Increasing Slip Velocity Research Articles

Theoretical analysis of effect of MHD, couple stress and slip velocity on squeeze film lubrication of rough Triangular plates

In this study, Christensen's stochastic theory is utilized on rough surfaces' hydrodynamic lubricating effect to examine how surface roughness, couple stress fluid, slip velocity, magnetohydrodynamic (MHD), and the triangular surface interact. Modified Reynolds equation is derived analytically using combining theories of Stokes couple stresses, Lorentz forces, and Christensen's stochastic hypothesis about hydrodynamic lubrication. Pressure, load carrying capacity and squeeze film time expression is derived mathematically using Reynolds equation that accounts for surface roughness and coupling stress. For various parameters including rough parameter, slip velocity, Hartmann number, and couple stress, the lubricating characteristics are analysed graphically. Squeeze film time, load carrying capacity, and pressure are enhanced by an increase in slip velocity, couplestress and magnetic field. The lubrication characteristics decreases (increases) on squeeze film pressure, load carrying capacity and squeeze film time through increasing values of the longitudinal (transverse) roughness parameter.

MHD nanofluid flow and heat transfer caused by a stretching sheet that is heated convectively: An approximate solution using ADM

The investigation detailed in this paper explores the behavior of a slippery nanofluid flowing over a permeable stretched sheet under the influence of magnetohydrodynamic forces, considering factors like thermal radiation, viscous dissipation, and convective boundary conditions. The analysis systematically establishes principles for conserving mass, heat, momentum, and nanoparticle concentration, deriving a set of nonlinear ordinary differential equations from the governing partial differential equations. To tackle these challenges, the Adomian decomposition approach is utilized as a central element of the solution methodology. Graphical representations are employed to depict the solutions across various physical parameters. Despite the significance of nanofluids in both industrial and scientific contexts, there exists a noticeable research gap concerning the combined impacts of thermal radiation, viscous dissipation, and convective boundary conditions on heat and mass transfer, especially when coupled with a permeable linear rough stretched sheet. This study aims to fill this void by offering quantitative insights into these intricate phenomena, thereby enhancing our understanding of nanofluid dynamics and their practical implications. The findings indicate that increasing slip velocity and magnetic parameters reduce the boundary layer thickness of the velocity profile but increase it for the temperature profile, suggesting a nuanced interplay between slip velocity and magnetic effects on velocity boundary layers, while the temperature boundary layer exhibits distinct thermal dynamics within the system.

Geological fingerprints of deep slow earthquakes: A review of field constraints and directions for future research

Abstract Slow earthquakes, including low-frequency earthquakes, tremor, and geodetically detected slow-slip events, have been widely detected, most commonly at depths of 40–60 km in active subduction zones around the Pacific Ocean Basin. Rocks exhumed from these depths allow us to search for structures that may initiate slow earthquakes. The evidence for high pore-fluid pressures in subduction zones suggests that they may be associated with hydraulic fractures (e.g., veins) and with metamorphic reactions that release or consume water. Loss of continuity and resulting slip at rates exceeding 10−4 m s–1 are required to produce the quasi-seismic signature of low-frequency earthquakes, but the subseismic displacement rates require that the slip rate is slowed by a viscous process, such as low permeability, limiting the rate at which fluid can access a propagating fracture. Displacements during individual low-frequency earthquakes are unlikely to exceed 1 mm, but they need to be more than 0.1 mm and act over an area of ~105 m2 to produce a detectable effective seismic moment. This limits candidate structures to those that have lateral dimensions of ~300 m and move in increments of <1 mm. Possible candidates include arrays of sheeted shear veins showing crack-seal structures; dilational arcs in microfold hinges that form crenulation cleavages; brittle-ductile shear zones in which the viscous component of deformation can limit the displacement rate during slow-slip events; slip surfaces coated with materials, such as chlorite or serpentine, that exhibit a transition from velocity-weakening to velocity-strengthening behavior with increasing slip velocity; and block-in-matrix mélanges.

Power law dependence of unstable slip velocity on decreasing shear loading stiffness

Shear loading stiffness plays a critical role in conditioning the stability of slip on reactivated faults. However, a relationship linking peak slip velocities and shear loading stiffness is lacking. To explore this, we shear granite faults in double direct shear with shear loading stiffnesses spanning two orders to define the effects of shear loading stiffness in conditioning the transition from stable to unstable slip. Our results show that peak slip velocity and acceleration decrease as power law relationships with respect to the shear loading stiffness ratio, with identical exponent, and with a linear relationship between the peak slip velocity and acceleration. The maximum acceleration occurs during the velocity weakening process that limits the peak slip velocity. The power law exponent increases linearly with increasing normal stress. Experimental results also indicate that slip magnitude, stress drop and recurrence time of unstable slip events increase, and slip durations decrease with decreasing stiffness ratios. The spans of limit cycles of velocity versus shear stress decrease, and their shapes evolve from triangular to semicircular with increasing loading stiffness ratio. Stress drops mostly occur during deceleration. The deceleration phase dominates the unstable slip duration that decreases as peak slip velocity increases. Our results indicate that the average stress drop rates over a slip duration increase as a power law relationship with reducing shear loading stiffness, which also contributes to a lower shear loading stiffness producing increased slip velocities and accelerations. Our findings highlight that loading stiffness ratio is an underlying mechanism defining unstable slip behaviors with the normal stress merely conditioning the exponent. The present relationship of unstable slip velocity with shear loading stiffness suggests a way to evaluate hazard of an impending instability event based on the initial shear loading stiffness ratio that can be calculated through the linear-elastic behaviors at the early quasi-static phase.

Simulation of polymer solution slip motion and composite fiber fabrication in rotary jet spinning

Composite nanofibers are widely used as a novel nanomaterial in various fields, and the key technologies of preparation methods and equipment optimization have become the focus of research. Rotary jet spinning uses the centrifugal force generated by high-speed rotation to produce slip motion of two polymer solutions in the nozzle, and as the slip velocity increases, a rotating jet is eventually formed at the nozzle to eject the composite nanofibers. The slip motion of the polymer solution is one of the important factors affecting the rotating jet composite spinning, which directly affects the velocity distribution and flow stability of the polymer solution, and ultimately affects the morphology and quality of the composite nanofibers. By simulating the flow process of polymer solution inside the nozzle, the effect of slip motion on the flow of polymer solution is verified, which further illustrates that the rotational speed has the greatest influence on the preparation of composite nanofibers. Finally, PEO/PVA composite nanofibers were successfully prepared and collected by using a rotary jet spinning device in the range of 1500–3000 rpm, and the morphology and quality of the fibers were characterized and analyzed by scanning electron microscopy (SEM), which provided experimental bases for the simulation of the slip motion of the polymer solution and the study of composite fiber preparation.

Exploring the effects of TiO2${\rm TiO}_2$–Ag/water hybrid nanofluid on MHD flow over a permeable exponentially stretching–shrinking sheet with radiative heat transfer and slip conditions

AbstractThe objective of this article is to study the importance of velocity and thermal slip in the exponentially stretching or shrinking sheet with the megnetohydrodynamic (MHD) hybrid nanofluid flow along with magnetic field, radiative, heat generation effects. This study has practical importance in enhancing heat transfer efficiency, improving energy conversion and optimizing thermal management systems. The findings can also contribute to the development of sustainable energy systems and aid in assessing the stability and safety of nanofluid applications. The governing partial differential equations are transformed into nonlinear ordinary differential equations using similarity transformation. The ODEs are solved using bvp4c solver in MATLAB. The dual solutions are achieved for specific range of the stretching or shrinking parameter and mass suction parameter. The first solution is physically significant after considering stability analysis. The hybrid nanofluid has numerous real‐life and industrial applications, such as microelectronics, manufacturing, naval structures, nuclear system cooling, biomedical, and drug reduction. The skin‐friction increases but Nusselt number decreases over the stretching sheet whereas the opposite effect shows over shrinking sheet for the both solution with the increasing velocity slip parameter. On the other hand, The Nusselt number decreases over the shrinking or stretching sheet for both solutions with the increasing in the thermal slip parameter. The skin friction increases over shrinking sheet but decreases over stretching sheet for the first solution with increasing silver volume fraction parameter and porosity parameter (). Enhancing magnetic field parameter leads to the skin friction increases over the shrinking sheet but decreases over stretching sheet but Nusselt number shows opposite trend. The Nusselt number decreases over shrinking sheet but increases over stretching sheet for the first solution with increasing porosity parameter (). The Nusselt number decreases over shrinking or stretching sheet as the increases heat generation () and variable thermal conductivity parameter () but Nusselt number shows opposite trend as the increases radiative parameter ().

Chemically reacted blood Cu O nanofluid flow through a non-Darcy porous media with radially varying viscosity

The study investigates the flow of a Newtonian Cu O nanofluid through a non-Darcy porous medium with radially varying viscosity, which is crucial for various industries such as pharmaceuticals, chemicals, nuclear, solar, and solar technologies. The peristaltic motion of the nanofluid is studied with thermal radiation and chemical reaction effects, and the viscosity varies with both radius and axial coordinates. The study assumes low Reynolds and long wavelength assumptions and uses the homotopy perturbation technique to obtain a semi-analytical solution of velocity, temperature, nanoparticle concentration, and skin friction. The results show that axial velocity increases with the increase of slip velocity and viscosity parameters, while wave amplitude and chemical reaction parameters increase while nanoparticle concentration decreases. High viscosity parameters allow fluid nanoparticles to gain more active energy and move more freely, which is the main idea behind crude oil refinement. This physical modeling is essential for physiological flows, such as stomach juice flow during endoscope insertion.

Theoretical analysis of effect of MHD, couple stress and slip velocity on squeeze film lubrication characteristics of Long Cylinder and Infinite Rough Plate

The current research examines how a long cylinder, and an infinitely flat surface are affected by surface roughness, MHD, couple stress, and slip velocity using the stochastic theory of hydrodynamic lubrication of rough surfaces as developed by Christensen. Squeeze film time, load carrying capacity, and pressure are calculated using a derived mathematical form of Reynolds' modified equation that accounts for surface roughness and coupling stress. The amount of time needed to squeeze a film under a specific pressure and load can be determined using an analytical method called Reynolds' equation. The lubrication characteristics are graphically represented for various parameters. When a magnetic field occurs and the slip velocity increases, the pressure of the squeeze film, its capacity to carry loads, and the time it takes are all significantly increased. The lubricating properties caused a decrease or increase in the values of the longitudinal (transverse) roughness parameter.

Unveiling the Behavior of MHD Mixed Convective Nanofluid Slip Flow over a Moving Vertical Plate with Radiation, Chemical Reaction, and Viscous Dissipation

The effects of chemical reactions on heat and mass transfer with radiation are extremely important in hydrometallurgical industries and chemical technology, such as polymer synthesis and food processing. A mathematical model for a viscous, incompressible, mixed convective, and MHD slip flow over a moving vertical plate is proposed in the present research. On account of physical relevance, the combined effect of radiation and chemical reaction on MHD nanofluid is studied. Using the similarity transformation method, the governing equations are converted into a system of ODEs. The transformed equations are then numerically solved by the Galerkin finite element method (GFEM). To analyse the characteristics of flow and heat transfer, a number of parameters are examined, including the slip, magnetic, radiation, and chemical reaction parameters, as well as the Schmidt, Grashof, Eckert, and Prandtl numbers. The coefficient of skin friction, Nusselt number, and Sherwood numbers for selected parameters are numerically presented. Graphs are used to determine and study the effects of magnetic fields, slip conditions, radiation, and chemical reactions on the temperature, concentration, and velocity profiles of nanofluids. This study shows that the presence of chemical reactions and radiation causes an increase in the velocity profile and temperature profile, respectively. Additionally, it is discovered that the temperature profile grows with increasing velocity slip, and concentration increases with increasing thermal slip. The current work has broad applications in various fields and can lead to the development of more efficient and effective systems in different industries, such as heat exchangers, energy production, environmental engineering, and biomedical engineering.

Exploring the Influence of Induced Magnetic Fields and Double-Diffusive Convection on Carreau Nanofluid Flow through Diverse Geometries: A Comparative Study Using Numerical and ANN Approaches

This current investigation aims to explore the significance of induced magnetic fields and double-diffusive convection in the radiative flow of Carreau nanofluid through three distinct geometries. To simplify the fluid transport equations, appropriate self-similarity variables were employed, converting them into ordinary differential equations. These equations were subsequently solved using the Runge–Kutta–Fehlberg (RKF) method. Through graphical representations like graphs and tables, the study demonstrates how various dynamic factors influence the fluid’s transport characteristics. Additionally, the artificial neural network (ANN) approach is considered an alternative method to handle fluid flow issues, significantly reducing processing time. In this study, a novel intelligent numerical computing approach was adopted, implementing a Levenberg–Marquardt algorithm-based MLP feed-forward back-propagation ANN. Data collection was conducted to evaluate, validate, and guide the artificial neural network model. Throughout all the investigated geometries, both velocity and induced magnetic profiles exhibit a declining trend for higher values of the magnetic parameter. An increase in the Dufour number corresponds to a rise in the nanofluid temperature. The concentration of nanofluid increases with higher values of the Soret number. Similarly, the nanofluid velocity increases with higher velocity slip parameter values, while the fluid temperature exhibits opposite behavior, decreasing with increasing velocity slip parameter values.

Drag-reduction effect of staggered superhydrophobic surfaces in a turbulent channel flow

In this study, direct numerical simulations of turbulent channel flow with superhydrophobic surfaces (SHS) were performed. The staggered SHS pattern alternating the free-shear and no-slip regions was designed to be robust to variations in the main flow direction. A constant-pressure gradient condition was imposed, and the Reynolds number was set to Reτ=180 and 395. The bulk mean velocity in the SHS case increased compared with the no-slip case, and the effect was enhanced by increasing the size of the free-shear region lb+. The main reason for the increase in bulk mean velocity was the increase in slip velocity (or slip length). If the size of the free-shear region was small, the drag-reduction rate was found to be proportional to the slip velocity. However, the turbulent contribution to the bulk mean velocity remained almost unchanged in the no-slip case owing to the negative coherent component of the Reynolds shear stress.

Rate and State Simulation of Two Experiments With Pore Fluid Injection Under Creep Conditions

AbstractThis study uses a spring‐block model and rate and state friction to simulate experiments conducted in a double direct‐shear apparatus on carbonate fault gouge (Scuderi et al., 2017, https://doi.org/10.1016/j.epsl.2017.08.009) and on shale bearing rock (Scuderi & Collettini, 2018, https://doi.org/10.1029/2018jb016084). Both sets of experiments used the same loading protocol and injected pore fluid under creep conditions. When velocity strengthening rate and state friction is used to simulate the experiments on the carbonate fault gouge the results agree well with the observed onset of tertiary creep in the experiment. Thus, the simulation reinforces the observation that pore fluid injection can induce rapid slip even when the friction relation is velocity strengthening. The rate and state framework provides an interpretation alternative to the standard one of the Mohr's circle moving to the left as pressure increases. In the rate and state framework, the friction coefficient must increase with pore pressure increase. The shale has a low nominal friction coefficient (0.28) and is much more velocity strengthening than the carbonate. The simulation agrees with the observations that increases in pore pressure induce an increase in slip velocity but the magnitudes reach only about 100 microns/s by the end of the experiment. The simulation for the shale also agrees well with the magnitude of the observed displacement at the end of the experiment but observed displacement is increasing much more rapidly the calculated. Although the calculations agree well with features of the observations near failure, the overall curves of displacement and velocity are significantly different.

Analysis of biological mechanism of blood flow containing nanoparticles through an arterial stenosis

ABSTRACT This article aims to discuss the flow of nanoparticles in the blood through a stenosed artery in the presence of a magnetic field and periodic body acceleration. The overlapping shape of stenosis is chosen to show the impact of blood flow. The Bingham plastic fluid model is utilized to capture the non-Newtonian behavior of blood in the stenosed artery under diseased conditions. The resultant equations are solved analytically using the regular perturbation method. The impact of various emerging parameters on velocity, flow rate, effective viscosity, and wall shear stress are presented through graphs and discussed in detail. It is noticed that liquid velocity and flow rate increase whereas effective viscosity decreases with an increase in slip velocity and Womersley’s frequency parameter. It is also noted that liquid velocity and flow rate are decreased by enhancing the Lorentz force. The increase in body acceleration enhances fluid velocity.

Inferring forms of glacier slip laws from estimates of ice-bed separation during glacier slip

AbstractSea-level projections depend sensitively on the parameterization used for basal slip in glacier flow models. During slip over rock-beds, ice-bed separation increases with slip velocity and basal water pressure. We present a method for using these variables and measured bed topography to estimate the average bed slope in contact with ice, ${\bar m}$. Three-dimensional numerical modeling of slip over small areas of former beds has shown that changes in ${\bar m}$ with increasing slip velocity and water pressure mimic changes in basal drag. Computed values of ${\bar m}$ can thus provide the form of the slip law that relates drag to velocity and water pressure, avoiding computationally expensive numerical modeling. The method is applied to 618 sections from four former glacier beds. Results generally show an increase in ${\bar m}$, and hence inferred basal drag, with slip velocity up to a limiting value, consistent with a regularized Coulomb slip law.

Natural bio-convective flow of Maxwell nanofluid over an exponentially stretching surface with slip effect and convective boundary condition

The under-consideration article mainly focuses an unsteady three-dimensional Maxwell bio-convective nanomaterial liquid flow towards an exponentially expanding surface with the influence of chemical reaction slip condition. The feature of heat transport is achieving in the existenceof convective boundary condition and variable thermal conductivity. With the help of similarity variables, the flow form of equations is turned into a nonlinear form of coupled ODEs. The numerical solutions are calculated by adopting bvp4c function of MATLAB. Impact of distinct characteristics on the temperature, velocity microorganism and concentration field is graphically evaluated. Moreover, physical quantities are observed via graphs and tabulated data in details. It has been seen by the observation that the involvement of unsteadiness parameter restricts the change of laminar to turbulent flow. Further, for increasing velocity slip parameter velocity component in both directions shows lessening behavior. The Nusselt number exhibits diminishing behavior for larger values of Deborah number, and it shows the opposite behavior for larger values of convective parameter.

MHD Pulsatile Blood Flow Through an Inclined Stenosed Artery with Body Acceleration and Slip Effects

In this work, the combined effect of slip velocity, pulsatility of the blood flow and body acceleration effect on Newtonian unsteady blood flow past an artery with stenosis and permeable wall is theoretically studied with results discussed. The magnetic field is applied to the stenosed artery with permeable walls which is inclined at a varying angle with the fluid considered to be electrically conducting non-Newtonian elastic-viscous fluid. The momentum equation was transformed from dimensional form to dimensionless form with the Frobenius power series method used to solve the axially symmetric differential momentum equation with suitable boundary conditions. For clarity of the applicability of the study, results was shown graphically with behavior of the blood flow through the artery with stenosis shown for the velocity in the axial direction, blood acceleration, wall shear stress and volumetric flow rate. Results showed that, an increase in the body acceleration Go and pulsatile pressure Pl causes an increase in the blood flow, blood acceleration, shear stress at the artery walls and volumetric flow rate. The increase in the magnetic field M causes a decrease in the blood flow velocity, blood acceleration, shear stress at the artery walls and volumetric flow rate. The increase in the artery inclination ϕ results to an increase in the blood flow velocity, wall shear stress and the volumetric flow rate but an irregular behavior in the blood acceleration while the increase in slip velocity h at the wall decreases the velocity and blood acceleration, while the shear stress at the wall increases and the volumetric flow rate decreases.

Frictional Characteristics of Oceanic Transform Faults: Progressive Deformation and Alteration Controls Seismic Style

AbstractOceanic transform faults are inferred to be weak relative to surrounding oceanic crust and primarily slip aseismically. Neither their weakness nor tendency to creep are well‐explained. We test the effects of fault‐rock evolution on oceanic transform fault frictional strength and stability using direct‐shear experiments (at room temperature, 10 MPa normal stress, and fluid‐saturated conditions) on dolerite from the East Pacific Rise and natural fault rocks from the exhumed Southern Troodos Transform, Cyprus. Dolerites and cemented breccias are frictionally strong (μ = 0.52–0.85) and velocity‐weakening (strength decreases with increasing slip velocity, characteristic of earthquakes). In contrast, matrix‐rich chlorite‐bearing fault breccias and gouges are frictionally weak (μ = 0.25–0.48) and velocity‐strengthening (characteristic of stable creep). This transition implies that seismic behavior is controlled by degree of damage and alteration, such that earthquakes can nucleate within relatively intact oceanic crust, whereas fault segments of increased damage and chlorite content tend to slip aseismically.

Multiple slip effects on nanofluid dissipative flow in a converging/diverging channel: A numerical study

AbstractA mathematical model is developed for viscous slip flow and heat transfer in water/Ethylene glycol‐based nanofluids containing metallic oxide nanoparticles, through a converging/diverging channel. We adopt the single‐phase Tiwari–Das model. The governing equations are transformed to a set of similarity differential equations with the help of similarity transformation, before being solved numerically using Maple 20. Validation of the velocity gradient and temperature solutions is achieved with the second‐order implicit finite difference Keller Box method. Further validation is included for the special case of no‐slip nanofluid flow in the absence of viscous heating. The effects of the parameters, namely velocity slip, thermal jump, channel apex angle, Eckert number, Prandtl number, Reynolds number, and nano‐particle volume fraction on velocity, temperature, skin friction, and heat transfer rate are investigated in detail. It is found that with increasing velocity slip, for water‐TiO2 and ethylene glycol‐TiO2 nanofluids, the channel bulk flow is decelerated whilst with greater solid (nanoparticle) volume and in the presence of momentum slip, the flow is also retarded. With the increasing semivertex angle, the channel flow is generally accelerated. An increase in divergent semiangle leads to decelerate the flow from the centerline for the core flow region, whereas near and at the channel wall, it results in a weak acceleration. Higher temperatures are achieved with greater thermal slip values, for both water‐TiO2 and ethylene glycol‐TiO2 nanofluids, whereas for greater nanoparticle volume fraction, temperatures are weakly decreased for water‐TiO2 whereas a more significant decrease is observed for ethylene glycol‐TiO2 nanofluid. With a greater diverging channel angle, a substantial decrease in temperatures is caused by greater Reynolds numbers, and the reverse effect is computed for the converging channel. The novelty of the current work is that it extends previous studies to include multiple slip effects and viscous heating (Eckert number effects), which are shown to exert a significant influence on heat and momentum transfer characteristics. The study is relevant to certain pharmaco‐dynamics devices (drug delivery), next‐generation 3D nanotechnological printers, and also nano‐cooling systems in energy engineering where laminar flows in diverging/converging channels arise

Significance of non-similar modeling in the entropy analysis of chemically reactive magnetized flow of nanofluid subjected to thermal radiations and melting heat condition

Melting is a physical development that is associated with phase transition of materials (PCM). Melting thermal transport has fascinated researchers because of its immense usage in technological processes. In this paper, a non-similar mathematical model is established for melting aspects in the chemically reactive, radiative flow of magnetized nanofluid. The fluid flow over a vertically heated surface is triggered as a result of its linear stretching and by means of buoyancy forces. The considered setup deals with the melting thermal transport and velocity slip at the surface. The linear buoyancy in the framework of concentration and temperature is accounted for in the x-momentum equation. Frictional heating in view of viscous dissipation is convincing because of large surface velocity. An effective Buongiorno model is employed in the energy and concentration expressions with chemical reaction and magnetic and viscous dissipations. The dimensionless non-similar structure is numerically simulated by adopting local non-similarity via bvp4c. The repercussion of vital numbers on flow, entropy generation, and thermal and mass transport is discussed through graphs and tables. The graphical transport analysis suggests that the increase in buoyancy reduces the fluid flow; however, the implication of increasing velocity slip and magnetic and buoyancy ratio numbers is to enhance the fluid flow. Furthermore, the increasing radiative parameter increases the temperature in the thermal boundary layer. Concentration boundary layer analysis suggests that the impact of the increase in the Schmidt number increases the concentration and the increase in the chemical reaction decreases the concentration. The range of stable solutions for important numbers is obtained. Furthermore, the validity of results is demonstrated by comparing with the existing literature. Comparison between non-similar and local similar approximations has been made. It is finally accomplished that non-similar analysis, contrary to local similar models, is more generic and authentic in convection thermal transport analysis in the existence of buoyancy and viscous dissipation.

A slip law for hard-bedded glaciers derived from observed bed topography.

Ice-sheet responses to climate warming and associated sea-level rise depend sensitively on the form of the slip law that relates drag at the beds of glaciers to their slip velocity and basal water pressure. Process-based models of glacier slip over idealized, hard (rigid) beds with water-filled cavities yield slip laws in which drag decreases with increasing slip velocity or water pressure (rate-weakening drag). We present results of a process-based, three-dimensional model of glacier slip applied to measured bed topographies. We find that consideration of actual glacier beds eliminates or makes insignificant rate-weakening drag, thereby uniting process-based models of slip with some ice-sheet model parameterizations. Computed slip laws have the same form as those indicated by experiments with ice dragged over deformable till, the other common bed condition. Thus, these results may point to a universal slip law that would simplify and improve estimations of glacier discharges to the oceans.