In:
Journal of Rheology, Society of Rheology, Vol. 58, No. 4 ( 2014-07-01), p. 999-1038
Abstract:
The interfacial stress rheometer (ISR), uses the oscillations of a magnetic needle suspended on an interface to characterize the dynamic moduli of thin films. Mathematical theories to interpret the device have developed slowly because of the strong coupling between the stresses in the surface and the bulk subphase. In this work, we simplify the equations of motion by introducing new length scales and reinterpreting the dimensionless numbers. Several Green's functions are developed for typical ISR geometries, leading to a set of boundary element methods for the full numerical solution of the equations of motion. Using Taylor series, a multipole expansion is extracted from the boundary integral equations, and we show that both numerical methods converge in under five elements. Analytical theories are developed for the cases of small and large interfacial stress, proving that the finite size of the needle has an O(1) effect and reinforcing the physics behind the length scales and dimensionless groupings. We directly compare our numerical and analytical solutions to published interfacial velocity data, showing good agreement, and discuss the implications of our results.
Type of Medium:
Online Resource
ISSN:
0148-6055
,
1520-8516
Language:
English
Publisher:
Society of Rheology
Publication Date:
2014
detail.hit.zdb_id:
1461060-7
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