Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids

Wang, Jing; Joseph, Daniel D.

doi:10.1063/1.1589483

Cited by 11 publications

(10 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Correlation of formulae exhibiting the dependence of prefactors and exponents onā requires more computation. Wang & Joseph (2003) compared the lift correlation (4.7) with analytical lift expressions in the literature. Their comparison was limited because the correlation (4.7) is for a two-dimensional cylindrical particle, whereas the lift expressions of…”

Section: Correlations For the Particle Parameters At Equilibriummentioning

confidence: 99%

“…There is no reason why 'empirical' formulae of the type used in engineering which correlate experimental data cannot be generated from the data produced by numerical simulations. Correlations have already been obtained for single particle lift (Patankar et al 2001a;Wang & Joseph 2003) and for the bed expansion of many particles (Choi & Joseph 2001;Patankar et al 2001b) by processing numerical data. Our works have established general rules for the interrogation of data from numerical simulation to be used in developing models for complex fluid dynamics problems such as the fluidization by lift or drag.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, this discrepancy can be used to account for the migration toward the intermediate equilibrium position from the centreline and the wall (the Segré-Silberberg effect). Following Joseph & Ocando's analysis, Wang & Joseph (2003) constructed correlations for the lift force by analogy with the classical lift formula L = ρU Γ of aerodynamics; they showed that the proper analogues of U and Γ were U s and Ω s − Ω se . Their correlations apply to a freely rotating two-dimensional circular particle without accelerations in a plane Poiseuille flow.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Migration of a sphere in tube flow

et al. 2005

Self Cite

View full text Add to dashboard Cite

The cross-stream migration of a single neutrally buoyant rigid sphere in tube flow is simulated by two packages, one (ALE) based on a moving and adaptive grid and another (DLM) using distributed Lagrange multipliers on a fixed grid. The two packages give results in good agreement with each other and with experiments. A lift law L = CU s (Ω s − Ω se ) analogous to L = ρU Γ which was proposed and validated in two dimensions is validated in three dimensions here; C is a constant depending on material and geometric parameters, U s is the slip velocity and it is positive, Ω s is the slip angular velocity and Ω se is the slip angular velocity when the sphere is in equilibrium at the Segré-Silberberg radius. The slip angular velocity discrepancy Ω s − Ω se is the circulation for the free particle and it changes sign with the lift. A method of constrained simulation is used to generate data which is processed for correlation formulas for the lift force, slip velocity, and equilibrium position. Our formulae predict the change of sign of the lift force which is necessary in the Segré-Silberberg effect. Our correlation formula is compared with analytical lift formulae in the literature and with the results of two-dimensional simulations. Our work establishes a general procedure for obtaining correlation formulae from numerical experiments. This procedure forms a link between numerical simulation and engineering practice.

show abstract

Section: Correlations For the Particle Parameters At Equilibriummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Migration of a sphere in tube flow

et al. 2005

Self Cite

View full text Add to dashboard Cite

show abstract

“…[14][15][16] Most of the nonlinear flow behavior observed in these studies arises from the extra elastic stresses due to the presence of polymer molecules. Mechanical stresses in these fluids are history dependent and depend on a characteristic time that in dilute solutions is proportional to the relaxation time of a single polymer molecule.…”

Section: Introductionmentioning

confidence: 99%

Stretching and mixing of non-Newtonian fluids in time-periodic flows

2005

View full text Add to dashboard Cite

Arratia, Paulo E.; Voth, Greg A.; and Gollub, J. P., "Stretching and mixing of non-Newtonian fluids in time-periodic flows" (2005). Departmental Papers (MEAM). 172. http://repository.upenn.edu/meam_papers/172 Stretching and mixing of non-Newtonian fluids in time-periodic flows AbstractThe stretching of fluid elements and the dynamics of mixing are studied for a variety of polymer solutions in nearly two-dimensional magnetically driven flows, in order to distinguish between the effects of viscoelasticity and shear thinning. Viscoelasticity alone is found to suppress stretching and mixing mildly, in agreement with some previous experiments on time-periodic flows. On the other hand, the presence of shear thinning viscosity (especially when coupled with elasticity) produces a dramatic enhancement in stretching and mixing compared to a Newtonian solution at the same Reynolds number. In order to understand this observation, we study the velocity field separately in the sheared and elongational regions of the flow for various polymer solutions. We demonstrate that the enhancement is accompanied by a breaking of time-reversal symmetry of the particle trajectories, on the average. Finally, we discuss possible causes for the time lags leading to this temporal symmetry breaking, and the resulting enhanced mixing. The stretching of fluid elements and the dynamics of mixing are studied for a variety of polymer solutions in nearly two-dimensional magnetically driven flows, in order to distinguish between the effects of viscoelasticity and shear thinning. Viscoelasticity alone is found to suppress stretching and mixing mildly, in agreement with some previous experiments on time-periodic flows. On the other hand, the presence of shear thinning viscosity ͑especially when coupled with elasticity͒ produces a dramatic enhancement in stretching and mixing compared to a Newtonian solution at the same Reynolds number. In order to understand this observation, we study the velocity field separately in the sheared and elongational regions of the flow for various polymer solutions. We demonstrate that the enhancement is accompanied by a breaking of time-reversal symmetry of the particle trajectories, on the average. Finally, we discuss possible causes for the time lags leading to this temporal symmetry breaking, and the resulting enhanced mixing.

show abstract

“…Interested readers are referred to [1,2,5] for details. The only change is that in this paper the coordinate is at the centerline of channel.…”

Section: Governing Equations and Dimensionless Parametersmentioning

confidence: 99%

Numerical Study of Particle Migration in Tube and Plane Poiseuille Flows

Yang

Wang

Joseph

et al.

Fluid Mechanics and Its Applications

Self Cite

View full text Add to dashboard Cite

Abstract. The lateral migration of a single spherical particle in tube Poiseuille flow is simulated by ALE scheme, along with the study of the movement of a circular particle in plane Poiseuille flow with consistent dimensionless parameters. These particles are rigid and neutrally buoyant. A lift law L = CU s ( s − se ) analogous to L = ρU is validated in both two dimensions and three dimensions here; U s and s are slip velocity and angular slip velocity, se is the angular slip velocity at equilibrium. A method of constrained simulation is used to generate data which is processed for correlation formulas for the lift force, slip velocity, and equilibrium position. Our formulas predict the change of sign of the lift force which is necessary in the Segré-Silberberg effect. Correlation formulas are compared between tube and plane Poiseuille flows by fixing the dimensionless size of particle and the Reynolds number. Our work provides a valuable reference for a better understanding of the migration of particle in Poiseuille flows and the Segré-Silberberg effect.

show abstract

Lift forces on a cylindrical particle in plane Poiseuille flow of shear thinning fluids

Cited by 11 publications

References 20 publications

Migration of a sphere in tube flow

Migration of a sphere in tube flow

Stretching and mixing of non-Newtonian fluids in time-periodic flows

Numerical Study of Particle Migration in Tube and Plane Poiseuille Flows

Contact Info

Product

Resources

About