ISSN:
0044-2275
Keywords:
Key words. Fiber spinning; Giesekus model; Phan-Thien-Tanner model; quasilinear hyperbolic equation; existence and uniqueness of solutions.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract. Elongational flows of viscoelastic melts are frequently encountered in manufacturing processes in the textile industry. The most common stretching flow is melt-spinning. In this process, a polymeric melt is withdrawn from a reservoir, axially stretched, and simultaneously cooled down until the melt freezes.¶This paper addresses the fundamental question of existence of solutions for the system of quasilinear hyperbolic equations governing the melt-spinning process of a Giesekus fluid and a Phan-Thien--Tanner fluid. The problem is originally posed as a free boundary problem. It will be shown that the free boundary problem can be reformulated as an equivalent boundary-initial value problem for which we prove the (local in time) existence of classical solutions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00001526
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