14 research outputs found
Confined flow of suspensions modeled by a frictional rheology
We investigate in detail the problem of confined pressure-driven laminar flow
of neutrally buoyant non-Brownian suspensions using a frictional rheology based
on the recent proposal of Boyer et al., 2011. The friction coefficient and
solid volume fraction are taken as functions of the dimensionless viscous
number I defined as the ratio between the fluid shear stress and the particle
normal stress. We clarify the contributions of the contact and hydrodynamic
interactions on the evolution of the friction coefficient between the dilute
and dense regimes reducing the phenomenological constitutive description to
three physical parameters. We also propose an extension of this constitutive
law from the flowing regime to the fully jammed state. We obtain an analytical
solution of the fully-developed flow in channel and pipe for the frictional
suspension rheology. The result can be transposed to dry granular flow upon
appropriate redefinition of the dimensionless number I. The predictions are in
excellent agreement with available experimental results, when using the values
of the constitutive parameters obtained independently from stress-controlled
rheological measurements. In particular, the frictional rheology correctly
predicts the transition from Poiseuille to plug flow and the associated
particles migration with the increase of the entrance solid volume fraction. We
numerically solve for the axial development of the flow from the inlet of the
channel/pipe toward the fully-developed state. The available experimental data
are in good agreement with our predictions. The solution of the axial
development of the flow provides a quantitative estimation of the entrance
length effect in pipe for suspensions. A analytical expression for development
length is shown to encapsulate the numerical solution in the entire range of
flow conditions from dilute to dense.Comment: Submitted to J. Fluid Mech. on Dec. 24, 2013, Revised version July
10, 2014, Accepted for publication Sept. 19, 201
Pressurization of a PKN Fracture in a Permeable Rock During Injection of a Low Viscosity Fluid
Shear heating of a fluid-saturated slip-weakening dilatant fault zone : 2. quasi-drained regime
[1] The one-dimensional model o
Fault-size dependent fracture energy explains multi-scale seismicity and cascading earthquakes
Earthquakes vary in size over many orders of magnitude, yet the scaling of
the earthquake energy budget remains enigmatic. We propose that fundamentally
different "small-slip" and "large-slip" fracture processes govern earthquakes.
We combine seismological observations with a physics-based mechanical
earthquake model under flash-heating friction. We find that dynamic weakening
and restrengthening effects are non-negligible in the energy budget of small
earthquakes and establish a simple linear scaling relationship between
small-slip fracture energy and fault size. We use supercomputing to apply this
scaling and unveil volumetric "Mode-4" earthquake cascades involving
multi-scale fractures within a fault damage zone, capable of dynamically
triggering large earthquakes. Our findings provide an intuitive explanation of
seismicity across all scales with important implications for comprehending
earthquake nucleation and multi-fault rupture cascades.Comment: 41 pages, 10 figure
Pressure-Driven Suspension Flow near Jamming
We report here magnetic resonance imaging measurements performed on suspensions with a bulk solid volume fraction (φ0) up to 0.55 flowing in a pipe. We visualize and quantify spatial distributions of φ and velocity across the pipe at different axial positions. For dense suspensions (φ0>0.5), we found a different behavior compared to the known cases of lower φ0. Our experimental results demonstrate compaction within the jammed region (characterized by a zero macroscopic shear rate) from the jamming limit φm≈0.58 at its outer boundary to the random close packing limit φrcp≈0.64 at the center. Additionally, we show that φ and velocity profiles can be fairly well captured by a frictional rheology accounting for both further compaction of jammed regions as well as normal stress differences. © 2015 American Physical Society