Fine particles negligible

MIP are often generated as simple bulk polymers to be ground into fine particles, which are subsequently sieved and sedimented - admittedly a time-consuming process, which requires large amounts of solvents. The loss of fine polymer particles in the sedimentation procedure is also not negligible. The result usually is a polymer powder with particle sizes of a relative broad size distribution. After the template has been extracted, this material can be packed into LC-columns [17,29,30], CE-capillaries, or be used directly in the batch mode. 

Resistances to the mass transfer of oxygen and carbon dioxide (and also of substrates and products) at the cell surface can be neglected because of the minute size of the cells, which may be only a few microns. The existence of liquid films or the renewal of a liquid surface around these fine particles is inconceivable. The compositions of the broths in well-mixed fermentors can, in practical terms, be assumed uniform. In other words, mass transfer resistance through the main body ofthe broth maybe considered negligible. 

The relation between proposed equations (6-10) and (6-18) merits discussion. When = 1 (no reaction) and m = (no partition to particles), kat, as calculated by Eq. (6-10) or (6-16) is smaller than that by Eq. (6-18) for fine particles, since the former takes s for bubble velocity and the latter uses Md, which is larger than u. Equations (6-20) and (6-13) are generally different because m and e r re not necessarily equal. The bubble-void resistance to mass transfer has been assumed negligible in Eq. (6-21). This equation is rendered applicable to the case of arbitrary m by utilizing Eq. (6-22). Equation (6-13) can be rewritten in a form similar to Eq. (6-22), with the observations that m = Cfe + wJs e. and Cf =... 

The external surface area of even very fine particles has been shown (Example 8-1) to be small with respect to the internal surface of the pores. Hence, in a catalyst pellet the surface resides predominantly in the small pores within the particles. The external surface of the particles, and of course the external area of the pellets, is negligible. 

SBR is an amorphous elastomer, with irregular chains. It does not exhibit crystallisation either on stretching or cooling and therefore exhibits negligible gum strength, unless it is reinforced with a fine particle size carbon black. It is compounded much like natural rubber. 

Of course most industrial catalytic reactors (except fluidized bed catalytic reactors) use relatively large particle sizes for the catalyst to avoid the excessive pressure drop associated with fine particles. This gives rise to intraparticle mass transfer resistances. However, in most industrial reactors, but not all, the gas flowrate is quite large rendering external mass transfer resistances usually negligible. 

The JKR theory was developed in the early 1970s to account for the adhesion between spherical bodies, especially fine particles (see Powder Adhesion), making elastic contact. Previously, most studies of elastic contacts had presumed that bodies like steel railway wheels behaved as though adhesion was zero. In other words, no adhesion interaction seemed to be acting in most engineering contact situations. Negligible adhesion force is generally detected as a wheel is lifted from a rail, and the size of the contact spot between wheel and rail can usually be predicted accurately from the laws of elastic deformation, without any molecular attractive forces. 

A colloid is any system consisting of a finely divided phase in a fluid. A colloidal suspension (or sol) consists of fine particles dispersed in a liquid. The particles, referred to as colloidal particles, undergo Brownian motion and have a slow (often negligible) sedimentation rate under normal gravity. The size range for colloidal particles is approximately 1 nm to 1 p.m. 

This is effective in general for the two-three first layers. Likewise, magnetic perturbations are expected at the surface of fine particles. They are not negligible, becoming more and more important with decreasing particle size. For example, the two first layers represent about 40% of the volume for a spherical particle with a diameter of 4nm. The possible effect of these perturbations on the relaxation time will be discussed in Section D. 

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