Direct numerical simulation of two-phase flow: Effective rheology and flow patterns of particle suspensions

Deubelbeiss, Y.; Kaus, Boris; Connolly, J. A. D.

doi:10.1016/j.epsl.2009.11.041

Cited by 16 publications

(21 citation statements)

References 37 publications

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“…Shear heating increases with solid fraction probably because (1) the average stress in the aggregate increases with solid fraction, and (2) at high solid fractions, local strain rates are considerably greater than the applied background strain rate [ Deubelbeiss et al , 2010]. Similar to simulations in which strain rate is varied, viscosities decrease with increasing strain (Figure 7c).…”

Section: Effective Aggregate Rheology In 2‐d Numerical Simulationsmentioning

confidence: 85%

“…The Lagrangian FE method yields accurate results for our problem configuration [ Deubelbeiss and Kaus , 2008] and has been successfully applied in an earlier study dealing with particle suspensions [ Deubelbeiss et al , 2010]. Tracers are employed to track material properties.…”

Section: Governing Equations Numerical Method and Model Setupmentioning

confidence: 99%

“…The amount of viscosity reduction increases with increasing solid fraction (Figure 7d). These effects are not investigated in detail because the effect of solid fraction on aggregate viscosities have been addressed in a number of experimental or theoretical studies [ Roscoe , 1952; Pinkerton and Stevenson , 1992; Lejeune and Richet , 1995; Costa , 2005; Caricchi et al , 2007; Cordonnier et al , 2009; Costa et al , 2009; Petford , 2009; Deubelbeiss et al , 2010].…”

Section: Effective Aggregate Rheology In 2‐d Numerical Simulationsmentioning

confidence: 99%

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Potential causes for the non‐Newtonian rheology of crystal‐bearing magmas

Deubelbeiss

Kaus

Connolly

et al. 2011

Geochem Geophys Geosyst

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[1] Experimental studies indicate that crystal-bearing magma exhibits non-Newtonian behavior at high strain rates and solid fractions. We use a zero-dimensional (0-D) inversion model to reevaluate rheological parameters and shear heating effects from laboratory data on crystal-bearing magma. The results indicate non-Newtonian behavior with power law coefficients of up to n = 13.5. It has been speculated that finite strain effects, shear heating, power law melt rheology, or plasticity are responsible for this non-Newtonian behavior. We use 2-D direct numerical crystal-scale simulations to study the relative importance of these mechanisms. These simulations demonstrate that shear heating has little effect on aggregate (bulk) rheologies. Finite strain effects result in both strain weakening and hardening, but the resulting power law coefficient is modest (maximum n = 1.3). For simulations with spherical crystals the strain weakening and hardening behavior is related to rearrangement of crystals rather than strain rate related weakening. Finite strain effects were insignificant in a numerical simulation with naturally shaped crystals. Strain partitioning into the melt phase may induce microscopic stresses that are adequate to provoke a nonlinear viscous response in the melt. Large differential stresses and low effective stresses revealed by the simulations are sufficient to cause crystals to fail plastically. Numerical experiments that account for plastic failure show large power law coefficients (n ≈ 50 in some simulations). We conclude that this effect is the dominant cause of the strong nonlinear viscous response of crystal-bearing magmas observed in laboratory experiments.

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Section: Effective Aggregate Rheology In 2‐d Numerical Simulationsmentioning

confidence: 85%

Section: Governing Equations Numerical Method and Model Setupmentioning

confidence: 99%

Section: Effective Aggregate Rheology In 2‐d Numerical Simulationsmentioning

confidence: 99%

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Potential causes for the non‐Newtonian rheology of crystal‐bearing magmas

Deubelbeiss

Kaus

Connolly

et al. 2011

Geochem Geophys Geosyst

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“…Evidently, all three sources of error decrease as the viscosity contrast increases, but assessing the viscosity contrast needed to accurately capture a given problem is unclear. Deubelbeiss et al [2010] argue that the test performed by Schmid and Podladchikov [2003] indicates that a viscosity contrast of three orders of magnitude is sufficient to prevent viscous deformation in the solid phase. However, Schmid and Podladchikov [2003]study only an isolated viscous inclusion, and the viscosity contrast needed to prevent unrealistic fluid‐like behavior in the solid phase probably also depends on the crystal fraction and the collision mode.…”

Section: Discussionmentioning

confidence: 99%

Crystals stirred up: 1. Direct numerical simulations of crystal settling in nondilute magmatic suspensions

Suckale¹,

Sethian²,

Yu³

et al. 2012

J. Geophys. Res.

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[1] This is the first paper in a two-part series examining the fluid dynamics of crystal settling and flotation in the lunar magma ocean. A key challenge in constraining solidification processes is determining the ability of individual crystals to decouple from vigorous thermal convection and settle out or float. The goal of this paper is to develop a computational methodology capable of capturing the complex solid-fluid interactions that determine settling and flotation. In the second paper, we use this computational approach to explore the conditions under which plagioclase feldspar would be able to buoyantly float and form the earliest crust on the Moon. The direct numerical method described in this paper relies on a fictitious domain approach and captures solid-body motion in 2D and 3D with little overhead beyond single fluid calculations. The two main innovations of our numerical implementation of a fictitious domain approach are an analytical quadrature scheme, which increases accuracy and reduces computational expense, and the derivation of a multibody collision scheme. Advantages of this approach over previous simulations of crystal-bearing magmatic suspensions include the following: (1) we fully resolve the two-way interaction between fluid and solid phases, implying that crystals are not only passively advected in an ambient flow field but are also actively driving flow, and (2) we resolve the flow around each individual crystal without assuming specific settling speeds or drag coefficients. We present several benchmark problems and convergence tests to validate our approach.

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“…The reference state must be defined in terms of a tensor invariant (specifically some form of the second invariant, as a measure of the magnitude of the deviatoric component) and could be defined in terms of a state of stress or, as is generally done, strain rate [e.g., Gilormini and Montheillet , 1986; Gilormini and Germain , 1987; Schmalholz et al , 2008]. We also chose strain rate, with the effective viscosity given by [see Deubelbeiss et al , 2010, Appendix A] where μ 0 is the reference viscosity at the reference strain rate E 0 , and n is the power law stress exponent. The “effective strain rate,” E , is defined as [e.g., Ranalli , 1995, equation 4.20], which, for incompressible behavior, is the square root of the second invariant of the deformation rate tensor D , with components of D given by where v i are the velocity components and x i are the material coordinates.…”

mentioning

confidence: 99%