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A general fluid–sediment mixture model and constitutive theory validated in many flow regimes

Published online by Cambridge University Press:  28 December 2018

Aaron S. Baumgarten  and
Ken Kamrin Open the ORCID record for Ken Kamrin [Opens in a new window]
Aaron S. Baumgarten
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Ken Kamrin*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present a thermodynamically consistent constitutive model for fluid-saturated sediments, spanning dense to dilute regimes, developed from the basic balance laws for two-phase mixtures. The model can represent various limiting cases, such as pure fluid and dry grains. It is formulated to capture a number of key behaviours such as: (i) viscous inertial rheology of submerged wet grains under steady shearing flows, (ii) the critical state behaviour of grains, which causes granular Reynolds dilation/contraction due to shear, (iii) the change in the effective viscosity of the fluid due to the presence of suspended grains and (iv) the Darcy-like drag interaction observed in both dense and dilute mixtures, which gives rise to complex fluid–grain interactions under dilation and flow. The full constitutive model is combined with the basic equations of motion for each mixture phase and implemented in the material point method (MPM) to accurately model the coupled dynamics of the mixed system. Qualitative results show the breadth of problems which this model can address. Quantitative results demonstrate the accuracy of this model as compared with analytical limits and experimental observations of fluid and grain behaviours in inhomogeneous geometries.

JFM classification

Granular media: Granular media Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 861 , 25 February 2019 , pp. 721 - 764
Copyright
© 2018 Cambridge University Press 

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Baumgarten and Kamrin supplementary movie 1

Simulated collapses for the loose initial packing (bottom) and the dense initial packing (top) described in section 5.1.2. Solid phase material points are colored by equivalent plastic shearing-rate according to the scale. Fluid phase material points are colored light gray.

Download Baumgarten and Kamrin supplementary movie 1(Video)
Video 3.7 MB

Baumgarten and Kamrin supplementary movie 2

Simulated erosion flows described in section 5.1.3 and table 5. Solid phase material points are colored by packing fraction according to the scale. Fluid phase material points are colored light gray.

Download Baumgarten and Kamrin supplementary movie 2(Video)
Video 9.4 MB

Baumgarten and Kamrin supplementary movie 3

Simulated intruder problem described in section 5.2.1. Solid phase material points are colored by packing fraction according to the scale. Fluid phase material points are colored dark gray. The intruder material points are colored dark gray.

Download Baumgarten and Kamrin supplementary movie 3(Video)
Video 3 MB

Baumgarten and Kamrin supplementary movie 4

Simulated slope failures for dry slope (top) and partially submerged slope (bottom) as described in section 5.2.2. Solid phase material points are colored by equivalent plastic shearing-rate according to the scale. Fluid phase material points are colored light gray.

Download Baumgarten and Kamrin supplementary movie 4(Video)
Video 10 MB