Stability of Concentrated Suspensions under Couette and Poiseuille Flow
نویسندگان
چکیده
The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated and connections to the stability problem for the related classical Bingham-flow problem are discussed.
منابع مشابه
Transition from circular Couette flow to Taylor vortex flow in dilute and semi-concentrated suspensions of stiff fibers
We report the results of a theoretical study of the stability of a Couette flow of dilute and concentrated suspensions of stiff fibers. The Ericksen anisotropic fluid rheological equation of state in the wide-gap situation is used to compute the critical Taylor number and wavenumber of the suspension as a function of the aspect ratio of the fibers and the gap-width
متن کاملThe Couette–Poiseuille flow of a suspension modeled as a modified third-grade fluid
In this paper, we modify the thermodynamically compatible third-grade fluid model by introducing a shear-rateand volume-fraction-dependent viscosity into the equation. With this new model, it is possible to predict not only the normal stress differences, but also the variable viscosity observed in many suspensions.We study the Couette–Poiseuille flow of such a fluid between two horizontal flat ...
متن کاملUsing Burnett Equations to Derive an Analytical Solution to Pressure-Driven Gas Flow and Heat Transfer in Micro-Couette Flow
The aim of the present study is deriving an analytical solution to incompressible thermal flow in a micro-Couette geometry in the presence of a pressure gradient using Burnett equations with first- and second-order slip boundary conditions. The lower plate of the micro-Couette structure is stationary, whereas the upper plate moves at a constant velocity. Non-dimensional axial velocity and tempe...
متن کاملChebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems
The Chebyshev tau method is examined in detail for a variety of eigenvalue problems arising in hydrodynamic stability studies, particularly those of Orr-Sommerfeld type. We concentrate on determining the whole of the top end of the spectrum in parameter ranges beyond those often explored. The method employing a Chebyshev representation of the fourth derivative operator, D 4, is compared with th...
متن کاملTwo-phase Flow Measurements by Nuclear Magnetic Resonance (nmr)
We pioneered NMR studies of concentrated suspensions starting in the late 1980’s (Majors, et al., 1989; Altobelli, et al., 1991; Abbott, et al., 1991). In those studies, we measured concentration and velocity of the liquid component in either in pipe or Couette flow. If we compare these early studies of suspensions with more recent ones (Hampton, et al., 1997), imaging time has gone from 40 min...
متن کامل