Spreading power

The major requirement of a foam inhibitor is cost-effectiveness accordingly, some useful characteristics are low volatility (to prevent stripping from the system before it is dispersed and does its work), ease of dispersion and strong spreading power, and surface attraction origination. Also important are effects on product quality, downstream units, and on the environment and health. Several common types are discussed elsewhere (36, 216, 319, 339). Often, a foam inhibitor does not use a single compound, but a combination also including a carrier (usually a hydrocarbon oil or water, which supports the release and spread of the primary defoamer) a secondary defoamer an emulsifier, which enhances the speed of dispersion and a stabilizer, which enhances the inhibitor s stability. 

This symmetry implies dh(u)/du = 0 at m = 0. With this scaiing, we can take the derivatives with respect to h and k independently. We define the spreading power, S by... 

We now consider the case of complete wetting (spreading power 5 > 0) for the case where there are van der Waals interactions, which tend to thicken the film. For a finite amount of fluid spreading on an infinite solid substrate, the equilibrium film profile will therefore not be a monolayer, but a pancake with a maximum thickness that is determined by the balance of the surface tensions and the van der Waals energies (see Fig. 4.3). 

All three surfaetant transfer processes are favorable to spreading, as they result in both an increase of the spreading power, ysv - y- ysi, and, hence, a decrease of the contact angle (Fig. 5). As it was mentioned above, the transfer of surfactant molecules from the drop onto the solid-vapor interface in front of the drop results in an increase of local surface tension, y. Hence, it is the slowest process that will be the rate determining step. Let us define the initial contact angle by... 

Coverage—The spreading power of an adhesive over the surface area of the adherend. 

Fig. 1. Aspect of drop, as observed through a microscope, by ellipsocontrast techniques. The precursor film appears like a bright halo all around the macroscopic drop. This halo is uniform when the drop is deposited on a bare wafer, but when a silanated wafer is used like in the picture, irregularities of the spreading power of the surface are revealed by the presence of the film, and attributed to inhomogeneities in the grafted monolayer.

In order to test the influence of the spreading power of the solid, two surface states have been achieved ... 

The spreading power of the surface can be quantified by the spreading parameter S = y y - - yry with y and y y the solid-vapor solid-... 

All the results presented above seem to agree qualitatively well, with de Gennes and Joanny s predictions small spreading drops of a nonvolatile liquid indeed separate into two parts having very different characteristics. The macroscopic part evolves independently of the spreading power of the surface. On the contrary, the thin precursor film... 

This construction however requires a partial wetting condition that can be expressed on the sign of the spreading power which is the difference of interfacial tensions... 

In usual situations this thickness is of the order of a molecular size. It may be larger in the vicinity of a wetting transition where the spreading power S vanishes. 

This law often referred to as Tanner lawl seems well verified experimentally. One should notice that the macroscopic contact angle 0solid surface (as soon as there is complete wetting) it is in particular not affected by heterogeneities of the solid surface. 

The precursor film cannot be thinner than the equilibrium static value e(S) given by equation (6) when the thickness reaches this value, it decays rapidly to zero at the nominal contact line. This leads to a length 1 of the precursor film increasing with the spreading power as... 

In a constant velocity experiment, the contact line remains pinned in regions with a lower spreading power, the important feature is the depinning mechanism for strong heterogeneities, this leads to a relation between the... 

S is the spreading power that takes in account the various surface tensions[ll]. The second term on the right-hand side of equation (4) is the contribution of the stretching energy of the chains in the molten layer[12]. The third term accoimts for the direct interactions between the wall-anchor ana anchor-solvent interfaces[13], which we approach by a van der Waals energy. A is there the Hamacker constant which is positive in this case the interaction tends to pull the surfaces apart. In a melt there is no confinement energy of the chains [14]. 

Earth-motion-induced Doppler shifts, and intrinsic frequency evolution of the sources, will reduce the narrow-band signal-to-noise by spreading power across many frequency bins therefore, it is necessary to correct for these effects before performing the Fourier transform. The corrections can be implemented by a parametrized model in which one searches over a discrete set of points in the parameter space of corrections. The signal-to-noise ratio required for a confident detection depends on the number of points which must be considered in the search. 

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