Suspensions of spheroids

A. Okagawa and S. G. Mason, Kinetics of flowing dispersions. X. Oscillations in optical properties of streaming suspensions of spheroids, Can. J. Chem., 55,4243 (1977). 

Figure 6.14 Intrinsic viscosity versus Peclet numberfor dilute suspensions of spheroidal particles of (a) oblate shape and (b) prolate shape, (From Macosko 1994, adapted from Brenner 1974, with permission from Pergamon Press.)...

Figure 17. Low shear limit viscosity variation with solid volume fraction and aspect ratio for suspensions of spheroids and cylinders (118).

At the same time, it is necessary to recall that some theories predict the dependence of the sign of Ni on the molecular orientation of the system. It was shown in [108] for a model system, a dilute suspension of spheroids, that in conditions of flow of the medium around a spheroid and generation of its rotation, strain arises along the long axis. Negative normal stresses arise for a certain position of this axis relative to the direction of flow. 

Morphological analysis of the nanoparticle suspensions by SEM showed a homogeneous distribution of spheroidal particles with diameters less than 1 pm embedded in a continuous matrix (Figure 4) consisting of polymeric material not incorporated within the microspheres. 

It follows from (8.47) that the average dielectric function of a suspension of identical oblate spheroids is... 

Wolf, B., Frith, W. J., Singleton, S., Tassieri, M., and Norton, 1. T. 2001. Shear behaviour of biopolymer suspensions with spheroidal and cylindrical particles. Rheol. Acta 40 238-247. 

Viscometric Coefficients for Dilute Suspensions of Rigid Spheroids Low Shear Rates ... 

Figure 6.16 Frequency-dependence of reduced intrin-sic moduli [G ]j = (5/3) YiTny oG /vkBT [G"]r = (5/3) ]im , o(G" — (orjsl/vksT for dilute suspensions of tobacco mosaic virus (TMV). The concentration v is the number of particles per unit volume of solution, and is given by y = cN /M, where c is mass of TMV per unit volume, Na is Avogadro s number, and M is the mass of a TMV particle. The lines are the predictions for a dilute suspension of long prolate spheroids. (From Nemoto et al.. Biopolymers, 14 407, Copyright 1975. Reprinted by permission of John Wiley Sons, Inc.)...

Problem 6.7(a) (Worked Example) Estimate the first normal stress difference Ni for a suspension of long, thin particles (approximated as spheroids) with p = 100 and L = 0.1/ m, if the solvent viscosity is 1 P, the shear rate y is 100 sec, and the particle concentration is 0 = 0.001, which is in the dilute regime. 

H. Fricke, A mathematical treatment of the electric conductivity and capacity of disperse systems, I. The electric conductivity of a suspension of homogeneous spheroids, Phys., Rev., 24, 575-587 (1924). 

In order to sustain life, a bioartificial liver device should contain at least 10-30% of the normal liver mass (i.e., 150-450 g of cells in the case of an adult). In a bioartificial liver device, the animal or human liver cells can conceivably be cultured and used in several forms, including (i) independent single-cell suspensions (ii) spheroid (i.e., globular) aggregates of cells of 100-150 pm diameter (iii) cylindroid, rod-like aggregates of cells of 100-150 pm diameter (iv) encapsulated cells and (v) cells attached to solid surfaces, such as microcarriers, flat surfaces, and the inside or outside of hollow fibers. In order to facilitate mass transfer, a direct contact between the cells and the blood seems preferable. Among the various types of bioartificial liver device tested to date, four distinct groups can be identified [19] ... 

For a suspension of rigid spheroids, Leal and Hinch (102) determined the Einstein constant (intrinsic viscosity) for the limiting case of large axis (aspect) ratio, re = long axis/short axis - oo, as follows ... 

For suspension of solid particles in a liquid, the theoretical and experimental works indicate that the angle of orientation of a spheroid can be expressed as ... 

Drop Deformability When a neutrally buoyant, initially spherical droplet is suspended in another liquid and subjected to shear or extensional stress, it deforms and then breaks up into smaller droplets. Taylor [1932,1934] extended the work of Einstein [1906, 1911] on dilute suspension of solid spheres in a Newtonian liquid to dispersion of single Newtonian liquid droplet in another Newtonian liquid, subjected to a well-defined deformational field. Taylor noted that at low deformation rates in both uniform shear and planar hyperbolic fields, the sphere deforms into a spheroid (Figure 7.9). 

The electrical conductivity of a suspension of homogeneous spheroids. Phys. Rev. 24, 575—587. 

Fricke, H., 1925. A mathematical treatment of the electrical conductivity and capacity of disperse systems, n. The capacity of a suspension of conducting spheroids surrounded by a non-conducting membrane for a current of low frequency. Phys. Rev. 26, 678—681. 

Ahmed S, Irons BM, Zienkiewicz OC (1970) Analysis of thick and thin shell structures by curved finite elements. Int J Numer Meth Eng 2 419-451 Akczurowski E, Mason SG (1968) Particle motions in sheared suspensions XXIV rotation of spheroids and cylinders. Trans Soc Rheol 12 209-215 Albert C, Femlund G (2002) Spring-in and warpage of angled composite laminates. Compos Sci Technol 62 1895-1912... 

Addition of the spherical micelle-forming surfactants DTAB and 12-10-12, 2Br to vesicular suspensions of 12-20-12, 2Br was found to result in the progressive transformation of the vesicles into mixed spheroidal micelles (Fig. 17) [129]. No intermediate structures, such as bilayer membrane fragments and/or giant thread-like micelles usually appearing during such a transformation, were observed [129]. 

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