The results obtained are evaluated for various dimensionless parameters such as suction/injection parameter a, the Deborah number
p, Hartmann number M, and Reynolds number Re.
5 describes the influence of Deborah number
With this long relaxation time, the Deborah number
is extremely large given the short time (a fraction of a second or less) used for applying the step strain to the embossing film.
They defined Deborah number
as the ratio of polymer fluid relaxation time to Rayleigh instability growth time to evaluate the beads formation parameters.
where De, the ratio of the material relaxation time to a process characteristic time h/[u.sub.0], is the Deborah number
, A is a geometric ratio, and [phi] the dimensional stretching force.
To characterize a melt deformation in a polymer processing operation, a nondimensional measure of the overall deformation rate (Deborah number
) is needed.
The ratio of the stress relaxation time to the process time is called the Deborah number
Calculating a Deborah number
for an indentation is trickier.
The Reynolds number Re is a measure of the ratio of inertial force to viscous force and the Deborah number
De is a measure of the ratio of elastic force to viscous force.
where De is the thermal Deborah number
(De = [[alpha]t.sub.c]/[D.sup.2]) and St is the Stefan number (St = [H.sub.f]/(Cp([T.sub.i] - [T.sub.[infinity]]))).
The Deborah number
which is the ratio of the material relaxation time to the process or deformation time affects the stability of polymer processing operations.
For each value of the Deborah number
, a critical value of the Draw ratio exists beyond which it is no longer possible to obtain a solution of the differential system.