%% Papers Published
@article{fds346592,
Author = {Wong, J and Lindstrom, M and Bertozzi, AL},
Title = {Fast equilibration dynamics of viscous particle-laden flow
in an inclined channel},
Journal = {Journal of Fluid Mechanics},
Volume = {879},
Pages = {28-53},
Year = {2019},
Month = {November},
url = {http://dx.doi.org/10.1017/jfm.2019.685},
Abstract = {A viscous suspension of negatively buoyant particles
released into a wide, open channel on an incline will
stratify in the normal direction as it flows. We model the
early dynamics of this stratification under the effects of
sedimentation and shear-induced migration. Prior work
focuses on the behaviour after equilibration where the bulk
suspension either separates into two distinct fronts
(settled) or forms a single, particle-laden front (ridged),
depending on whether the initial concentration of particles
exceeds a critical threshold. From past experiments, it is
also clear that this equilibration time scale grows
considerably near the critical concentration. This paper
models the approach to equilibrium. We present a theory of
the dramatic growth in this equilibration time when the
mixture concentration is near the critical value, where the
balance between settling and shear-induced resuspension
reverses.},
Doi = {10.1017/jfm.2019.685},
Key = {fds346592}
}
@article{fds340247,
Author = {Taranets, RM and Wong, JT},
Title = {Existence of weak solutions for particle-laden flow with
surface tension},
Journal = {Discrete and Continuous Dynamical Systems Series
A},
Volume = {38},
Number = {10},
Pages = {4979-4996},
Publisher = {American Institute of Mathematical Sciences
(AIMS)},
Year = {2018},
Month = {October},
url = {http://dx.doi.org/10.3934/dcds.2018217},
Abstract = {We prove the existence of solutions for a coupled system
modeling the flow of a suspension of fluid and negatively
buoyant non-colloidal particles in the thin film limit. The
equations take the form of a fourth-order nonlinear
degenerate parabolic equation for the film height h coupled
to a second-order degenerate parabolic equation for the
particle density ψ. We prove the existence of physically
relevant solutions, which satisfy the uniform bounds 0≤6
ψ/h≤1 and h > 0.},
Doi = {10.3934/dcds.2018217},
Key = {fds340247}
}
@article{fds335546,
Author = {Mavromoustaki, A and Wang, L and Wong, J and Bertozzi,
AL},
Title = {Surface tension effects for particle settling and
resuspension in viscous thin films},
Journal = {Nonlinearity},
Volume = {31},
Number = {7},
Pages = {3151-3173},
Publisher = {IOP Publishing},
Year = {2018},
Month = {May},
url = {http://dx.doi.org/10.1088/1361-6544/aab91d},
Abstract = {We consider flow of a thin film on an incline with
negatively buoyant particles. We derive a one-dimensional
lubrication model, including the effect of surface tension,
which is a nontrivial extension of a previous model (Murisic
et al 2013 J. Fluid Mech. 717 203-31). We show that the
surface tension, in the form of high order derivatives, not
only regularizes the previous model as a high order
diffusion, but also modifies the fluxes. As a result, it
leads to a different stratification in the particle
concentration along the direction perpendicular to the
motion of the fluid mixture. The resulting equations are of
mixed hyperbolic-parabolic type and different from the
well-known lubrication theory for a clear fluid or fluid
with surfactant. To study the system numerically, we
formulate a semi-implicit scheme that is able to preserve
the particle maximum packing fraction. We show extensive
numerical results for this model including a qualitative
comparison with two-dimensional laboratory
experiments.},
Doi = {10.1088/1361-6544/aab91d},
Key = {fds335546}
}
@article{fds329103,
Author = {Wong, JT and Bertozzi, AL},
Title = {A conservation law model for bidensity suspensions on an
incline},
Journal = {Physica D: Nonlinear Phenomena},
Volume = {330},
Pages = {47-57},
Publisher = {Elsevier BV},
Year = {2016},
Month = {September},
url = {http://dx.doi.org/10.1016/j.physd.2016.05.002},
Abstract = {We study bidensity suspensions of a viscous fluid on an
incline. The particles migrate within the fluid due to a
combination of gravity-induced settling and shear induced
migration. We propose an extension of a recent model
(Murisic et al., 2013) for monodisperse suspensions to two
species of particles, resulting in a hyperbolic system of
three conservation laws for the height and particle
concentrations. We analyze the Riemann problem and show that
the system exhibits three-shock solutions representing
distinct fronts of particles and liquid traveling at
different speeds as well as singular shock solutions for
sufficiently large concentrations, for which the mechanism
is essentially the same as the single-species case. We also
consider initial conditions describing a fixed volume of
fluid, where solutions are rarefaction–shock pairs, and
present a comparison to recent experimental results. The
long-time behavior of solutions is identified for settled
mono- and bidisperse suspensions and some leading-order
asymptotics are derived in the single-species case for
moderate concentrations.},
Doi = {10.1016/j.physd.2016.05.002},
Key = {fds329103}
}
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Mathematics Department