Solid-Fluid Interfaces

S. Toxvaerd. The structure and thermodynamics of a solid-fluid interface. J Chem Phys 74 1998-2005, 1981. 

Mathpati, C.S. and Joshi, J.B. (2007) Insight into theories of heat and mass transfer at the solid/fluid interface using direct numerical simulation and large eddy simulation. Joint 6th International Symposium on Catalysis in Multiphase Reactors/5th International Symposium on Multifunctional Reactors (CAMURE-6/ISMR-5-), 2007, Pune. 

The double integral represents the nonzero terms of the dissipation rate tensor as adapted by Middleman [61] and Bernhardt and McKelvey for adiabatic extrusion [62]. The nontensorial approach was adopted by Tadmor and Klein in their classical text on extrusion [9]. In essence these are the nonzero terms of the dissipation rate tensor when it is applied to the boundary of the fluid at the solid-fluid interface. In the following development this historic analysis was adopted for energy dissipation for a rotating screw. In this case the velocities Ui are evaluated at the screw surface s and calculated in relation to screw rotation theory. The work in the flight clearance was previously described in the literature [9]. The shear... 

Hence the difference between the tensions at the two solid-fluid interfaces which is the quantity always involved in equations of equilibrium can be expressed in terms of the fluid-fluid tension and an angle, called the angle of contact which is plainly susceptible of direct measurement. 

McCready et al., 1986). The surface renewal theory can be made to fit the transfer data at fluid-fluid interfaces. The exception to this is bubbles with a diameter less than approximately 0.5 mm. Even though there is a fluid on both sides, surface tension causes these small bubbles to behave as though they have a solid-fluid interface. There is also some debate about this 1 /2 power relationship at free surfaces exposed to low shear, such as wind-wave flumes at low wind velocity (Jahne et al., 1987) and tanks with surfactants and low turbulence generation (Asher et al., 1996). The difficulty is that these results are influenced by the small facilities used to measure Kl, where surfactants wiU be more able to restrict free-surface turbulence and the impact on field scale gas transfer has not been demonstrated. 

A number of authors [46 to 48] employ the single sphere model in which the packed bed is considered as a set of equal spheres that are under the same state of extraction, and the fluid flowing around them is solute-free. That is, equation (3.4-90) would be valid, but without the generation term [46], The transport at the solid-fluid interface obeys the boundary condition (Eqn. 3.4-94) with C = 0 (fluid-flows at a large velocity). Under these assumptions, there is an analytical solution to the above problem (without axial dispersion) in terms of the Biot number (Bi = k, R/De), included in the following equation ... 

Surface effects are negligible in many cases. However, when the surface-to-volume ratio of the system is large, surface effects may become appreciable. Moreover, there are phenomena associated with surfaces that are important in themselves. Only an introduction to the thermodynamics of surfaces can be given here, and the discussion is limited to fluid phases and the surfaces between such phases. Thus, consideration of solid-fluid interfaces are omitted, although the basic equations that are developed are applicable to such interfaces provided that the specific face of the crystal is designated. Also, the thermodynamic properties of films are omitted. 

Let us consider an elementary volume V of saturated porous material. At the microscopic scale, the porous material appears as a heteregeneous material in which the solid and fluid phases occupy two distinct domains. V and Vj- are the volume of the solid phase and of the fluid phase respectively, and the solid-fluid interface is denoted by l js. The unit outward normal to the solid phase is denoted by ns. We denote by x, v, e and a, the position vector, the velocity, the strain and the stress at the microscopic scale, respectively. 

In particular, when p + ps(i[rc — irt) is uniform along the solid-fluid interface, the dissipation can be formulated in terms of the macroscopic variables E, p, 4>c and ... 

Rickayzen, G. (1989). Theoretical studies of the solid-fluid interface. In Food Colloids, Bee, R. D., Richmond, P., and Mingins, J. (Eds.), Special Publication series 75, p. 153. Royal Chem. Soc., London. 

The second important effect is that irradiation absorption generates active states of the photoadsorption centers with trapped electrons and holes. By definition (Serpone and Emeline, 2002) the photoadsorption center is a surface site which reaches an active state after photoexcitation and then it is able to form photoadsorbed species by chemical interaction with substrate (molecules, or atoms, or ions) at solid/fluid interface. In turn, the active state of a surface photoadsorption center is an electronically excited surface center, i.e. surface defect with trapped photogenerated charge carrier that interacts with atoms, molecules or ions at the solid/gas or solidfiquid interfaces with formation of chemisorbed species. ... 

CUBIULATIVE SUBJECT INDEX OF VOLUMES I (FUNDAMENTALS) AND n (SOLID-FLUID INTERFACES)... 

The first boundary condition is equivalent to the well-known Levich approach (ca=1 for according to which, it is supposed that the concentration values vary only within a very thin concentration layer while it is supposed to keep its bulk value elsewhere [9], Eq. (3b) has been proposed by Coutelieris et al. [8] in order to ensure the continuity of the concentration upon the outer boundary of the cell for any Peclet number. Furthermore, eq. (3c) and (3d) express the axial symmetry that has been assumed for the problem. The boundary condition (3e) can be considered as a significant improvement of Levich approach, where instantaneous adsorption on the solid-fluid interface cA(ri=Tia,ff)=0) is also assumed for any angular position 0. In particular, eq. (3e) describes a typical adsorption, order reaction and desorption mechanism for the component A upon the solid surface [12,16] where ks is the rate of the heterogeneous reaction upon the surface and the concentration of component A upon the solid surface, c,is, is calculated by solving the non linear equation... 

The density functional method as applied by Tarazona to deal with classical fluids has been used to calculate the orientation of triatomic molecular fluids near the solid-liquid interface. The results give valuable suggestions about the effect of molecular shape on the orientation of real molecules such as liquid crystals near the solid-fluid interface. 

In some foods, a thin layer of low-viscosity fluid forms at the solid-fluid interface that in turn contributes to lower viscosity values. The boundary condition that at the solid-fluid interface the fluid velocity is that of the wall is not satisfied. This phenomenon is known as slip effect. Mooney (1931) outlined the procedures for the quantitative determination of slip coefficients in capillary flow and in a Couette system. The development for the concentric cylinder system will be outlined here for the case of the bob rotating and details of the derivation can be found in Mooney (1931). 

S. Toxvaerd, The Structure and Thermodynamics of a Solid-Fluid Interface, J. Chem. Phys. 74 (1981) 1998-2005. 

P. Adams and J. R. Henderson, Molecular Dynamics Simulations of Wetting and Drying in U Models of Solid-Fluid Interfaces in the Presence of Liquid-Vapor Coexistence, Mol. Phys. 73 (1991) 1383-1399 S. Sokolowski and J. Fischer, Wetting Transitions at the Ar-C02 Interface Molecular Dynamics Studies, Phys. Rev. A 41 (1990) 6866-6870 S. Dhawan, M. E. Reimel, L. E. Scriven and H. T. Davis, Wetting transitions at a Solid-Fluid Interface, J. Chem. Phys. 94 (1991), 4479-4489. 

Manias et al. [28] used the same bead-spring model in their simulations and analyzed viscosities inside the solid-fluid interface and the inner fluid film. They found that nearly all the shear thining takes place inside the solid-oligomer interface and the shear thining inside the interfacial area is determined by the wall affinity. While the loads used in Manias simulations are much smaller than the ones used in experiments [28], the loads used in Robbins simulations are quite high so that fluids are near the... 

In the SFA experiments there is no way to determine whether shear occurs primarily within the film or is localized at the interface. The assumption, made by experimentalists, of a no-slip flow boundary condition is invalid when shear localizes at the interface. It has also not been possible to examine structural changes in shearing films directly. MD simulations offer a way to study these properties. Simulations allow one to study viscosity profiles of fluids across the slab [21], local effective viscosity inside the solid-fluid interface and in the middle part of the film [28], and actual viscosity of confined fluids [29]. Manias et al. [28] found that nearly all the shear thinning takes place inside the adsorbed layer, whereas the response of the whole film is the weighted average of the viscosity in the middle and inside the interface. Furthermore, MD simulations also allow one to examine the structures of thin films during a shear process, resulting in an atomic-scale explanation [12] of the stick-slip phenomena observed in SFA experiments of boundary lubrication [7]. 

The Navier-Stokes equations are valid when A is much smaller than the characteristic flow dimension L. When this condition is violated, the flow is no longer near equilibrium and the linear relations between stress and rate of strain and the no-slip velocity condition are no longer valid. Similarly, the linear relation between heat flux and temperature gradient and the no-jump temperature condition at a solid-fluid interface are no longer accurate when A is not much smaller than L. The different Knudsen number regimes are delineated in Fig. 2. 

Having laid down the physico-chemical basis of interface and colloid science in Volume 1, and then presented a systematic treatment of solid-fluid interfaces in Volume 11, we now conclude the interface science part of FICS with a treatment of liquid-fluid interfaces. Colloids will be discussed in Volumes fV and V. 

Measuring the surface tensions of solids poses a problem because it is almost impossible to extend a solid-fluid interface isothermally and reversibly. Stretching a solid-fluid interface is not performed against the interfacial tension, but against the interjacial stress r. The difference between r and y depends on the kinetics and history of the extension, so that generally the work w performed is not a sole characteristic of y or, for that matter, a function of state. Only when the extension can be ceirried out reversibly is it possible to relate r emd y. As r is a second order tensor (it has normal and shear components) and y is a scalar, this relation is complicated. For the very simple case that r does not depend on direction (a rather unrealistic situation for solids) and assuming reversibility the relation is ... 

Scanning probe microscopy (STM, AFM,. ..) High resolution topology (nm scale) in 3D local physico-chemical properties depending on specific technique (e.g., mechanical stability, adhesion, potential). Restricted to solid/fluid interfaces., i.e., supported monolayers and LB films precautions to avoid deformation and damage of the layers may be necessary. 

The use of an evanescent wave to excite fluorophores selectively near a solid-fluid interface is the basis of the technique total internal reflection fluorescence (TIRF). It can be used to study theadsorption kinetics of fluorophores onto a solid surface, and for the determination of orientational order and dynamics in adsorption layers and Langmuir-Blodgett films. TIRF microscopy (TIRFM) may be combined with FRAP ind FCS measurements to yield information about surface diffusion rates and the formation of surface aggregates. 

The chemical reaction between a solid and a reactive fluid is of interest in many areas of chemical engineering. The kinetics of the phenomenon is dependent on two factors, namely, the diffusion rate of the reactants toward the solid/fluid interface and the heterogenous reaction rate at the interface. Reactions can also take place within particles, which have accessible porosity. The behavior will depend on the relative importance of the reaction outside and inside the particle. Fractal analysis has been applied to several cases of dissolution and etching in such natural occurring caves, petroleum reservoirs, corrosion, and fractures. In these cases fractal theory has found usefulness for quantifying the shape (line or surface) with only a few parameters the fractal dimension and the cutoffs. There have been some attempts to use a fractal dimension for reactivity as a global parameter. Finally, fractal concepts have been used to aid in the interpretation of experimental results, if patterns quantitatively similar to DLA are obtained. 

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