Grain radius

Fig. 1s Structure of a dust driven wind mean grain radius , hydrodynamioal velocity v, optical depth of the dust shell at X = Ip, degree of condensation f.

The mean grain radius results to be rather small. In our calculations it ranges from 0.005 p up to 0.05 p which is significantly smaller than the size interval from 0.1 p up to 10 p which is usually adopted. The size of the grains increases with decreasing effective temperature of the star. 

Condensation degree, mean grain radius and the terminal velocity show only weak dependencies on the stellar mass. 

In the case of a kinetic equation of an arbitrary form, the well-known differential equation describing a combined progress of a reaction and diffusion cannot be integrated. The first terms of series expansion of the efficiency factor in powers of the grain radius, a, can be found. A rather cumbersome calculation gives (77)... 

Fig. 61. Effect of pore size and grain radius on the stability of the macroporous catalyst activity for HDM (Agrawal, 1980).

Fig. 5. Concentrations of CD4 and CH4 (as ng/g carbon) released by DC1 dissolution plotted against the reciprocal of the mean grain radius of sieved fractions (Apollo 11 bulk fines)...

The CH4 and CD4 concentrations are directly proportional (Fig. 5) to the reciprocal of the mean grain radius for sieved fractions of Apollo 11 fines for the range 48 p to 152 ju mean grain diameter47. The coarser particles (> 152 /a) show methane concentrations in excess of the surface related component, indicating that there is a volume related component which increases with grain size. 

FIGURE IMS <3onditioiis fie- pore stability as determined for the ratio of prare radius to grain radius, Cp/Rg = 0. When this ratio is negative, the pores will tend to grow and when this ratio is positive, the pwes will tend to shrink. Taken from Kingety et al. [2, p. 488]. Copyright 1976 by John Wiley Sons, Inc. Reprinted by permission of J[Pg.805]

As defined by Radke and Ransohoff (Equation 7), the "snap-off" capillary number, C, contains the effective grain radius, R the permeability, K anS the relative permeability of the nonwetting phase, k ( ). In field applications, the values of all of these parameters are set by the reservoir. Also contained in C are the total superficial velocity, U, and the distance between injection and production wells, L. Within narrow limits, L can be changed by... 

Figure 2. Relative effective charge Z versus grain radius determined as Z = p/pD at r a. Other parameters are Z 25 I 0.1(h) 0.05(B). The curve (C) corresponds to the linear DLVO approximation the dashed line is the DH theory.

Figure 8. Critical distance rc (dividing the region with bound ionic states and that where they are absent) vs. the grain radius for r = 0.08 (1) 0.4 (2) 1.0 (3). The amplitude A = 1.0.

Figure 11. Relative charge distributions versus ionization rates for BC (II) at a fixed bulk plasma density. The dimensionless intensity of plasma sources, io = Ioa6/Di is (1) 1.25-10-2 (2) 2.5 10-3 (3) 5 10-4 (4) 10-4. The bold line is the linear DH theory dashed line is DD approach for BC (I). The grain radius a/ro is 0.158.

A dispersed-element model for kinetic-diffusion controlled growth. Assuming that a total number ns of spherical crystals are nucleated per unit volume at a supercooling of A Tsc =Tm-T(, then these crystals can grow to final grain radius of Rc... 

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