. Along each path of length x0, the motion is approximated by the quasi-steady laminar flow of a semiinfinite fluid along a plate. This implies that the hydrodynamic and diffusion boundary layers which develop in each of the paths are assumed to be smaller than the thickness of the fluid elements brought to the wall by turbulent fluctuations. Since the diffusion coefficient is small in liquids, the depth of penetration by diffusion in the liquid element is also small. Therefore one can use the first terms in the Taylor expansion of the Blasius expressions for the velocity components. The rate of mass transfer in the laminar microstructure can be obtained by solving the equation... 

Linking this molecular model to observed bulk fluid PVT-composition behavior requires a calculation of the number of possible configurations (microstructures) of a mixture. There is no exact method available to solve this combinatorial problem (28). ASOG assumes the athermal (no heat of mixing) Flory-Huggins equation for this purpose (118,170,171). UNIQUAC claims to have a formula that avoids this assumption, although some aspects of athermal mixing are still present in the model. 

The steady-state flow numerical experiment was primarily designed to evaluate the phasic relative permeability relations. The numerical experiment is devised within the two-phase lattice Boltzmann modeling framework for the reconstructed CL microstructure, generated using the stochastic reconstruction technique described earlier. Briefly, in the steady-state flow experiment two immiscible fluids are allowed to flow simultaneously until equilibrium is attained and the corresponding saturations, fluid flow rates and pressure gradients can be directly measured and correlated using Darcy s law, defined below. 

Wang, L., Fritton, S.P., et al. (1999) Fluid pressure relaxation depends upon osteonal microstructure modeling of an oscillatory bending experiment. Journal of Biomechanics 32 663-672... 

After, the essential features of a mechanical model of adsorption and diffusion to characterize, e.g., the transport of a contaminant with rainwater through the soil will be outlined in particular, the model consists of a fluid carrier of an adsorbate, the adsorbate in the liquid state and an elastic skeleton with ellipsoidal microstructure it means that each pore has different microdeformation along principal axes, namely a pure strain, but rotates locally with the matrix of the material (see [5, 6]). 

As an example we consider the flow of a fluid/adsorbate mixture through the big pores of a skeleton, thought like an elastic solid with an ellipsoidal microstructure, and propose suitable constitutive equations to study the coupling of adsorption and diffusion under isothermal conditions in particular, we insert the concentration of adsorbate and its gradient in the usual variables, other than microstructural ones. Finally, the expression of the dissipation shows clearly its dependence on the adsorption and the diffusion, other than on the micro-structural interactions. The model was already applied by G. and Palumbo [7] to describe the transport of pollutants with rainwater in soil. 

Latour LL, Warach S (2002) Cerebral spinal fluid contamination of the measurement of the apparent diffusion coefficient of water in acute stroke. Magn Reson Med 48 478-486 Latour LL, Svoboda K, Mitra PP, Sotak CH (1994) Time-depen-dent diffusion of water in a biological model system. Proc Natl Acad Sci USA 91 1229-1233 Le Bihan D (1995) Molecular diffusion, tissue microdynamics and microstructure. NMR Biomed 8 375-386 Le Bihan D (2003) Looking into the functional architecture of the brain with diffusion MRI. Nat Rev Neurosci 4 469-480 Le Bihan D, van Zijl P (2002) From the diffusion coefficient to the diffusion tensor. NMR Biomed 15 431-434 Le Bihan D, Mangin JF, Poupon C, Clark CA, Pappata S, Molko... 

Third, a serious need exists for a data base containing transport properties of complex fluids, analogous to thermodynamic data for nonideal molecular systems. Most measurements of viscosities, pressure drops, etc. have little value beyond the specific conditions of the experiment because of inadequate characterization at the microscopic level. In fact, for many polydisperse or multicomponent systems sufficient characterization is not presently possible. Hence, the effort probably should begin with model materials, akin to the measurement of viscometric functions [27] and diffusion coefficients [28] for polymers of precisely tailored molecular structure. Then correlations between the transport and thermodynamic properties and key microstructural parameters, e.g., size, shape, concentration, and characteristics of interactions, could be developed through enlightened dimensional analysis or asymptotic solutions. These data would facilitate systematic... 

Three-periodic hyperbolic surfaces of infinite genus carve space into two intertwined sub-volumes, both resembling three-dimensional arrays of interconnected tubes. They are simple candidates for the interfaces in bicontinuous structures, consisting of two continuous subvolumes [4, 5]. As such they have attracted great interest as models for microstructured complex fluid interfaces, biological membranes, and structures of condensed atomic and molecular systems, to be explored in subsequent Chapters. 

This series of the pores with various sizes apparently provide various potential strengths, but their excess potential energy relative to the fluid s solid state is commonly zero for these methane walls. Thus the results would not suffer from the complication by the enhancing effect, and the geometrical effect only would prevail here, showing reasonable tendency of greater hindrance for smaller pores. The observed depressions will be utilized to model the hindrance effect, together with information on microstructure of the frozen state in cylindrical pores, which is hoped to be published soon. 

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