Apparent contact

Secondary nucleation results from the presence of solute particles in solution. Recent reviews [16,17] have classified secondary nucleation into three categories apparent, true, euid contact. Apparent secondary nucleation refers to the small fragments washed from the surface of seeds when they are introduced into the crystallizer. True secondary nucleation occurs due simply to the presence of solute particles in solution. Contact secondary nucleation occurs when a growing particle contacts the walls of the container, the stirrer, the pump impeller, or other particles, producing new nuclei. A review of contact nucleation, frequently the most significant nucleation mechanism, is presented by Garside and Davey [18], who give empirical evidence that the rate of contact nucleation depends on stirrer rotation rate (RPM), particle mass density, Mj>, and saturation ratio. 

However, if sand becomes saturated with water (that is, its pores become completely water-filled as they are in quick sand), then the sand will flow in a process known as lateral spreading. Water-saturated sand flows because the weight of the sand is supported (at least temporarily) by the water, and so the grains are not continuously in contact. Apparently then, the slope of a pile of sand is dependent on water content, and either too little or too much water lowers the stable slope. This illustrates how slope stability is a function of water content. 

Soot oxidation profiles as obtained fi r K2M0O4 in tight contact and loose contact are shown in figure 1. The maximum of the exothomic heat effect is located at 685 K for the ball milled sample ( tight contact ) and 790 K for the spatula mixture ( loose contact ). Apparently the milling procure lowers the catalytic soot oxidation temperature by approximately 100 K, and is essential for a high soot oxidation activity. Non-catalytic soot oxidation occurs at 875 K. Neeft et aL [14]... 

Mean contact apparent elastic shear modulus G. ie... 

The capillary effect is apparent whenever two non-miscible fluids are in contact, and is a result of the interaction of attractive forces between molecules in the two liquids (surface tension effects), and between the fluids and the solid surface (wettability effects). 

If a pressure measuring device were run inside the capillary, an oil gradient would be measured in the oil column. A pressure discontinuity would be apparent across the interface (the difference being the capillary pressure), and a water gradient would be measured below the interface. If the device also measured resistivity, a contact would be determined at this interface, and would be described as the oil-water contact (OWC). Note that if oil and water pressure measurements alone were used to construct a pressure-depth plot, and the gradient intercept technigue was used to determine an interface, it is the free water level which would be determined, not the OWC. 

The effect of surface roughness on contact angle was modeled by several authors about 50 years ago (42, 45, 63, 64]. The basic idea was to account for roughness through r, the ratio of the actual to projected area. Thus = rA. lj apparent and similarly for such that the Young equation (Eq.-X-18) becomes... 

The coefficient of friction /x between two solids is defined as F/W, where F denotes the frictional force and W is the load or force normal to the surfaces, as illustrated in Fig. XII-1. There is a very simple law concerning the coefficient of friction /x, which is amazingly well obeyed. This law, known as Amontons law, states that /x is independent of the apparent area of contact it means that, as shown in the figure, with the same load W the frictional forces will be the same for a small sliding block as for a laige one. A corollary is that /x is independent of load. Thus if IVi = W2, then Fi = F2. 

The basic law of friction has been known for some time. Amontons was, in fact, preceded by Leonardo da Vinci, whose notebook illustrates with sketches that the coefficient of friction is independent of the apparent area of contact (see Refs. 2 and 3). It is only relatively recently, however, that the probably correct explanation has become generally accepted. 

The true area of contact is clearly much less than the apparent area. The former can be estimated directly from the resistance of two metals in contact. It may also be calculated if the statistical surface profiles are known from roughness measurements. As an example, the true area of contact. A, is about 0.01% of the apparent area in the case of two steel surfaces under a 10-kg load [4a]. 

In summary, it has become quite clear that contact between two surfaces is limited to a small fraction of the apparent area, and, as one consequence of this, rather high local temperatures can develop during rubbing. Another consequence, discussed in more detail later, is that there are also rather high local pressures. Finally, there is direct evidence [7,8] that the two surfaces do not remain intact when sliding past each other. Microscopic examination of the track left by the slider shows gouges and irregular pits left in the softer metal... 

Equation (8.97) shows that the second virial coefficient is a measure of the excluded volume of the solute according to the model we have considered. From the assumption that solute molecules come into surface contact in defining the excluded volume, it is apparent that this concept is easier to apply to, say, compact protein molecules in which hydrogen bonding and disulfide bridges maintain the tertiary structure (see Sec. 1.4) than to random coils. We shall return to the latter presently, but for now let us consider the application of Eq. (8.97) to a globular protein. This is the objective of the following example. 

Phenomena at Liquid Interfaces. The area of contact between two phases is called the interface three phases can have only aline of contact, and only a point of mutual contact is possible between four or more phases. Combinations of phases encountered in surfactant systems are L—G, L—L—G, L—S—G, L—S—S—G, L—L, L—L—L, L—S—S, L—L—S—S—G, L—S, L—L—S, and L—L—S—G, where G = gas, L = liquid, and S = solid. An example of an L—L—S—G system is an aqueous surfactant solution containing an emulsified oil, suspended soHd, and entrained air (see Emulsions Foams). This embodies several conditions common to practical surfactant systems. First, because the surface area of a phase iacreases as particle size decreases, the emulsion, suspension, and entrained gas each have large areas of contact with the surfactant solution. Next, because iaterfaces can only exist between two phases, analysis of phenomena ia the L—L—S—G system breaks down iato a series of analyses, ie, surfactant solution to the emulsion, soHd, and gas. It is also apparent that the surfactant must be stabilizing the system by preventing contact between the emulsified oil and dispersed soHd. FiaaHy, the dispersed phases are ia equiUbrium with each other through their common equiUbrium with the surfactant solution. 

A Apparent area of indentor contact cm in K Agglomerate deformabihty ... 

---