Effect of chemical heterogeneity

In 1944, Cassie and Baxter derived an equation describing contact angle hysteresis for composite smooth solid surfaces with varying degrees of heterogeneity  

When air pockets are present on a rough surface, the Cassie-Baxter equation can also be applied to the contact angle estimate of a water drop on such a surface. Since the contact angle of water in air is equal to 180°, by taking 02 = 180°, which corresponds to (cos ft = -1), Equation (676) then becomes 

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Gerke H. H., Molson J. W., and Frind E. O. (1998) Modelling the effect of chemical heterogeneity on acidification and solute leaching in overburden mine spoils. J. Hydrol. 209, 166-185. 

Because we are concerned in this tutorial with the effects of chemical heterogeneity at the nanoscale on the behavior of the confined film, we expect the details of the atomic structure not to matter greatly for our purpose. Therefore, we adopt a continuum representation of the interaction of a film molecule with the substrate, which we obtain by averaging the film substrate interaction potential over positions of substrate atoms in the x-y plane. The resulting continuum potential can be expressed as... 

The significance of the latter parameters can be realised if one considers the initial drop impact. In a fibrous structure such as paper a liquid is unable to discern differences in pore depth until entering the bulk structure. Prior to penetration, following dissipation of mechanical forces, drop wetting and spreading of an aqueous ink jet drop will be primarily determined by the combined effects of chemical heterogenity and physical roughness. The combination of these effects can be approximated (24) in terms of Cassie and Baxter (25) and Shuttleworth and Bailey s (26) equations ... 

Cassie and Baxter analyzed the effect of chemical heterogeneity on wettability and developed the equation. 

Filella, M., van Leeuwen, H. P., Buffle, J. and Holub, K. (2000). Voltammetry of chemically heterogeneous metal complex systems. Part II. Simulation of the kinetic effects induced on polarographic waves, J. Electroanal. Chem., 485, 144-153. 

We have already considered steady-state one-dimensional diffusion in the introductory sections 1.4.1 and 1.4.2. Chemical reactions were excluded from these discussions. We now want to consider the effect of chemical reactions, firstly the reactions that occur in a catalytic reactor. These are heterogeneous reactions, which we understand to be reactions at the contact area between a reacting medium and the catalyst. It takes place at the surface, and can therefore be formulated as a boundary condition for a mass transfer problem. In contrast homogeneous reactions take place inside the medium. Inside each volume element, depending on the temperature, composition and pressure, new chemical compounds are generated from those already present. Each volume element can therefore be seen to be a source for the production of material, corresponding to a heat source in heat conduction processes. 

Franz, M., Arafat, H.A., and Pinto, N.G. (2000). Effect of chemical surface heterogeneity on the adsorption mechanism of dissolved aromatics on activated carbon. Carbon, 38, 1807-19. 

A recent example from the literature which is particularly illustrative of this approach is the so-called WISE experiment [137], in which the lineshape is detected as a function of chemical shift in a two-dimensional experiment. This sequence has also been modified to permit observation of the effects of spin diffusion in what is essentially a heteronuclear two-dimensional variant of the Goldman-Shen type experiment. This has allowed clear observation of the effects of micro heterogeneity in compatible blends of PS/PVME. 

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