ISSN:
0449-2951
Keywords:
Chemistry
;
Polymer and Materials Science
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Physics
Notes:
The spatial orientation of rigid ellipsoidal particles was analyzed as proceeding in a dilute solution flowing in a velocity field with parallel gradient, i.e., in a field characterized by the deformation rate tensor: \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm V}_{ij} = \left( {\begin{array}{*{20}c} q & 0 & 0 \\ 0 & { - 1/2q} & 0 \\ 0 & 0 & { - 1/2q} \\ \end{array}} \right) $\end{document} On the basis of general relations given by Jeffery, the hydrodynamic equations of motion of a single ellipsoid were obtained as Ψ = 0, ϕ = 0, θ = -¾qR sin 2θ, where q = ∂Vκ/∂κ is the parallel velocity gradient and R = (a2 - b2)/(a2 + b2) is the shape coefficient of ellipsoids. Considering the action of velocity field and that of Brownian motion (rotational diffusion), a distribution density function ρ(t, θ) was derived, which describes the spatial orientation of the axes of symmetry of the ellipsoids: \documentclass{article}\pagestyle{empty}\begin{document}$ \rho (t,\theta ){\rm = }F_0 {\rm } - {\rm }[F_0 {\rm } - {\rm (1}/4\pi )]{\rm exp }\left\{ { - {\rm }\lambda _{1{\rm }} tD} \right\} $\end{document} where \documentclass{article}\pagestyle{empty}\begin{document}$ F_0 \left( \theta \right) = \left( {{1 \mathord{\left/ {\vphantom {1 {4\pi }}} \right. \kern-\nulldelimiterspace} {4\pi }}} \right)\left\{ {1{\rm } + {\rm }\left( {{{\alpha R} \mathord{\left/ {\vphantom {{\alpha R} 4}} \right. \kern-\nulldelimiterspace} 4}} \right)\left( {3\cos ^2 \theta {\rm } - {\rm }1} \right) + \left( {{9 \mathord{\left/ {\vphantom {9 4}} \right. \kern-\nulldelimiterspace} 4}} \right)\left( {\alpha R} \right)^2 \left[ {.{\rm }.{\rm }.} \right]{\rm } + {\rm }{\rm . }{\rm . }{\rm . }} \right\} $\end{document} is the steady-state distribution. In a similar way, the axial orientation factor f0 = 1 - 3/2 sin2θ was obtained: \documentclass{article}\pagestyle{empty}\begin{document}$ f_0 = \left( {{7 \mathord{\left/ {\vphantom {7 5}} \right. \kern-\nulldelimiterspace} 5}} \right)\left[ {\left( {{{\alpha R} \mathord{\left/ {\vphantom {{\alpha R} {14}}} \right. \kern-\nulldelimiterspace} {14}}} \right) + \left( {{{\alpha R} \mathord{\left/ {\vphantom {{\alpha R} {14}}} \right. \kern-\nulldelimiterspace} {14}}} \right)^2 - \left( {{7 \mathord{\left/ {\vphantom {7 5}} \right. \kern-\nulldelimiterspace} 5}} \right)\left( {{{\alpha R} \mathord{\left/ {\vphantom {{\alpha R} {14}}} \right. \kern-\nulldelimiterspace} {14}}} \right)^3 + \left( {{{\alpha R} \mathord{\left/ {\vphantom {{\alpha R} {14}}} \right. \kern-\nulldelimiterspace} {14}}} \right)^4 \left( {.{\rm }.{\rm }.} \right) + {\rm }{\rm . }{\rm . }{\rm .}} \right] $\end{document}
Additional Material:
8 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/pol.1963.100010143
