Crowding factor

Barnea and Mizrahi (1973) considered the effects of the modified density and viscosity of the suspending fluid, as represented by Eq. (14-21), as well as a crowding or hindrance effect that decreases the effective space around the particles and increases the drag. This additional crowding factor is 1 + k2(pl/3, which, when included in Eq. (14-21), gives... 

Providing that c is less than 0.1, good agreement with the Einstein equation is found when glass spheres are suspended in ethylene glycol. Equation 8.1 has been modified by including a hydrodynamics or crowding factor (/8). The modified Mooney equation (8.2) resembles the Einstein equation when (3 = 0. 

Zavras, E.T. and Roberts, L.S. (1985) Developmental physiology of cestodes cyclic nucleotides and the identity of putative crowding factors in Ffymenolepis diminuta. journal of Parasitology 71, 96-105. 

Insler, G. D. Roberts, L. S. (1980a). Developmental physiology of cestodes. XV. A system for testing possible crowding factors in vitro. Journal of Experimental Zoology, 211 45-54. 

Many experimental results on viscosity were empirically correlated by Rutgers (1962a,b) and Thomas (1965). A useful semiempirical formula is that of Mooney (1951). Its derivation is based on an approximate functional argument together with the introduction of an ad hoc crowding factor k. Upon contemplating two possible ways of reaching the same total concentration + 2, Mooney proposed the formula... 

In describing the viscosity of an emulsion, the volume fraction of the dispersed phase is the most important parameter. A model suggested by M. Mooney (15) in 1951 for solid suspensions and emulsions with highly viscous dispersed phase described the relative viscosity as a function of volume fraction and a coefficient, k, called the self-crowding factor. 

Boltzmann constant corrective growth crowding factor coordination number for an aggregate particle mass-transfer coefficient... 

Cook, R. L. and Roberts, L. S. (1991) In vivo effects of putative crowding factors on development of Hymenolepis diminuta. J. Parasitol. 77 21-25. 

Crowding factor Permeability of porous medium Rate constant, I th-order homogeneous reaction Thermal conductivity or thermal conduction coefficient Wave number, Eqs. (10.4.2b), (10.4.28) Wetting coefficient, Eq. (10.1.9)... 

There is, however, an excluded volume effect since when the particle fraction was added, not all the fluid volume was available, part being already taken up by the particle fraction ,. Krieger and Dougherty therefore assumed that the volume fraction available to the new particles was only 1 — k(f>, where is a constant termed a crowding factor. It follows that Eq. (9.3.2) should be written... 

Assume that the crowding factor, k, in Eq. (9.3.5) varies linearly with ()> from the value jfeg at ( = 0 to / , at (/> = viscosity expression take under this assumption ... 

Here a is a factor related to the intrinsic viscosity (typically in the range of 1-10) and k is a crowding factor (typically in the range 1.3-2) that takes into account the maximum packing fraction of the system. 

Pfeuderer, P., Williams, P. Francis, A. A. 1974. Partial purification of the crowding factor from Carassius aura-tus and Cyprinus carpio. J. Exp. Zool. 187, 375-382. 

Table 10.1 shows reasonable values for the crowding factor k. However, a is much larger than the theoretical value of 2.5. This discrepancy is due to the presence of the surfactant layer, which causes an increase in the core volume fraction. 

Mooney [97] proposed that at very high concentrations an Arrhenius type equation (with the addition of crowding factor (1 — a )) of the following form could be used ... 

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