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Polymer Sciences | ISSN: 2471-9935
October 02-03, 2017 Chicago, USA
3
rd
International Conference on
Polymer Science and Engineering
On linear instability of flows of an incompressible polymeric fluid with a strong discontinuity
Andrey Yu Goldin
1
, Andrey I Marinov
1
and
Alexander M Blokhin
2
1
Novosibirsk State University, Russia
2
Sobolev Institute of Mathematics, Russia
Statement of the problem:
Nowadays there are a lot of models which describe the behavior of flows of polymeric fluids. But, some
important properties such as stability or instability of solutions for these models have been studied insufficiently. Particularly, we
consider the so-called Vinogradov-Pokrovskii model using the mesoscopic approach to the mathematical modelling of polymers.
The stability of a polymeric fluid at rest and the stability of a strong discontinuity are analyzed. Two different ways of realization of
the state of rest are discussed: the state of rest of one fluid in a flat infinite channel and the state of rest of two fluids with different
parameters separated by a strong discontinuity. Also some results on the stability of a strong discontinuity in an infinite medium with
the possibility of overflowing have been obtained. Methodology: The standard Lyapunov’s method is used for studying stability and
instability. We derive the linearized equations of the initial system of partial differential equations. The linearization is performed with
respect to the state of rest. Then, special solutions are found. Algebraic conditions for the eigenvalues, which are responsible for the
time growth, can be determined by cumbersome calculations. Results: The state of rest of one fluid in a flat channel is stable to small
perturbations whereas time-growing solutions are constructed and, so, instability is shown for the case of two fluids with a strong
discontinuity in an infinite medium with overflowing.
Conclusion & Significance:
Nowadays polymeric materials have an important role in different fields of industry and technologies.
In attempts to understand their behavior we can propose and study a lot of mathematical models. Then some main properties such
as stability of flows and discontinuities can be studied. According to this information modern devices and technologies based on
polymeric materials can be created or improved
goldinandrey@list.ruPolym Sci, 3:3
DOI: 10.4172/2471-9935-C1-003