Physical liquid/solid interface

Given the difficulties outlined above in measuring or simulating the surface free energy of the liquid-solid interface, the natural question is whether theoretical methods can predict its magnitude and the physical processes that affect it. In this section we outline a number of theoretical approaches developed between 1950 and 1980, and in the next section we give a more extensive discussion of a recent density functional approach. 

Equations 15 and 16 develop Equation (14) for gas-to-condensed-phase transitions. It would also be desirable to develop Equation (14) for liquid-to-crystalline nucleation to assign physical meaning to An. However, development of Equation (14) is difficult both because d can be a large correction factor for liquid/solid interfaces and because the molecular density differences between liquids and solids are smaller than between gases and condensed phases (Kashchiev 1982). 

Additional difficulties in formulating an adsorption theory for the liquid - solid interface result from a variety of interactions between components of a liquid mixture and from a complex structure of the adsorbent, which may possess different types of pores and strong surface heterogeneity. Our considerations will be limited to physical adsorption on heterogeneous solid surfaces of components of comparable molecular sizes from non-electrolytic (non ideal or ideal) miscible binary liquid mixtures. 

Bedzyk MJ (1992) X-ray standing wave studies of the liquid/solid interface and ultrathin organic films. In Springer Proceedings in Physics. Vol 61 Surface X-ray and Neutron Scattering. Zabel H, Robinson IK (eds) Springer-Verlag, Berlin, p 113-117... 

Ultrasonic cavitation in liquid-solid systems produces interesting effects. Physical effects include (a) improvement of mass transfer in turbulent mixing and acoustic flow, (b) generation of surface damage at the liquid-solid interfaces due to shock waves, (c) generation of high-velocity interparticle collisions in the suspension (slurry), and (d) fragmentation of solids to increase their surface area. 

Phenomena at the gas-liquid and at the liquid-solid interfaces are governed by properties of the gas, the liquid and the solid such as density, viscosity, surface tension, wettability... These properties are numerous to characterize a three phase system which therefore shall be very difficult to simulate by another one let us for instance mention here the non validity for organic systems of the physical kinetics correlations determined with aqueous systems. Moreover, the interfacial phenomena and the significant physico-chemical properties to be considered are far being well known for instance, the foaming ability of organic liquids is not determined univocally by their density. 

Jinnouchi, R. and A.B. Anderson, Electronic structure calculations of liquid-solid interfaces Combination of density functional theory and modified Poisson-Boltzmaim theory. Physical Review B, 2008. 77(24). 

Eirich, F. R., Bulas, R., Rothstein, E., and Rowland, F. Structure of Macromolecules at Liquid-Solid Interfaces , Chemistry and Physics of Interfaces, ACS publication, Washington, 1965. 

Because of the wider variety of fouling mechanisms from liquids than from thermal fouling is classified with the liquid-solid interface as the prototype. The classification is based on the key physical/chemical process essential to the particular fouling phenomenon. Six primary categories have been identified ... 

This volume focuses on examining physical phenomena that occur in colloidal systems such as micellar solutions, microemulsions, emulsions, dispersions, slurries, etc. It principally concentrates on liquid/air, liquid/ liquid, and liquid/solid interfaces. 

The mathematical model was constracted on the basis of a three-phase plug-flow reactor model developed by Korsten and Hoffmaim [63]. The model incorporates mass transport at the gas-liquid and liquid-solid interfaces and uses correlations to estimate mass-transfer coefficients and fluid properties at process conditions. The feedstock and products are represented by six chemical lumps (S, N, Ni, V, asphaltenes (Asph), and 538°C-r VR), defined by the overall elemental and physical analyses. Thus, the model accounts for the corresponding reactions HDS, HDN, HDM (nickel (HDNi) and vanadium (HDV) removals), HD As, and HCR of VR. The gas phase is considered to be constituted of hydrogen, hydrogen sulfide, and the cracking product (CH4). The reaction term in the mass balance equations is described by apparent kinetic expressions. The reactor model equations were built under the following assumptions ... 

HOPG. (c) STM image of a 1 10 mixture of HBC-AQ and DMA at the liquid-solid interface, (d) I-V curves measured through the HBC cores before (open triangles) and after (solid circles) the formation of AQ-DMA charge-transfer complexes. Inset shifted and normalized data (see text), (e) A schematic of the resultant prototype CFET. (Reproduced with permission from Ref. 60. American Physical Society, 2004.)... 

A systematic study of physical effects that influence the water structure at the water/metal interface has been made. Water structure, as characterized by the atom density proflles, depends most strongly on the adsorption energy and on the curvature of the water-metal interaction potential. Structural differences between liquid/liquid and liquid/solid interfaces, investigated in the water/mercury two-phase system, are small if the the surface inhomogeneity is taken into account. The properties of a polarizable water model near the interface are almost identical to those of unpolarizable models, at least for uncharged metals. The water structure also does not depend much on the surface corrugation. 

Interphase Mass Transfer. There are a number of interphase mass transfer steps that must occur in a trickle flow reactor. The mass transfer resistances can be considered as occurring at the more or less stagnant fluid layer interfaces, i.e., on the gas and/or the liquid side of the gas/llquld Interface and on the liquid side of the liquid/solid Interface. The mass transfer correlations (8) indicate that the gas/llquld Interface and the liquid/solid interface mass transfer resistances decrease with higher liquid velocity and smaller particle size. Thus, in the PDU, the use of small inert particles partially offsets the adverse effect of low velocity. These correlations indicate that for this system, external mass transfer limitations are more likely to occur in the PDU than in the commercial reactor because of the lower liquid velocity, but that probably there is no limitation in either. If a mass transfer limitation were present, it would limit conversion in a way similar to that shown for axial dispersion and incomplete catalyst wetting illustrated in Figure 1. Due to the uncertainty in the correlations and in the physical properties of these systems, particularly the molecular diffuslvities, it is of interest to examine if external mass transfer is influencing the PDU results. 

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