Roger T. Bonnecaze

Particle-driven gravity currents.

Gravity currents created by the release of a fixed volume of a suspension into a lighter ambient fluid are studied theoretically and experimentally. The greater density of the current and the buoyancy force driving its motion arise primarily from dense particles suspended in the interstitial fluid of the current. The dynamics of the current are assumed to be dominated by a balance between inertial and buoyancy forces; viscous forces are assumed negligible. The currents considered are two-dimensional and flow over a rigid horizontal surface. The flow is modelled by either the single- or the twolayer shallow-water equations, the two-layer equations being necessary to include the effects of the overlying fluid, which are important when the depth of the current is comparable to the depth of the overlying fluid. Because the local density of the gravity current depends on the concentration of particles, the buoyancy contribution to the momentum balance depends on the variation of the particle concentration. A transport equation for the particle concentration is derived by assuming that the particles are vertically well-mixed by the turbulence in the current, are advected by the mean flow and settle out through the viscous sublayer at the bottom of the current. The boundary condition at the moving front of the current relates the velocity and the pressure head at that point. The resulting equations are solved numerically, which reveals that two types of shock can occur in the current. In the late stages of all particle-driven gravity currents, an internal bore develops that separates a particle-free jet-like flow in the rear from a dense gravity-current flow near the front. The second type of bore occurs if the initial height of the current is comparable to the depth of the ambient fluid. This bore develops during the early lock-exchange flow between the two fluids and strongly changes the structure of the current and its transport of particles from those of a current in very deep surroundings. To test the theory, several experiments were performed to measure the length of particle-driven gravity currents as a function of time and their deposition patterns for a variety of particle sizes and initial masses of sediment. The comparison between the theoretical predictions, which have no adjustable parameters, and the experimental results are very good.

Sediment-laden gravity currents with reversing buoyancy

There are many natural occurrences of sediment-laden gravity currents in which the density of the interstitial fluid is less than that of the ambient fluid, although the bulk density of the current is greater. Such currents are driven by the excess density of suspended particles. However, after sufficient particles have sedimented, the current will become buoyant, cease its lateral motion and ascend to form a plume. Examples of such currents include brackish underflows in deltas, turbidity currents and pyroclastic flows. Experimental studies are described which show that, due to sedimentation, sediment-laden gravity currents decelerate more rapidly than saline currents of the same density. There is little difference in the experiments between a sediment-laden current with neutrally buoyant interstitial fluid and one with buoyant interstial fluid until sufficient sediment has been lost to cause the latter kind of current to lift-off. A marked deceleration is then observed and a plume is generated, with lift-off occurring along the length of the current. The resulting buoyant plume then generates a gravity current below the upper surface of the fluid in the tank. The deposit from a current with buoyant fluid shows a fairly abrupt decrease in thickness beyond the lift-off distance and has a flatter profile than that from a simple sediment current. A theoretical model is presented, which is based on the two-layer shallow-water equations and incorporates a model of the sedimentation in which particles are assumed to be uniformly suspended by the turbulence of the current. The model shows good agreement with the observed lengths of the experimental currents as a function of time and predicts the lift-off distance reasonably well. These processes have implications for the behaviour of turbidity currents, the interpretation of turbidites, mixing processes in the oceans and the lift-off of pyroclastic flows.

Slip and flow in pastes of soft particles: Direct observation and rheology

Microgel pastes and concentrated emulsions are shown to exhibit a generic slip behavior at low stresses when sheared near smooth surfaces. The magnitude of slip depends on the applied stress. Well above the yield stress, slip is negligible compared to the bulk flow. Just above the yield stress, slip becomes significant and the total deformation results from a combination of bulk flow and slip. At and below the yield stress, the bulk flow is negligible and the apparent motion is entirely due to wall slip. By directly imaging the deformation of pastes and from rheological measurements, we show that slip is characterized by universal scaling properties, which depend on solvent viscosity, bulk shear modulus, and particle size. A model based on elastohydrodynamic lubrication between the squeezed particles and the shearing surface explains these properties quantitatively.

Yield stresses in electrorheological fluids

We describe and determine the static and dynamic (Bingham) yield stresses in an electrorheological (ER) fluid from a microstructural model. The model relates both these yield stresses to the electrostatic energy determined from the suspension capacitance matrix, which we developed previously for the dynamic simulation of an ER fluid. The static yield stress is determined from nonlinear elasticity strain‐energy theory applied to an ER fluid for a variety of volume fractions and particle‐to‐fluid dielectric constant ratios. The static yield stress increases with the dielectric constant ratio and exhibits a maximum at 40 Vol % particles for dielectric constant ratios of 4 or less. From the capacitance of the suspension we also compute the zero‐frequency birefringence of the ER fluid and show that it follows a nonlinear stress‐optical rule. The dynamic yield stress, as we have observed in our previous simulations, dominates the rheology of the ER fluid at large electric field strengths. At the same time the e...

Extracellular Matrix Stiffness and Architecture Govern Intracellular Rheology in Cancer

Little is known about the complex interplay between the extracellular mechanical environment and the mechanical properties that characterize the dynamic intracellular environment. To elucidate this relationship in cancer, we probe the intracellular environment using particle-tracking microrheology. In three-dimensional (3D) matrices, intracellular effective creep compliance of prostate cancer cells is shown to increase with increasing extracellular matrix (ECM) stiffness, whereas modulating ECM stiffness does not significantly affect the intracellular mechanical state when cells are attached to two-dimensional (2D) matrices. Switching from 2D to 3D matrices induces an order-of-magnitude shift in intracellular effective creep compliance and apparent elastic modulus. However, for a given matrix stiffness, partial blocking of beta1 integrins mitigates the shift in intracellular mechanical state that is invoked by switching from a 2D to 3D matrix architecture. This finding suggests that the increased cell-matrix engagement inherent to a 3D matrix architecture may contribute to differences observed in viscoelastic properties between cells attached to 2D matrices and cells embedded within 3D matrices. In total, our observations show that ECM stiffness and architecture can strongly influence the intracellular mechanical state of cancer cells.

A micromechanical model to predict the flow of soft particle glasses

Soft particle glasses form a broad family of materials made of deformable particles, as diverse as microgels, emulsion droplets, star polymers, block copolymer micelles and proteins, which are jammed at volume fractions where they are in contact and interact via soft elastic repulsions. Despite a great variety of particle elasticity, soft glasses have many generic features in common. They behave like weak elastic solids at rest but flow very much like liquids above the yield stress. This unique feature is exploited to process high-performance coatings, solid inks, ceramic pastes, textured food and personal care products. Much of the understanding of these materials at volume fractions relevant in applications is empirical, and a theory connecting macroscopic flow behaviour to microstructure and particle properties remains a formidable challenge. Here we propose a micromechanical three-dimensional model that quantitatively predicts the nonlinear rheology of soft particle glasses. The shear stress and the normal stress differences depend on both the dynamic pair distribution function and the solvent-mediated EHD interactions among the deformed particles. The predictions, which have no adjustable parameters, are successfully validated with experiments on concentrated emulsions and polyelectrolyte microgel pastes, highlighting the universality of the flow properties of soft glasses. These results provide a framework for designing new soft additives with a desired rheological response.

The Effective Conductivity of Random Suspensions of Spherical Particles

The effective conductivity of an infinite, random, mono-disperse, hard-sphere suspension is reported for particle to matrix conductivity ratios of ∞, 10 and 0.01 for sphere volume fractions, c, up to 0.6. The conductivities are computed with a method previously described by the authors, which includes both far- and near-field interactions, and the particle configurations are generated via a Monte Carlo method. The results are consistent with the previous theoretical work of D. J. Jeffrey to O(c2) and the bounds computed by S. Torquato and F. Lado. It is also found that the Clausius-Mosotti equation is reasonably accurate for conductivity ratios of 10 or less all the way up to 60% (by volume). The calculated conductivities compare very well with those of experiments. In addition, percolation-like numerical experiments are performed on periodically replicated cubic lattices of N nearly touching spheres with an infinite particle to matrix conductivity ratio where the conductivity is computed as spheres are removed one by one from the lattice. Under suitable normalization of the conductivity and volume fraction, it is found that the initial volume fraction must be extremely close to maximum packing in order to observe a percolation transition, indicating that the near-field effects must be very large relative to far-field effects. These percolation transitions occur at the accepted values for simple (SC), body-centred (BCC) and face-centred (FCC) cubic lattices. Also, the vulnerability of the lattices computed here are exactly those of previous investigators. Due to limited data above the percolation threshold, we could not correlate the conductivity with a power law near the threshold ; however, it can be correlated with a power law for large normalized volume fractions. In this case the exponents are found to be 1.70, 1.75 and 1.79 for SC, BCC and FCC lattices respectively.

Cancer Cell Stiffness: Integrated Roles of Three-Dimensional Matrix Stiffness and Transforming Potential

While significant advances have been made toward revealing the molecular mechanisms that influence breast cancer progression, much less is known about the associated cellular mechanical properties. To this end, we use particle-tracking microrheology to investigate the interplay among intracellular mechanics, three-dimensional matrix stiffness, and transforming potential in a mammary epithelial cell (MEC) cancer progression series. We use a well-characterized model system where human-derived MCF10A MECs overexpress either ErbB2, 14-3-3ζ, or both ErbB2 and 14-3-3ζ, with empty vector as a control. Our results show that MECs possessing ErbB2 transforming potential stiffen in response to elevated matrix stiffness, whereas non-transformed MECs or those overexpressing only 14-3-3ζ do no exhibit this response. We further observe that overexpression of ErbB2 alone is associated with the highest degree of intracellular sensitivity to matrix stiffness, and that the effect of transforming potential on intracellular stiffness is matrix-stiffness-dependent. Moreover, our intracellular stiffness measurements parallel cell migration behavior that has been previously reported for these MEC sublines. Given the current knowledge base of breast cancer mechanobiology, these findings suggest that there may be a positive relationship among intracellular stiffness sensitivity, cell motility, and perturbed mechanotransduction in breast cancer.

Influence of short-range forces on wall-slip in microgel pastes

Concentrated suspensions of soft deformable particles, e.g., polymer microgel pastes and compressed emulsions, display a generic slip behavior [Meeker et al., J. Rheol. 92, 18302 (2004a); Meeker et al., J. Rheol. 48, 1295–1320 (2004b)]. When sheared with smooth surfaces, they exhibit apparent motion due to slip at the wall. Wall-slip stops at a sliding yield stress the value of which is much lower than the bulk yield stress. The physical mechanism of slip at low stresses and the origin of the sliding yield stress have so far been unresolved issues. We propose that the paste-wall interactions control the wall-slip behavior and determine the occurrence of the sliding yield point. We present experiments performed with different shearing surfaces. Two distinct slip behaviors are identified: depending on whether the interaction between the microgel particles and the wall is attractive or repulsive, wall-slip can be either suppressed or promoted. We provide an extension to the elastohydrodynamic slip model of M...

A Method for Determining the Effective Conductivity of Dispersions of Particles

A general method is developed to predict the effective conductivity of an infinite, statistically homogeneous suspension of particles in an arbitrary (ordered or disordered) configuration. The method follows closely that of ‘stokesian dynamics’, and captures both far-field and near-field particle interactions accurately with no convergence difficulties. This is accomplished by forming a capacitance matrix, the electrostatic analogue of the low-Reynolds-number resistance matrix, which relates the monopole (charge), dipole and quadrupole of the particles to the potential held of the system. A far-field approximation to the capacitance matrix is formed via a moment expansion of the integral equation for the potential. The capacitance matrix of the infinite system is limited to finite number of equations by using periodic boundary conditions, and the Ewald method is used to form rapidly converging lattice sums of particle interactions. To include near-field effects, exact two-body interactions are added to the far-field approximation of the capacitance matrix. The particle dipoles are then calculated directly to determine the effective conductivity of the system. The Madelung constant of cohesive energy of ionic crystals is calculated for simple and body-centred cubic lattices as a check on the method formulation. The results are found to be in excellent agreement with the accepted values. Also, the effective conductivities of spherical particles in cubic arrays are calculated for particle to matrix conductivity ratios of infinity, 10 and 0.01.