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- Title
Orientation Distribution Function Pattern for Rigid Dumbbell Suspensions in Any Simple Shear Flow.
- Authors
Jbara, Layal M.; Giacomin, Alan Jeffrey
- Abstract
For rigid dumbbells suspended in a Newtonian solvent, the viscoelastic response depends exclusively on the dynamics of dumbbell orientation. The orientation distribution function ψ(θ, φ, t) represents the probability of finding dumbbells within the range (θ, θ + dθ) and (φ, φ + dφ). This function is expressed in terms of a partial differential equation (the diffusion equation), which, for any simple shear flow, is solved by postulating a series expansion in the shear rate magnitude. Each order of this expansion yields a new partial differential equation, for which one must postulate a form for its solution. This paper finds a simple and direct pattern to these solutions. The use of this pattern reduces the amount of work required to determine the coefficients of the power series expansion of the orientation distribution function, ψi. To demonstrate the usefulness of this new pattern, new expressions for these coefficients are derived up to and including the sixth power of the shear rate magnitude. This work also completes previous findings that ended at the fourth power of the shear rate magnitude. This paper finds a simple and direct pattern to the solution of orientation distribution function for rigid dumbbells suspended in a Newtonian solvent, for any simple shear flow. This work completes previous findings that ended at the fourth power of the shear rate magnitude, and arrives at a new expression up to and including the sixth power.
- Subjects
SHEAR flow; DUMBBELLS; CLASSICAL mechanics; PARTIAL differential equations; HEAT equation
- Publication
Macromolecular Theory & Simulations, 2019, Vol 28, Issue 1, pN.PAG
- ISSN
1022-1344
- Publication type
Article
- DOI
10.1002/mats.201800046