The relaxation time spectrum
The determination of the relaxation spectrum of a visco-elastic fluid from
various dynamic shear measurements has been discussed by many workers
(e.g. see, Orbey and Dealy, 1991; Baumgaertel and Winter, 1989; Sullivan et
al., 1994) and, in the case of a visco-elastic fluid, the problem of deter-mining
the relaxation spectrum from oscillatory shear measurements involves the
inversion of the following pair of integral equations.
This is an ‘ill-posed’ problem and small perturbations in (measured) G0.!/
or G00.!/ can produce large perturbations in H./. In addition to H./, various
techniques have been described to determine the discrete relaxation spectrum,
in terms of a set of modulus-relaxation time-pairs, using the generalised
Maxwell model [Ferry, 1980]. However, infinitely many parameter sets may be
derived, all of which are adequate for the purpose of representing experimental
data.
Methods of overcoming this problem to obtain a physically meaningful
relaxation spectrum have been discussed at length in the literature: these
include linear regression [Honerkamp and Weese, 1989] and non-linear regression
techniques [Baumgaertel and Winter, 1989]. A commercial version of the
latter is available as the software program “IRIS” which has been used to model
the relaxation behaviour of high molecular weight polydimethylsiloxanes. The
relaxation modulus, G.t/, can also be obtained by direct conversion from the
frequency domain (to the time domain) using the Fourier transform [Kamath
and Mackley, 1989].
Recently, the issue of sampling localisation in determining the relaxation
spectrum has been considered [Davies and Anderssen, 1997]. It is usually
assumed that G0 and G00 measured over the frequency range !min < ! < !max
yield information about the relaxation spectrum over the range of relaxation
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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