Particle spherically isotropic

For a particle which is spherically isotropic (see Chapter 2), the three principal resistances to translation are all equal. It may then be shown (H3) that the net drag is — judJ regardless of orientation. Hence a spherically isotropic particle settling through a fluid in creeping flow falls vertically with its velocity independent of orientation. 

For a cube of side /, Eq. (4-50) gives the resistance as 12.70/, compared with experimental values of 12.58/ (P6), 12.63/ (H4), and 12.71/ (Cl). To the accuracy of the determinations, the resistance can be taken as 4ti / (DI). It is noteworthy that Eqs. (4-26) and (4-27) predict that a spherically isotropic cylinder with aspect ratio 0.812 should have a drag ratio of 1.050, while Eq. (4-50) gives Ag = 1.054. Agreement is so favorable that Eq. (4-50) may be useful for spherically isotropic particles other than the simple shapes for which it was developed. 

For a suspension of non-spherical, non-monosize non-adsorbing, isotropic particles, in the absence of multiple scattering ... 

It is convenient to describe the free fall of nonspherical isotropic particles by using the sphericity parameter... 

When the particles are spherically isotropic these reduce to the forms D —0 and... 

The basic theory of gel formation from colloidal particles has been formulated by Thomas and McCorkle (228), who show that the Verwey-Overbeek theory for the interaction of two spherical double layers around adjacent spherical colloidal particles leads to isotropic flocculation. New particles can be attached more readily to the ends of a chainlike floe where the repulsion energy barrier is at a minimum. It is this type of aggregation that converts a sol to a gel at a certain point by forming an infinite network of chains of particles throughout the sol volume. (See also Chapter 3.)... 

The particle size is one or more linear dimensions appropriately defined to characterize an individual particle. For example, an ideal particle like a sphere is uniquely characterized by its diameter. Particles of regular shapes other than spherical can usually be characterized by two or three dimensions. Cubes can be uniquely defined by a single dimension, while cuboids require all three dimensions, length, width, and height. Two dimensions are required for regular isotropic particles such as cylinders, spheroids, and cones. 

Consider the spherical solid particle in Figure 6.11, which is assumed to have isotropic surface properties. In this case calculation of the vapor pressure requires the use of Equation (6.33) and, for an infinitesimal change in radius,... 

The spherical shape of the PbSe NCs obtained from TOPSe remained unaffected irrespective of the presence or absence of free phosphine. However, there was a drastic change in morphology from nanorods to isotropic particles in the absence of free phosphine for the TDPSe based synthesis. The P H NMR spectra showed similar decomposition yield for neat TOPSe (12%) and IM TOPSe in TOP (11%), whereas the decomposition rate of the precursor was increased (38%) in IM TDPSe in TDP compared to neat TDPSe (7% ). TGA-MS analysis indicated the formation of NEt2 ... 

The coefficient cig depends on the spherical particle volume fraction, v, and on the material parameters of the particle q = p) and the matrix q = m),S q, s 2q, and considering ci8 as a function of v, the critical spherical particle volume fraction, vq G (0,tc/6), related to determination of a direction of the particle cracking, can be derived from the condition, Ci8 = 0, for a concrete isotropic particle-matrix system by a numerical method. 

Resulting from the surface elastie energy density, the thermal-stress strengthening in the spherical particle, the eubie eell matrix and the infinite matrix of the isotropic particle-matrix systems are derived (see sections 2.1.6, 2.2.5). 

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