A mathematical model for Bingham-like fluids with visco-elastic core

Abstract

In this paper we present a new mathematical model for Bingham-like materials in which the core behaves as a visco-elastic Maxwell fluid. We deduce the model in a general 3D framework, using a thermodynamical approach based on the theory of natural configurations. We apply the model to the case of a plane Poiseuille flow driven by a time-dependent pressure gradient. The mathematical formulation of the latter case turns out to be a free boundary problem in which a parabolic equation and a dissipative wave equation are coupled together.

Pressure-driven flow of a rate-type fluid with stress threshold in an infinite channel

“…Using the maximization of the rate of dissipation criterion we look for the tensor D 1G which maximizes the energy dissipated 3 . Thus we solve the problem…”

“…The first extension was to the case in which the region where the stress is below the threshold behaves like a Neo-Hookean elastic solid (see 2 ) and we have subsequently extended this case to the one in which the same region behaves like a visco-elastic Maxwell fluid 3 . We have then studied the case of an elastic material such that no deformation occurs above a certain threshold 4 and we have investigated the case in which the transition from rigid to elastic occurs when the stress becomes greater than the threshold (see 5 , 6 ).…”

On a parabolic free boundary problem arising from a Bingham-like flow model with a visco-elastic core

“…In other words, we can never have a rigid-fluid transition. For this reason, in previous papers [11,12] we have extended the classical Bingham model allowing deformability below the threshold. In particular, in [11] we have modeled the "nonfluid" part as a non-linear elastic material, whereas in [12] as a visco-elastic upper convected Maxwell fluid.…”

“…The mathematical problems emerging from the models presented in [11,12] are free boundary problems that present a very peculiar coupling between a hyperbolic and a parabolic equation, with non-standard free boundary conditions.…”

Development of an intelligent model for wax deposition in oil pipeline

“…Due to the high content of wax deposition in the oil industry, numerous studies have been conducted in the past decade (Reistle 1928(Reistle , 1932Bilderback and McDougall 1963;Haq MA 1978;Smith and Ramsden 1978;Asperger et al 1981). Many different authors have designed models for the flow of waxy crude oils and the associated deposition of solid wax within pipelines, including Farina and Fasano (1997) and Fusi and Farina (2004).…”