Squeeze film flow of viscoplastic Bingham fluids

Student thesis: Doctoral Thesis


Squeeze film flow of a viscoplastic Bingham fluid between nonparallel plates has been analysed. It is assumed that the force applied to the plates is known, therefore, their velocity must be found, and the film thickness decreases then as time proceeds. Moreover, for non-parallel plates, the position along the plates at which flow reverses direction is found as part of the solution. In the Newtonian limit, the thickness of the gap between the plates in the parallel system never quite reaches zero at any finite time, while for the nonparallel case a finite time can be obtained when the plates touch one another at a point. In squeeze flow of a viscoplastic Bingham fluid between parallel and non-parallel plates, under a fixed applied force, a final steady film thickness can sometimes be reached. This final thickness turns out to be sensitive not just to the plate tilt angle but also to the so called Oldroyd number which is defined as the ratio between yield stress and imposed stress. Nevertheless for squeeze film flow of Bingham viscoplastic fluid between nonparallel plates, the results show that other cases exist in which the lubrication force cannot always balance the applied force, leading to the plates approaching and touching at the narrowest end of the gap. Moreover torques that develop within the system have been analysed. On the other hand, there are flows of viscoplastic Bingham fluids in which motion decays to zero in finite time typically after a load is removed: a final state is thereby reached after finite time. Analogous flows of Newtonian fluids need however an infinite time for motion to decay to zero. In this thesis, a flow of a Bingham fluid squeezed between two parallel and non-parallel plates is considered with the plates subject to a constant load. This admits a final state without any motion despite the load remaining present. Asymptotic analysis close to that final state is considered, which reveals that in the squeeze film configuration, a Bingham fluid requires an infinite (rather than a finite time) to stop moving. That said, the decay of the motion of the Bingham fluid is still shown to be asymptotically much faster than that of the equivalent Newtonian fluid. It is known that the squeeze film flows have a myriad applications, one of which can be the foam-based papermaking process. As a case in point, in this thesis, the squeeze film flow of Newtonian and non-Newtonian fluids between two parallel and non-parallel plates has been investigated in an effort to understand the behaviour of foam-fibre suspensions in the foam formed papermaking process. Pore size distributions in foam-formed paper tend to be more uniform than in water-formed paper, so the hypothesis explored is that this distribution might reflect uniformity or non-uniformity of gaps between fibres as either foam or water is squeezed out from between them. Data we examine however tend to contradict that hypothesis, suggesting that foam rheology alone is insufficient to account for pore size distributions.
Date of Award7 Dec 2022
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsUniversity of Strathclyde
SupervisorPaul Grassia (Supervisor) & Leo Lue (Supervisor)

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