On the flow of a Bingham fluid passing through an electric field

We study the action of an electric field on a Bingham fluid from the point of view of existence and uniqueness of solutions. We also give an upper bound for the stopping time.     

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

The USM-θmodel of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θmodel in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θmodel has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θmodel was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.     

An implicit solution of bi-penalty approximation with orthogonality projection for the numerical simulation of Bingham fluid flow

1.IntroductionItisamajordiffct.encefi-omtheNewtonnuidflowthattheBinghammodelofNonNewtonfluidflowischaracterizedbytwoparameters:ayieldstressandaviscosity.WhenthestressoftheBinghalnmaterialbelowtheyieldstress,materialisrigidotherwisethequasiNewtolliannowresultstll:'71.Hence,therearesomeofthefloating"rigidcores"involvedintheBinghamfluidfloworsomeofthe'rigidcores"attachedtotheboundaries,inwhichthelocationsalldshapesofthese"rigidcores"maychangeforthetransientBinghamfluid,flow.ThisBingllammodelh…     

Peristaltic flow of a Bingham fluid in a channel

We study the peristaltic transport of a Bingham fluid in a channel with small aspect ratio whose walls behave as a periodic traveling wave. The governing equations in the unyielded phase are obtained writing the integral formulation for the momentum balance. As shown in Fusi et al. (2015), this approach allows to overcome the so-called “lubrication paradox” which may arise in the thin film approximation. We consider the case in which the inlet flux is prescribed and the one in which the flow is driven by a given pressure drop. In both cases the solution of the problem is determined solving a nonlinear integral equation for the yield surface. We perform some numerical simulations to illustrate the behavior of the yield surface, assuming that the traveling wave describing the peristaltic motion has a sinusoidal shape.     

Heat transfer and Helmholtz-Smoluchowski velocity in Bingham fluid flow

A mathematical study is developed for the electro-osmotic flow of a nonNewtonian fluid in a wavy microchannel in which a Bingham viscoplastic fluid model is considered. For electric potential distributions, a Poisson-Boltzmann equation is employed in the presence of an electrical double layer(EDL). The analytical solutions of dimensionless boundary value problems are obtained with the Debye-Huckel theory, the lubrication theory, and the long wavelength approximations. The effects of the Debyelen...     

Nonlinear stability of Poiseuille flow of a Bingham fluid: theoretical results and comparison with phenomenological criteria

We present new results on the nonlinear stability of Bingham fluid Poiseuille flows in pipes and plane channels. These results show that the critical Reynolds number for transition, Re_c, increases with Bingham number, B, at least as fast as Re_cB^1/2 as B→∞. Estimates for the rate of increase are also provided. We compare these bounds and existing linear stability bounds with predictions from a series of phenomenological criteria for transition, as B→∞, concluding that only Hanks [AIChE J. 9 (1963) 306; 15 (1) (1963) 25] criteria can possibly be compatible with the theoretical criteria as B→∞. In the more practical range of application, 0≤B≤50, we show that there exists a large disparity between the different phenomenological criteria that have been proposed.     

Dispersion in a Bingham plastic fluid: Effects of peripheral layer

The dispersion of a soluble matter in a plastic fluid flowing through a tube and a channel has been analysed by taking into account the variations of viscosity, diffusivity and yield stress. It has been shown that in the special case of a Bingham fluid, surrounded by a peripheral layer of a Newtonian fluid, the effective dispersion coefficient with which the solute disperses across a plane moving with the mean speed of the flow decreases with the viscosity of the peripheral layer fluid but increases as the molecular diffusion coefficient of this layer decreases. Further, the effective dispersion coefficient also decreases as the yield stress of the Bingham fluid increases.     

Squeeze flow of Bingham fluids under slip with friction boundary condition

This paper develops a theoretical analysis of a Bingham fluid in slipping squeeze flow. The flow field decomposition consists in combining a central extensional flow zone in the plane of symmetry and shear flow zones near the plates. It is also considered that the slipping zone is located around a central sticking zone as previously shown from experiments. It is assumed that the shear stress at the plates is constant in the slipping zone and equals a fixed friction yield value. The squeeze force required to compress a Bingham fluid under the slipping behaviour as well as the radial evolution of the transition point between both sticking and slipping zones are finally determined.     

The analysis of stability of Bingham fluid flowing down an inclined plane

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Start-up Flow of a Bingham Fluid in a Pipe

We present an analytical solution of axisymmetric motion for a Bingham fluid initially at rest subjected to a constant pressure gradient applied suddenly. Using the Laplace transform, we obtain expressions which allow the calculation of the instantaneous velocity, plug radius and rate of flow as a function of time. We also give a relation for the shear stress in the plug and in the region where the behaviour of the fluid is Newtonian.