Constant Slip Velocity Research Articles

Complex ink flow mechanisms in micro-direct-ink-writing and their implications on flow rate control

Despite its simplicity, low cost, and ability to process a wide range of materials, direct-ink-writing (DIW) is an additive manufacturing process with low resolution and accuracy, in the multiple hundred microns to millimeter range. One of the main sources for this issue is the difficulty with accurately controlling ink flow rate at smaller size scales. Towards addressing this limitation, this paper elucidates complex ink flow mechanisms that renders flow rate control difficult and explores printing implementations to increase flow rate accuracy in direct-ink-writing at the micro scale. To this end, a DIW system utilizing hybrid pressure and velocity-controlled extrusion is used to obtain pressure-flow rate relationships for a water-based sodium carboxymethyl cellulose (NaCMC) solution ink, as a function of printing nozzle diameter (510–100 µm). These studies showed that the transient response of piston velocity-controlled extrusion significantly slows down with decreasing nozzle diameter. For pressure-controlled extrusion, the wall slip increases with decreasing nozzle diameter and the constant slip velocity assumption no longer holds as nozzle size decreases below a certain diameter. To contextualize the influence of such behavior on flow rate accuracy, temperature-controlled parallel plate rheometry was performed on the inks and rheological ink models were accordingly determined. It was shown that the associated flow rate predictions under predicted flow rates due to lack of wall-slip consideration, particularly for smaller nozzle sizes. Lastly, an iterative pressure-controlled DIW implementation was explored to address the accuracy issues for micro-DIW. Our results indicated significant improvement in the transient response and flow rate accuracy for nozzle diameters as small as 100 µm using this approach compared to both of the conventional pressure and velocity control approaches.

Some aspects regarding the influence of the anisotropy of an AA2021-T351 rolled thick plate on its tribological behaviour

This scientific paper aims to study the influence of the anisotropy of an aluminium AA2024-T251 rolled thick plate on the surface tribological properties based on previous experimental and numerical studies concerning bulk and surface mechanical behaviour. Experimental friction tests have been made on the aluminium alloy thick plate surface using sliding of an ultra-high-molecular-weight polyethylene (UHMWPE) cylindrical pin. The used tribological test involves the generation of local motion along specified trajectories with different orientations under the action of a constant normal force and a constant slip velocity. Three different normal forces (3N, 5N, 7N) have been applied using five different sliding speeds (0.005, 0.05, 0.5, 1 and 5mm/s) along a linear trajectory of 3 mm length. In order to analyze the influence of the aluminium alloy anisotropy, the tests have been performed along three directions: a longitudinal one, corresponding to the rolling direction of the sample (0°), a transverse one, perpendicular to the rolling direction (90°), and a median direction (45°). Taking into account the observed bulk and surface anisotropy, especially concerning a fractal nature of the surface topography, an investigation was performed in order to determine its influence on the anisotropic tribological properties. In this purpose, fractal friction characteristics have been determined for the sliding process using a constant normal force Fn = 7N and the above five sliding speeds.

“Virtual shear box” experiments of stress and slip cycling within a subduction interface mélange

What role does the progressive geometric evolution of subduction-related mélange shear zones play in the development of strain transients? We use a “virtual shear box” experiment, based on outcrop-scale observations from an ancient exhumed subduction interface – the Chrystalls Beach Complex (CBC), New Zealand – to constrain numerical models of slip processes within a meters-thick shear zone. The CBC is dominated by large, competent clasts surrounded by interconnected weak matrix. Under constant slip velocity boundary conditions, models of the CBC produce stress cycling behavior, accompanied by mixed brittle-viscous deformation. This occurs as a consequence of the reorganization of competent clasts, and the progressive development and breakdown of stress bridges as clasts mutually obstruct one another. Under constant shear stress boundary conditions, the models show periods of relative inactivity punctuated by aseismic episodic slip at rapid rates (meters per year). Such a process may contribute to the development of strain transients such as slow slip.

Confined KCl Solution between Two Mica Surfaces: Equilibrium and Frictional Properties

We have simulated the molecular dynamics of a KCl solution confined between two mica surfaces in equilibrium with a reservoir. For comparison, the simulations were also performed with pure water under the same conditions. The relation between normal pressure, lateral pressure in the solution layer, and quantity of water was first investigated. The position and orientation of the chemical species were then determined, showing the local molecular structure. Lastly, we simulated the mechanical response of the system submitted to a constant slip velocity for determining its frictional properties.

Numerical simulations of turbulent thermal, bubble and hybrid plumes

To understand the near-field dynamics of blowout plumes such as the one produced by the 2010 Deepwater Horizon oil spill in the Gulf of Mexico, the effects of gas bubbles on turbulent mixing and entrainment are studied via turbulence resolving simulations. We compare the evolution of three plumes where extremely large buoyancy anomalies are produced either thermally (single phase), solely by an imposed gas phase volume fraction, or by a combination of both buoyancy forcings. The plumes, with identical volume, momentum and buoyancy fluxes at the inlet, are released into an environment stratified with a constant temperature gradient. To clarify the first-order effects of dynamically active, dispersed bubbles, we employ a simple model which neglects the momentum of the gas phase while retaining bubble induced buoyancy in the seawater momentum equation. The gas phase is then distinguished by a single, measurable parameter, the slip velocity relative to that of the liquid phase. We find that bubbles, parameterized simply by a constant slip velocity, without any explicit assumptions of direct bubble induced turbulent production, significantly increase turbulent mixing in the plume in agreement with previous experimental results. Examination of mean momenta and turbulent kinetic energy budgets shows that the increased turbulence is due to direct modification of the mean profiles of both the momentum and the active scalar fields by the slipping gas phase. The narrowing of the active scalar field in the two-phase flow results in larger direct buoyancy production of turbulent energy at all vertical levels. The turbulence production is, however, primarily mechanical. At modest values of z/D, where the slip velocity is only a small fraction of the liquid phase velocity, slip stretches the mean vertical velocity field producing larger radial gradients and increased conversion of mean to turbulent energy. This first order effect, acting on the mean vertical velocity component and not directly on the turbulence, implies that even relatively small gas volume fractions significantly enhance turbulent mixing with respect to a single phase plume.

Finite difference modelling of rupture propagation with strong velocity-weakening friction

SUMMARY We incorporate rate- and state-dependent friction in explicit finite difference (FD) simulations of mode II dynamic ruptures in elastic media, using the Mimetic Operators Split-Node (MOSN) method, with adjustable order of spatial accuracy (second-, fourth- or mixed-order accurate), including an option that is fourth-order accurate at the fault discontinuity as well as in the elastic volume. At fault points, the rate and state equations combined with the spatially discretized momentum conservation equations form a coupled system of ordinary differential equations (ODEs) for slip velocity and state variable. As a consequence of the rapid damping of velocity perturbations due to the direct effect, this system exhibits numerical stiffness that is inversely proportional to velocity squared. Approximate solutions to this velocity-state system are achieved by two different implicit schemes: (i) a fourth-order Rosenbrock integration of the full system using multiple substeps and (ii) low order integrations (backward Euler and trapezoidal) of the velocity equation, time-staggered with analytic integration of the state equation under the approximation of constant slip velocity over the time step. In assessing the numerical schemes, we use three test problems: ruptures with frictional resistance controlled by (i) a slip evolution law with strong velocity-weakening behaviour at high slip rates, representing thermal weakening due to flash heating of microscopic asperity contacts, (ii) the classic (low-velocity) slip evolution law and (iii) the classic aging evolution law. A convergence analysis is carried out using reference solutions from a spectral boundary integral equation method (BIEM) (a method restricted to homogeneous media, with nominal spectral accuracy in space and second-order accuracy in time for smooth solutions). Errors are measured by root-mean-square differences of fault-plane time histories (slip, slip rate, traction and state). MOSN shows essentially the same convergence rates as BIEM: second-order convergence for slip and state-variable misfits, with slower (but at least first-order) convergence for slip rates and tractions. For a given grid spacing, fourth-order MOSN is as accurate as BIEM for all variables except slip-rate. MOSN-Rosenbrock nominally has fourth-order temporal accuracy for the fault-plane velocity-state ODE integration (compared to lower-order accuracy for the other two MOSN schemes) and therefore provides an important theoretical benchmark. However, it is sensitive to details of the elastic calculation scheme and occasionally its adaptive substepping performs poorly, leading to large excursions from the reference solution. In contrast, MOSN-trapezoidal is robust and reliable, much easier to implement than MOSN-Rosenbrock, and in all cases achieves precision as good as the latter without recourse to substepping. MOSN-Euler has the same advantages as MOSN-trapezoidal, except that its nominal first-order temporal accuracy ultimately leads to larger errors in slip and state variable compared with the higher-order MOSN schemes at sufficiently small grid spacings and time steps.

Experiments on granular rheology: Effects of particle size and fluid viscosity

We report the results of shear experiments of a thick layer of dry and liquid‐saturated glass beads, a simplified model of fault gouge, in order to clarify and to compare how the particle size and fluid viscosity affect the granular rheology. We sheared sorted glass beads and measured the temporal variation of stress that fluctuates owing to stick‐slip behavior. We found that the stress drop and slip recurrence intervals increase with the particle size because of larger static bulk friction. The forms of stress‐time series data for different particle size are not self‐similar; the form changes toward a sawtooth‐like temporal variation as the particle size increases, which can be characterized using two newly defined dimensionless numbers. In addition, we show that there is a continuous transition from constant slip velocity toward constant stress drop time as the particle size increases. We also determined the shear band width using the time‐lapsed images of the sheared glass beads and found that the number of particles comprising the shear band decreases with the particle size. When the glass beads are saturated with viscous liquid, lubrication causes the rheology to change from frictional to viscous and to increase the slip recurrence interval, and these properties can be used to distinguish from the particle size effects. Under a fixed loading rate, there is a viscosity that minimizes the stress needed for shearing, at which we can separate the frictional and viscous regimes.

A Gas hold‐up model for slurry bubble columns

AbstractA phenomenological model of the gas bubble hold‐up in slurry bubble columns is presented. The slurry moves upward in the core of the column and downward in the annulus, resembling the riser and downer of an air‐lift loop reactor, respectively. The model virtually divides the column in a riser and a downer. The cross‐sectional areas of the riser and the downer are experimentally found to be approximately equal. A macroscopic momentum balance over the riser and downer gives the liquid circulation velocity. The gas bubble hold‐up is modeled for two size classes: small and large. In the homogeneous regime only small gas bubbles are present. Above the regime transition velocity the churn‐turbulent regime exists, characterized by the presence of small and large gas bubbles. High speed video imaging shows that the gas flow up to the regime transition velocity generates small gas bubbles and that the gas flow in excess of the regime transition velocity generates large gas bubbles. Small gas bubbles are present in the riser and in the downer and have a constant slip velocity. The Wallis drift‐flux model describes the small gas bubble hold‐up in the riser and in the downer. Large gas bubbles are only present in the riser. The rise velocity of the large gas bubbles is the sum of the liquid velocity and the slip velocity according to the Davies‐Taylor equation. The large gas bubble hold‐up is obtained from the volume of gas flowing in large gas bubbles and the rise velocity of the large gas bubbles. For a given column diameter, column height, regime transition velocity, and physical properties of a gas–liquid system, the model predicts the total gas hold‐up, the hold‐up of the small and the large gas bubbles, and the average superficial liquid velocity in the riser and in the downer. Two parameters in the model are determined from experiments in a 29‐cm ID bubble column: the ratio of the small gas bubble hold‐up in the downer to that in the riser, and the energy dissipation at the top and bottom of the column. The model describes the gas hold‐up and liquid velocity data from literature with these parameter values within an error of 6%. The model shows that there is no effect of scale on the gas hold‐up for columns larger than 15 cm in diameter. © 2007 American Institute of Chemical Engineers AIChE J, 2007

Slip-Weakening Distance of Faults during Frictional Melting as Inferred from Experimental and Natural Pseudotachylytes

The slip-weakening distance, D c , over which a fault weakens during seismogenic fault motion, is one of most important parameters controlling fault instability. A paradox over the last decade has been the source of the large difference between laboratory-measured values of D c using conventional friction experiments (10 −5 –10 −3 m) and seismically determined D c values for natural earthquakes (10 −1 –10 0 m). D c is a difficult quantity to estimate for natural faults, but this study attempts to determine the order of D c values for natural faults containing pseudotachylytes based on a comparison between experimental and natural pseudotachylytes. Experiments at a constant slip velocity of 0.85 m/sec and a normal stress of 1.4 MPa on gabbro have revealed that the progressive growth of a molten layer causes marked slip weakening. Slip weakening (a reduction in frictional strength with displacement) and the growth of the molten layer (an increase in the thickness of the molten layer with displacement) are both characterized by exponential changes with nearly the same characteristic distances. The comparison suggests that the order of D c can be estimated from the relationship between pseudotachylyte thickness along its generation fault and fault displacement. Sibson’s (1975) data from the Outer Hebrides exhibit a similar pseudotachylyte-thickness-versus-fault-displacement curve with a characteristic distance of 0.38 m. This is the same order of magnitude as seismically inferred values of D c . The effect of frictional melting is a possible solution for the D c paradox, although it is not the only possible solution, since frictional melting along large faults is rather uncommon.

Dynamic Gas Disengagement in a High‐Pressure Bubble Column

AbstractBubble disengagement after stopping the gas supply is analyzed based on the concept of constant slip velocity; it is compared with the approaches used by previous investigators. The technique has been applied to study the gas density effect (0.17 to 46.6 kg·m—3) on the gas hold‐up structure in a bubble column with organic liquids (toluene, ethanol, 1‐butanol, decalin) and tap water. With increasing gas density, the large bubble rise velocity decreases; this indicates smaller bubble size. The small bubble hold‐up is correlated with the gas and the liquid properties whereas the large bubble hold‐up is hardly affected.

Stress on the seismogenic and deep creep plate interface during the earthquake cycle in subduction zones

The deep creep plate interface extends from the down-dip edge of the seismogenic zone down to the base of the overlying lithosphere in subduction zones. Seismogenic/deep creep zone interaction during the earthquake cycle produces spatial and temporal variations in strains within the surrounding elastic material. Strain observations in the Nankai subduction zone show distinct deformation styles in the co-seismic, post-seismic, and inter-seismic phases associated with the 1946 great earthquake. The most widely used kinematic model to match geodetic observations has been a 2-D Savage-type model where a plate interface is placed in an elastic half-space and co-seismic slip occurs in the upper seismogenic portion of the interface, while inter-seismic deformation is modeled by a locked seismogenic zone and a constant slip velocity across the deep creep interface. Here, I use the simplest possible 2-D mechanical model with just two blocks to study the stress interaction between the seismogenic and deep creep zones. The seismogenic zone behaves as a stick-slip interface where co-seismic slip or stress drop constrain the model. A linear constitutive law for the deep creep zone connects the shear stress (σ) to the slip velocity across the plate interface (s′) with the material property of interface viscosity (ζ ) as: σ = ζ s′. The analytic solution for the steady-state two-block model produces simple formulas that connect some spatially-averaged geodetic observations to model quantities. Aside from the basic subduction zone geometry, the key observed parameter is τ, the characteristic time of the rapid post-seismic slip in the deep creep interface. Observations of τ range from about 5 years (Nankai and Alaska) to 15 years (Chile). The simple model uses these values for τ to produce estimates for ζ that range from 8.4 × 1013 Pa/m/s (in Nankai) to 6.5 × 1014 Pa/m/s (in Chile). Then, the model predicts that the shear stress acting on deep creep interface averaged over the earthquake cycle ranges from 0.1 MPa (Nankai) to 1.7 MPa (Chile). These absolute stress values for the deep creep zone are slightly smaller than the great earthquake stress drops. Since the great earthquake recurrence time ( T recur) is much larger than τ for Nankai, Alaska, and Chile, the model predicts that rapid post-seismic creep should re-load the seismogenic zone to about (1/3) of the co-seismic change; geodetically observed values range from about (1/10) to more than (1/2). Also, for the case of (Trecur/τ) ≫1, the model predicts that the slip velocity across the deep creep interface during the inter-seismic phase should be about (2/3) the plate tectonic velocity (R). Thus the deep creep velocity used in Savage-type models should be less than R. Even complex 3-D models with non-linear creep laws should make a similar prediction for inter-seismic deep creep rates. At present, it seems that geodetic observations at Nankai and other subduction zones are more consistent with a deep creep rate of R rather than (2/3) R. This discrepancy is quite puzzling and is difficult to explain in the context of a 2-D steady-state earthquake cycle model. Future observational and modeling studies should examine this apparent discrepancy to gain more understanding of the earthquake cycle in subduction zones.

Active faulting and earthquake hazard: The case study of the Chihshang Fault, Taiwan

The Longitudinal Valley Fault Zone of eastern Taiwan is the present-day plate boundary between the Philippine Sea Plate and the South China block of Eurasia. Repeated surveys of active deformation were carried out at five sites along its most active segment, the Chihshang Fault. Annual surveys during the period 1990–1997 reveal a rather constant slip velocity of 2.2 cm/yr in a N40°W direction, involving both a thrust component with horizontal shortening of nearly 1.7 cm/yr and a left-lateral component of nearly 1.4 cm/yr. The fault trends N18°E and dips 39–45° to the east. The vertical displacement velocity is about 1.3 cm/yr and the actual oblique offset of the fault increases at a rate of 2.6 cm/yr. Comparison with GPS data suggests that some additional deformation occurs on the edge of the Valley. Active faulting of the Chihshang Fault and of the entire Longitudinal Valley Fault Zone accounts for 24% and 37% (respectively) of the total shortening across the Taiwan collision in the N54°W direction of relative motion between the Philippine Sea Plate and the South China shelf. This distribution of relative displacements illustrates the major role played by this boundary, as a zone of mechanical weakness where tectonic partitioning occurs. Permanent surveying of the displacement on the Chihshang Fault has the potential to detect significant decrease in slip rates, and hence to predict forthcoming locking stages, which would increase earthquake hazard.

Transport coefficients and life history of a vaporising liquid fuel droplet subject to retardation in a convective ambience

A numerical model has been developed for the process of droplet evaporation in a convective surrounding of high temperature gas. The model is based on numerical solution of unsteady conservation equations of mass, momentum, energy and species for both the gas and liquid phase. The important feature of the work is the consideration of continuous variation in free stream velocity with respect to the drop. This has been made in consideration of varying slip velocity (the velocity of droplet relative to free stream gas) of a moving droplet in a gaseous medium in real situation. The temporal reduction in free stream velocity has been evaluated from the droplet drag determined by the pressure and velocity fields of the gas phase surrounding the droplet. The relationships of drag coefficient and Nusselt number with the controlling variables like Reynolds number and Prandtl number have been established in the case of varying free stream velocity relative to the droplet, and have been compared with the standard laws for constant slip velocity. Other important charcteristics of vaporising droplet, like mass depletion history and temperature response, under the present situation, have been determined as a function of pertinent controlling parameters like initial Reynolds number of the droplet and the ratio of free stream to initial droplet temperature.

The statistical distribution of the mean squared weighted deviation — Comment: Isochrons, errorchrons, and the use of MSWD-values

What role does the progressive geometric evolution of subduction-related mélange shear zones play in the development of strain transients? We use a “virtual shear box” experiment, based on outcrop-scale observations from an ancient exhumed subduction interface – the Chrystalls Beach Complex (CBC), New Zealand – to constrain numerical models of slip processes within a meters-thick shear zone. The CBC is dominated by large, competent clasts surrounded by interconnected weak matrix. Under constant slip velocity boundary conditions, models of the CBC produce stress cycling behavior, accompanied by mixed brittle-viscous deformation. This occurs as a consequence of the reorganization of competent clasts, and the progressive development and breakdown of stress bridges as clasts mutually obstruct one another. Under constant shear stress boundary conditions, the models show periods of relative inactivity punctuated by aseismic episodic slip at rapid rates (meters per year). Such a process may contribute to the development of strain transients such as slow slip.

Boundary layer flow over a finite flat plate with a constant slip velocity

Two-dimensional incompressible laminar flow induced by a constant slip velocity on the surface of a finite flat plate is studied both analytically and numerically for large Reynolds numbers. It turned out that the thickness of the thin layer downstream of the trailing edge increases in square root of the distance from the trailing edge. Numerical integration of the boundary layer equations for the whole flow field confirmed two asymptotic natures of the flow field; near the trailing edge the analytic result is approached, and far downstream of the plate the jet flow solution is attained.

Measurements on isothermal flow of helium II in narrow tubes

Isothermal flow of He II in circular glass and metal tubes of inner diameter ∼0.2 mm is investigated. Different methods for the generation of the flow are used. The pressure heads required to drive the flow as well as the heat supply require to maintain isothermal conditions are measured. Earlier findings are confirmed and are shown to remain valid for smaller transport rates. The main features may be summarized as follows: (1) the pressure heads at given mass transport are almost independent of bath temperature, (2) they vary almost proportionally to the square of the mass flow rate, and (3) the flow becomes isothermal when there is a small, almost constant slip velocity (≲2.0 cm/sec) between the superfluid and normal components.

Ductile shear zones: some aspects of constant slip velocity and constant shear stress models

Summary. The thermomechanical differential equations governing deformation in viscous shear zones have been solved for both constant velocity and constant stress boundary conditions. The solutions show that the inertial term in these equations can be neglected everywhere. The starting condition of the constant velocity model has been shown to be a constant velocity gradient and not a Heaviside function. The temperature anomaly produced by shear heating at the centre of the shear zone is shown to increase gradually and continuously with time, not reaching an asymptotic value. Conclusions for the constant velocity boundary condition are otherwise generally similar to those presented by Yuen et d. and agree with Fleitout & Froidevaux. The temperatures reached by constant velocity shears are sufficient for partial melting. Constant stress boundary condition shear zone models show an initially broad shear zone with uniform shear velocity gradient. Depending on the level of applied shear stress and ambient temperature, localized intense shear heating may develop followed by thermal runaway. At lower ambient temperatures relatively high stresses are required to produce thermal runaway. The broadening of the constant velocity shear zone proceeds more rapidly with increased ambient temperature. This can be used to show that shear zones broaden with depth. The merging of parallel shear zone pairs has been investigated and shear zones separated by distances of less than lOkm coalesce to form a single shear zone within 3 Myr. Only shear zones separated by 50 km or more remain distinct over periods of tens of millions of years.

Flooding rates and holdup in packed liquid‐liquid extraction columns

AbstractCountercurrent flow of liquids in columns packed with Raschig rings was studied with fluids having a wide range of physical properties. These results, along with data reported previously from other studies, were used to develop a correlation for predicting flooding rates in packed columns that is significantly better than previous correlations. Dispersed phase holdup in packed columns can be estimated over a wide range of flow rates or flow ratio by assuming a constant slip velocity between the two phases which is dependent on the properties of the fluids and packing used. Although the slip velocity is thus essentially constant at flow rates below flooding, the flooding rate correlation indicates that this term is not necessarily constant at flooding conditions.