Force Balance Calculations Research Articles

Continuous Focusing of Particles by AC-Electroosmosis and Induced Dipole Interactions.

Continuous particle focusing by using microfluidics is an effective method for separating particles, cells, or droplets for analytical purposes. Previously, it was shown that an alternating current across rectangular microchannels with slightly deformed side walls results in vortex flow patterns caused by alternating current electroosmosis (AC-EOF) and could lead to particle focusing. In this work, we explore this mechanism by experimentally studying the particle focusing behavior for various fluid flow velocities through a microchannel. Since it is unlikely that the particles are kept in their focused position solely by convection, a theoretical force balance between the hydrodynamic and the induced dipole force was determined. In our experiments, it was found that there is no substantial effect of the pressure-driven fluid velocity on the particle focusing velocity within the studied range. From the theoretical force balance calculations, it was determined that while the addition of the induced dipole force can still not completely describe the experimentally observed particle focusing, the induced dipole can be strong enough to overcome the hydrodynamic force. Finally, it is hypothesized that under specific circumstances, including a repulsive electrostatic force between a particle and electrode wall can complete the theoretical particle focusing force balance. Alternative phenomena that could also play a role in particle focusing are proposed.

Pro+: Automated protrusion and critical shear stress estimates from 3D point clouds of gravel beds

AbstractThe dimensionless critical shear stress (τ*c) needed for the onset of sediment motion is important for a range of studies from river restoration projects to landscape evolution calculations. Many studies simply assume a τ*c value within the large range of scatter observed in gravel‐bedded rivers because direct field estimates are difficult to obtain. Informed choices of reach‐scale τ*c values could instead be obtained from force balance calculations that include particle‐scale bed structure and flow conditions. Particle‐scale bed structure is also difficult to measure, precluding wide adoption of such force‐balance τ*c values. Recent studies have demonstrated that bed grain size distributions (GSD) can be determined from detailed point clouds (e.g. using G3Point open‐source software). We build on these point cloud methods to introduce Pro+, software that estimates particle‐scale protrusion distributions and τ*c for each grain size and for the entire bed using a force‐balance model. We validated G3Point and Pro+ using two laboratory flume experiments with different grain size distributions and bed topographies. Commonly used definitions of protrusion may not produce representative τ*c distributions, and Pro+ includes new protrusion definitions to better include flow and bed structure influences on particle mobility. The combined G3Point/Pro+ provided accurate grain size, protrusion and τ*c distributions with simple GSD calibration. The largest source of error in protrusion and τ*c distributions were from incorrect grain boundaries and grain locations in G3Point, and calibration of grain software beyond comparing GSD is likely needed. Pro+ can be coupled with grain identifying software and relatively easily obtainable data to provide informed estimates of τ*c. These could replace arbitrary choices of τ*c and potentially improve channel stability and sediment transport estimates.

Surfactant flooding in oil-wet micromodels with high permeability fractures

Recovery in carbonate reservoirs is challenging because they are often oil wet and highly fractured. Surfactant flooding has been proposed as a possible enhanced oil recovery method to address these problems. To better understand the mechanisms of oil recovery from oil-wet, fractured rocks using surfactants, we created oil-wet glass micromodels, traversed by a deep fracture (130 µm) and conducted surfactant spontaneous imbibition experiments and floods at typical reservoir flow rates (approximately 2 ft/day). We compared the effects of capillary, viscous, and gravity forces as well as wettability alteration. We show, by conducting spontaneous imbibition experiments with negligible gravity effects (inverse Bond number ∼105) and by analyzing the results using simple force balance calculations, that in our micromodels low IFT plays the key role in balancing the viscous, gravity, and surface forces and hence the dynamics of imbibition. To quantify the role of viscous forces, we present displacement experiments at low IFT (10−3 mN/m) where transverse viscous pressure gradients mobilize oil from the matrix into the fracture. These results help rationalize and quantify the contributions of gravity, wettability alteration, and viscous crossflow to the rate of matrix-fracture transfer at low-IFT conditions.

Investigation of the thermal-hydraulic non-equilibrium in a 7 × 7 rod bundle during reflood

The current research aims at investigating the thermal–hydraulic non-equilibrium encountered in the dispersed flow film boiling (DFFB) regime under reflood conditions. A series of constant reflood tests have been performed at the 7 × 7 Rod Bundle Heat Transfer (RBHT) test facility and the experimental results have been analyzed in detail. The data not only is useful for the development of theoretical models for two-phase interfacial mass and heat transfer, void fraction, pressure drop, and rod bundle cooling prediction, but also can be used as a benchmark data base for evaluating the performance of various thermal–hydraulic analysis codes. In this paper, a complete data reduction methodology is employed to reveal and interpret important two-phase flow phenomena during reflood transients. The results show that for the region far away from the quench front location, significant thermal non-equilibrium may exist during reflood and thus poor heat removal capability of the flow mixture is expected. On the other hand, for the region immediately downstream of the quench front, the two-phase flow is found to be close to the thermal equilibrium state, indicating that both the interfacial heat transfer and the heat transfer between the rod surface and fluid mixture are very efficient. In addition, based on the liquid droplet measurement and force balance calculations, it is found that the slip ratio between the two separate phases is a strong function of the droplet size and reflood time. With a larger droplet size and a shorter distance from the quench location, the slip ratio is larger. The liquid carryover fraction at the exit of the test section is also determined as a function of the reflood time. Results indicate that only a small portion of the injected coolant mass is stored within the bundle. A significant amount of liquid mass into the test section is either evaporated or entrained in the vapor flow and eventually left the bundle.

An Empirical Approach for Estimating Stress-Coupling Lengths for Marine-Terminating Glaciers

Variability in the dynamic behavior of marine-terminating glaciers is poorly understood, despite an increase in the abundance and resolution of observations. When paired with ice thicknesses, surface velocities can be used to quantify the dynamic redistribution of stresses in response to environmental perturbations through computation of the glacier force balance. However, because the force balance is not purely local, force balance calculations must be performed at the spatial scale over which stresses are transferred within glacier ice, or the stress-coupling length (SCL). Here we present a new empirical method to estimate the SCL for marine-terminating glaciers using high-resolution observations. We use the empirically-determined periodicity in resistive stress oscillations as a proxy for the SCL. Application of our empirical method to two well-studied tidewater glaciers (Helheim Glacier, SE Greenland, and Columbia Glacier, Alaska, USA) demonstrates that SCL estimates obtained using this approach are consistent with theory (i.e., can be parameterized as a function of the ice thickness) and with prior, independent SCL estimates. In order to accurately resolve stress variations, we suggest that similar empirical stress-coupling parameterizations be employed in future analyses of glacier dynamics.

Dynamic crossflow filtration with a rotating tubular membrane: Using centripetal force to decrease fouling by buoyant particles

This paper describes a dynamic membrane filtration system that combines crossflow filtration and centrifugal separation in a rotating tubular membrane. Because of the no-slip boundary condition, membrane rotation leads to higher centripetal force near the lumen wall than introduction of a rotating flow. In this fundamental exploratory study, hollow glass microspheres (5–35μm diameters) serve as model low-density, separate-phase foulants during filtration of aqueous suspensions through a tubular ceramic membrane (nominal 0.14μm pore size). At low crossflow rates, membrane rotation at 1725rpm decreases fouling and shifts the microsphere size distribution in the membrane cake toward smaller diameters. Force balance calculations suggest that centripetal force should move particles with diameters >∼17μm away from the lumen surface. Moreover, azimuthal and longitudinal shear stresses will also selectively remove larger particles from the membrane cake. Computational fluid dynamics (CFD) simulations show that the rotational flow does not fully develop in the membrane lumen and the fluid radial velocity peaks before the membrane wall. Both of these factors will decrease movement of low-density particles away from the lumen wall. Nevertheless, consistent with experimental data, CFD simulations show greatly decreasing encounters of particles with the membrane wall as particle size increases.

Strain accumulation controls failure of a plate boundary zone: Linking deformation of the Central Andes and lithosphere mechanics

We make use of observations on orogenic strain accumulation and deformation partitioning in the Central Andes to explore the backarc strength evolution at the lithospheric scale. In plan view, the Altiplano‐Puna plateaux experienced rapid initial increase of surface area undergoing active deformation during the Cenozoic. Beyond the maximum lateral extent reached around 10–15 Ma (40–50% of entire proto‐Andes undergoing deformation) at 10–20% total strain, rapid localization initiated at the eastern flank of the Altiplano (Inter‐ and Subandean thrust belt) but not at the Puna latitude. Localization was associated with a significant increase in bulk shortening rate. Average fault slip rates equally increased by an order of magnitude following a protracted period of stable average rates. Estimates of strength evolution based on force balance calculations and critical wedge analysis suggest significant backarc weakening driving this change after the Middle Miocene. Strain accumulation led to localization and weakening with development of a detachment propagating through crust and upper mantle. We find that lithosphere‐scale failure resulting from strain weakening beyond a critical strain threshold (c. 20%) and fault coalescence with formation of a weak detachment in shales (effective coefficient of friction < 0.1) plays a key role in the evolution of the Andes. Strain‐related lithosphere weakening appears to dominate over the impact of external forcing mechanisms, such as variations of plate convergence, mantle‐assisted processes, or erosion. Comparison of these orogen‐scale observations with experimental rock rheology indicates substantial similarity of deformation behavior with similar weakening thresholds across a wide range of scales.

Splay fault slip in a subduction margin, a new model of evolution

In subduction zones, major thrusts called splay faults are thought to slip coseismically during large earthquakes affecting the main plate interface. We propose an analytical condition for the activation of a splay fault based on force balance calculations and suggest thrusting along the splay fault is generally conditioned by the growth of the accretionary wedge, or by the erosion of the hanging wall. In theory, normal slip on the splay fault may occur when the décollement has a very low friction coefficient seaward. Such a low friction also implies an unstable extensional state within the outer wedge. Finite element elasto-plastic calculations with a geometry based on the Nankai Kumano section were performed and confirm that this analytical condition is a valid approximation. Furthermore, localized extension at a shallow level in the splay hanging wall is observed in models for a wide range of friction coefficients (from ∼0 to the value of internal friction coefficient of the rock, here equals to 0.4). The timing of slip established for the splay fault branch drilled on Nankai Kumano transect suggests a phase of concurrent splay and accretionary wedge growth ≈2Ma to ≈1.5Ma, followed by a locking of the splay ≈1.3Ma. Active extension is observed in the hanging wall. This evolution can be explained by the activation of a deeper and weaker décollement, followed by an interruption of accretion. Activation of a splay as a normal fault, as hypothesized in the case of the Tohoku 2011 earthquake, can be achieved only if the friction coefficient on the décollement drops to near zero. We conclude that the tectonic stress state largely determines long-term variations of tightly related splay fault and outer décollement activity and thus influences where and how coseismic rupture ends, but that occurrence of normal slip on a splay fault requires coseismic friction reduction.

Critical Layer Thickness in Exponentially Graded Heteroepitaxial Layers

Exponentially graded semiconductor layers are of interest for use as buffers in heteroepitaxial devices because of their tapered dislocation density and strain profiles. Here we have calculated the critical layer thickness for the onset of lattice relaxation in exponentially graded InxGa1−xAs/GaAs (001) heteroepitaxial layers. Upwardly convex grading with \( x = x_{\infty } \left( {1 - {\rm e}^{ - \gamma /y} } \right) \) was considered, where y is the distance from the GaAs interface, γ is a grading length constant, and x∞ is the limiting mole fraction of In. For these structures the critical layer thickness was determined by an energy-minimization approach and also by consideration of force balance on grown-in dislocations. The force balance calculations underestimate the critical layer thickness unless one accounts for the fact that the first misfit dislocations are introduced at a finite distance above the interface. The critical layer thickness determined by energy minimization, or by a detailed force balance model, is approximately \( h_{\rm{c}} \approx 0.243\;\mu {\hbox{m}}\left( {\gamma /1\;\mu {\hbox{m}}} \right)^{0.5} \left( {x_{\infty } /0.1} \right)^{ -0.54} . \) Although these results were developed for exponentially graded InxGa1−xAs/GaAs (001), they may be generalized to other material systems for application to the design of exponentially graded buffer layers in metamorphic device structures such as modulation-doped field-effect transistors and light-emitting diodes.

India‐Asia collision and the Cenozoic slowdown of the Indian plate: Implications for the forces driving plate motions

The plate motion of India changed dramatically between 50 and 35 Ma, with the rate of convergence between India and Asia dropping from ∼15 to ∼4 cm/yr. This change is coincident with the onset of the India‐Asia collision, and with a rearrangement of plate boundaries in the Indian Ocean. On the basis of a simple model for the forces exerted upon the edges of the plate and the tractions on the base of the plate, we perform force balance calculations for the precollision and postcollision configurations. We show that the observed Euler poles for the Indian plate are well explained in terms of their locations and magnitudes if (1) the resistive force induced by mountain building in the Himalaya‐Tibet area is ∼5–6 × 1012 N/m, (2) the net force exerted upon the Indian plate by subduction zones is similar in magnitude to the ridge‐push force (∼2.5 × 1012 N/m), and (3) basal tractions exert a resisting force that is linearly proportional to the plate velocity in the hot spot reference frame. The third point implies an asthenospheric viscosity of ∼2–5 × 1019 Pa s, assuming a thickness of 100–150 km. Synthetic Euler poles show that crustal thickening in the Tibetan Plateau was the dominant cause of the Cenozoic slowdown of the Indian plate.

Dynamics and mass balance of Taylor Glacier, Antarctica: 2. Force balance and longitudinal coupling

Taylor Glacier, Antarctica, exemplifies an ice sheet outlet that flows through a region of rugged topography and dry climate. In contrast to other well‐studied outlets, Taylor Glacier moves very slowly, despite a thickness of order 1 km and driving stresses averaging 1.5 bars. Here we analyze new measurements of glacier geometry and surface velocity to elucidate flow dynamics of Taylor Glacier. Force balance and basal temperatures are calculated at six locations along the glacier's length using an algorithm developed for this study. The effects of stress‐gradient coupling on longitudinal flow variations are also examined; we ask whether Kamb and Echelmeyer's (1986) linearized theory adequately describes the observed response of flow to large‐amplitude variations in driving stress. The force balance calculations indicate that no basal motion is needed to explain the observed flow of Taylor Glacier. Inferred basal temperatures are within a few degrees of the melting point in regions of kilometer‐thick ice and well below the melting point elsewhere; deformation of subfreezing ice largely controls the flow of Taylor Glacier. Basal drags are mostly in the range 0.9 to 1.2 bars, and lateral drags are in the range 0.2 to 0.5 bar. Stress‐gradient coupling strongly reduces the variability of velocities along the glacier. The velocity variations can be described as the convolution of a forcing function with a spatial filter, as Kamb and Echelmeyer suggested, but the form of the forcing function differs from the theoretical relation derived for small‐amplitude perturbations (the power on driving stress is one, not three).

Manipulation and tracking of superparamagnetic nanoparticles using MRI

The use of magnetic fields in magnetic resonance imaging (MRI) for the tracking anddelivery of chemotherapeutics bound to superparamagnetic nanoparticles offers a promisingmethod for the non-invasive treatment of inoperable tumours. Here we demonstrate thatsuperparamagnetic magnetite nanoparticles fabricated by an easily scalable method can bedriven and tracked in real time at high velocities in vitro using MRI hardware. Forcebalance calculations are consistent with the magnetic properties of individual 10 nmdiameter particles that move collectively as micron sized agglomerates with hydrodynamicdiameter similar to that inferred from zero-magnetic-field dynamic light scatteringmeasurements.

Quasi-static and dynamic crushing of empty and foam-filled tubes

Metallic foam-filled tubes and their empty counterparts have been tested at quasi-static and dynamic strain rates in order to determine their energy absorption capabilities. Data from the Split-Hopkinson Pressure Bar have been used to generate force vs. displacement curves that are somewhat analogous to pseudo-engineering stress-strain curves. Force balance calculations have also been made. These results indicate that, on an equal weight basis, foam-filled tubes offer greater energy absorption capability than empty tubes at quasi-static strain rates. However, the benefit of foam filling does not appear to be extended to strain rates of the order of 200–500 s−1. Force balance calculations are shown to have potential as a method for monitoring the crushing of metallic foams at high strain rate.

Motion‐induced stresses in pack ice

We consider motion‐induced stresses in pack ice through the analyses of a variety of observations collected during the Sea Ice Mechanics Initiative study conducted in the Beaufort Sea during 1993. Motion‐induced components of in situ stress from stress gauge data are compared to stresses calculated as residuals based on a force balance argument using observed wind, current, and ice motion data. There is reasonable qualitative and quantitative agreement between the observed and calculated motion‐induced stresses in the north‐south direction if the residual stress is assumed to be distributed over a horizontal distance of ∼10 m. To obtain a general agreement with the magnitudes of the observed and calculated stresses in the east‐west direction, the residual stress must be considered to be distributed over a horizontal distance of ∼50 m. There are three significant stress events determined by the force balance calculations, but only the one event in the north‐south direction has a strong corresponding signal in the stress gauge data. There is very little indication of the two events in the east‐west direction in the gauge data. Numerical simulations of the distribution of motion‐induced stresses within a floe show that significant variations in the character of the stresses can occur over short horizontal distances throughout the floe. Hence a seeming lack of a clear correspondence between the observed and calculated stress may be due to our inability to properly recognize the modified signature of the event at the specific locations of the stress gauges. The results suggest that to effectively develop an understanding of the role that point stress measurements can play in developing our understanding of the process of ice deformation, it may be necessary to couple the stress measurements with models of the patterns of motion‐induced stresses within a floe. Finally, we consider the relationship between the residual stress and the differential motion of the ice pack as seen by a cluster of drifters on various floes. The three main stress events seen in the residual stresses all occurred during periods of convergence of the floes. However, we have tested various relationships between stress and strain, and they indicate that there should have been additional stress events as a result of other periods of substantial convergences of the ice pack. This suggests the possibility that the residual stresses were not locally generated.

Strength of Bentonite Water‐Well Annulus Seals in Confined Aquifers

The advantages of bentonite clay for sealing applications are well known. Bentonites have extremely low permeability, do not affect formation water chemistry, and have the ability to swell and deform in response to subsurface changes. The major limitation on the applicability of bentonite for water‐well annulus sealing is strength. Strength tests conducted in a physical model of a water well identified the expected magnitude of shear strength for several commercially available bentonite well‐sealing products. The dependence of bentonite strength in the annulus of a water well on both setting time and borehole geometry is discussed. Force balance calculations for seals constructed of both slurry grouts and granular products are presented. Seals constructed of bentonite slurry grouts do not have sufficient shear strength to resist hydrostatic forces in confined aquifer installations. Annulus seals constructed of granular bentonite products possess adequate shear strength to resist push‐out forces in limited...

Measurement of the fundamental band gaps of a strained GaInAs layer

All three strain- and spin-orbit-split energy gaps of the Γ15v-Γ1c series are measured for the first time for a thin, strained Ga0.526In0.474As layer by a combination of transmission, photoreflectance (PR), and photoluminescence experiments at 10 and 300 K. Values of strain and composition of the layer are calculated from the splitting of the (J=3/2, mj=±3/2) and (3/2, ±1/2) valence bands and from x-ray data. Force balance calculations predict the strain in the layer to be relaxed while energy balance calculations predict the layer to be strained. The onset of generation of misfit dislocations at the InP/GaInAs interface has recently been reported to be well described by the force balance model. Nevertheless, the data reported in the present study show the degree of plastic strain relaxation for the sample under investigation to be so small that it can be neglected for the interpretation of the optical spectra. Almost identical PR spectra are measured when the sample is excited at photon energies larger and smaller than the InP band gap. In both cases, the PR signal originates from modulation of built in fields at the heterointerfaces, rather than the surface field.

Adiabatic and isothermal resistivities.

The force-balance method is used to calculate the isothermal resistivity to first order in the electric field. To lowest order in the impurity potential, the isothermal resistivity disagrees with the adiabatic results of the Kubo formula and the Boltzmann equation. However, an expansion of the isothermal resistivity in powers of the impurity potential is divergent, with two sets of divergent terms. The first set arises from the density matrix of the relative electron-phonon system. The second set arises from the explicit dependence of the density matrix on the electric field, which was ignored by force-balance calculations. These divergent contributions are calculated inductively, by applying a recursion relation for the Green's functions. Using the ${\ensuremath{\lambda}}^{2}$t\ensuremath{\rightarrow}\ensuremath{\infty} limit of van Hove, I show that the resummation of these divergent terms yields the same result for the resistivity as the adiabatic calculations, in direct analogy with the work of Argyres and Sigel, and Huberman and Chester.