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Wide‐ranging Polynomial Approximations to Wilson's and Hill's Equations
Author(s) -
Shibusawa Takao
Publication year - 1985
Publication title -
journal of the society of dyers and colourists
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.297
H-Index - 49
eISSN - 1478-4408
pISSN - 0037-9859
DOI - 10.1111/j.1478-4408.1985.tb01028.x
Subject(s) - polyester , alkali metal , diffusion , alkaline hydrolysis , polynomial , mathematical analysis , disperse dye , hydrolysis , thermodynamics , chemistry , materials science , mathematics , physics , composite material , organic chemistry
A close approximation to Wilson's equation has been obtained that is applicable for exhaustion levels between 30 and 99. 9% at an accuracy of up to four significant figures, A similar approximation to Hill's equation was also obtained, which is shown to be highly accurate. The approximation to Wilson's equation has been used to calculate the diffusion coefficient of CI. Disperse Violet 1 in alkali‐corroded polyester fibres. The effects of removing the surface fibre layer by alkali hydrolysis on the ph ysicai characteristics of a polyester fibre and on the diffusion coefficient of the disperse dye in the fibre are discussed.