12 research outputs found
Toward a microscopic description of flow near the jamming threshold
We study the relationship between microscopic structure and viscosity in
non-Brownian suspensions. We argue that the formation and opening of contacts
between particles in flow effectively leads to a negative selection of the
contacts carrying weak forces. We show that an analytically tractable model
capturing this negative selection correctly reproduces scaling properties of
flows near the jamming transition. In particular, we predict that (i) the
viscosity {\eta} diverges with the coordination z as {\eta} ~
(z_c-z)^{-(3+{\theta})/(1+{\theta})}, (ii) the operator that governs flow
displays a low-frequency mode that controls the divergence of viscosity, at a
frequency {\omega}_min\sim(z_c-z)^{(3+{\theta})/(2+2{\theta})}, and (iii) the
distribution of forces displays a scale f* that vanishes near jamming as
f*/\sim(z_c-z)^{1/(1+{\theta})} where {\theta} characterizes the
distribution of contact forces P(f)\simf^{\theta} at jamming, and where z_c is
the Maxwell threshold for rigidity.Comment: 6 pages, 4 figure
Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions
Rheological properties of dense flows of hard particles are singular as one
approaches the jamming threshold where flow ceases, both for aerial granular
flows dominated by inertia, and for over-damped suspensions. Concomitantly, the
lengthscale characterizing velocity correlations appears to diverge at jamming.
Here we introduce a theoretical framework that proposes a tentative, but
potentially complete scaling description of stationary flows. Our analysis,
which focuses on frictionless particles, applies {\it both} to suspensions and
inertial flows of hard particles. We compare our predictions with the empirical
literature, as well as with novel numerical data. Overall we find a very good
agreement between theory and observations, except for frictional inertial flows
whose scaling properties clearly differ from frictionless systems. For
over-damped flows, more observations are needed to decide if friction is a
relevant perturbation or not. Our analysis makes several new predictions on
microscopic dynamical quantities that should be accessible experimentally.Comment: 13 pages + 3 pages S
Effect of particle collisions in dense suspension flows
We study non-local effects associated with particle collisions in dense
suspension flows, in the context of the affine solvent model known to capture
various aspects of the jamming transition. We show that an individual collision
changes significantly the velocity field on a characteristic volume
that diverges as jamming is approached, where is the deficit in coordination number required to jam the system. Such an
event also affects the contact forces between particles on that same volume
, but this change is modest in relative terms, of order , where is the typical contact force scale. We then
show that the requirement that coordination is stationary (such that a
collision has a finite probability to open one contact elsewhere in the system)
yields the scaling of the viscosity (or equivalently the viscous number) with
coordination deficit . The same scaling result was derived in
[E.~DeGiuli, G.~D\"uring, E.~Lerner, and M.~Wyart, Phys.~Rev.~E {\bf 91},
062206 (2015)] via different arguments making an additional assumption. The
present approach gives a mechanistic justification as to why the correct finite
size scaling volume behaves as , and can be used to recover a
marginality condition known to characterize the distributions of contact forces
and gaps in jammed packings
Breakdown of continuum elasticity in amorphous solids
We show numerically that the response of simple amorphous solids (elastic networks and particle packings) to a local force dipole is characterized by a lengthscale lc that diverges as unjamming is approached as lc ∼ (z − 2d)−1/2, where z ≥ 2d is the mean coordination, and d is the spatial dimension, at odds with previous numerical claims. We also show how the magnitude of the lengthscale lc is amplified by the presence of internal stresses in the disordered solid. Our data suggests a divergence of lc ∼(pc − p)−1/4 with proximity to a critical internal stress pc at which soft elastic modes become unstable