72 research outputs found
Symmetry Relations in Viscoplastic Drag Laws
The following note shows that the symmetry of various resistance formulae,
often based on Lorentz reciprocity for linearly viscous fluids, applies to a
wide class of non-linear viscoplastic fluids. This follows from Edelen's
non-linear generalization of the Onsager relation for the special case of
\emph{strongly dissipative} rheology, where constitutive equations are
derivable from his dissipation potential. For flow domains with strong
dissipation in the interior and on a portion of the boundary this implies
strong dissipation on the remaining portion of the boundary, with strongly
dissipative traction-velocity response given by a dissipation potential. This
leads to a non-linear generalization of Stokes resistance formulae for a wide
class of viscoplastic fluid problems. We consider the application to non-linear
Darcy flow and to the effective slip for viscoplastic flow over textured
surfaces
Continuum modelling and simulation of granular flows through their many phases
We propose and numerically implement a constitutive framework for granular
media that allows the material to traverse through its many common phases
during the flow process. When dense, the material is treated as a pressure
sensitive elasto-viscoplastic solid obeying a yield criterion and a plastic
flow rule given by the inertial rheology of granular materials. When
the free volume exceeds a critical level, the material is deemed to separate
and is treated as disconnected, stress-free media. A Material Point Method
(MPM) procedure is written for the simulation of this model and many
demonstrations are provided in different geometries. By using the MPM
framework, extremely large strains and nonlinear deformations, which are common
in granular flows, are representable. The method is verified numerically and
its physical predictions are validated against known results
Modeling tensorial conductivity of particle suspension networks
Significant microstructural anisotropy is known to develop during shearing
flow of attractive particle suspensions. These suspensions, and their capacity
to form conductive networks, play a key role in flow-battery technology, among
other applications. Herein, we present and test an analytical model for the
tensorial conductivity of attractive particle suspensions. The model utilizes
the mean fabric of the network to characterize the structure, and the
relationship to the conductivity is inspired by a lattice argument. We test the
accuracy of our model against a large number of computer-generated suspension
networks, based on multiple in-house generation protocols, giving rise to
particle networks that emulate the physical system. The model is shown to
adequately capture the tensorial conductivity, both in terms of its invariants
and its mean directionality
A general constitutive model for dense, fine particle suspensions validated in many geometries
Fine particle suspensions (such as cornstarch mixed with water) exhibit
dramatic changes in viscosity when sheared, producing fascinating behaviors
that captivate children and rheologists alike. Recent examination of these
mixtures in simple flow geometries suggests inter-granular repulsion is central
to this effect --- for mixtures at rest or shearing slowly, repulsion prevents
frictional contacts from forming between particles, whereas, when sheared more
forcefully, granular stresses overcome the repulsion allowing particles to
interact frictionally and form microscopic structures that resist flow.
Previous constitutive studies of these mixtures have focused on particular
cases, typically limited to two-dimensional, steady, simple shearing flows. In
this work, we introduce a predictive and general, three-dimensional continuum
model for this material, using mixture theory to couple the fluid and particle
phases. Playing a central role in the model, we introduce a micro-structural
state variable, whose evolution is deduced from small-scale physical arguments
and checked with existing data. Our space- and time-dependent model is
implemented numerically in a variety of unsteady, non-uniform flow
configurations where it is shown to accurately capture a variety of key
behaviors: (i) the continuous shear thickening (CST) and discontinuous shear
thickening (DST) behavior observed in steady flows, (ii) the time-dependent
propagation of `shear jamming fronts', (iii) the time-dependent propagation of
`impact activated jamming fronts', and (iv) the non-Newtonian, `running on
oobleck' effect wherein fast locomotors stay afloat while slow ones sink
Continuum modeling of mechanically-induced creep in dense granular materials
Recently, a new nonlocal granular rheology was successfully used to predict
steady granular flows, including grain-size-dependent shear features, in a wide
variety of flow configurations, including all variations of the split-bottom
cell. A related problem in granular flow is that of mechanically-induced creep,
in which shear deformation in one region of a granular medium fluidizes its
entirety, including regions far from the sheared zone, effectively erasing the
yield condition everywhere. This enables creep deformation when a force is
applied in the nominally quiescent region through an intruder such as a
cylindrical or spherical probe. We show that the nonlocal fluidity model is
capable of capturing this phenomenology. Specifically, we explore creep of a
circular intruder in a two-dimensional annular Couette cell and show that the
model captures all salient features observed in experiments, including both the
rate-independent nature of creep for sufficiently slow driving rates and the
faster-than-linear increase in the creep speed with the force applied to the
intruder
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