Quantitative measurement of sliding friction dynamics at mesoscopic scales: The lateral force apparatus

We describe an apparatus designed to quantitatively measure friction dynamics at the mesoscopic scale. This lateral force apparatus, LFA, uses double parallel leaf springs in leaf-spring units as force transducers and two focus error detection optical heads, optical heads, to measure deflections. The design of the leaf-spring units is new. Normal spring constants are in the range of 20–4000 N/m, and lateral spring constants are 7–1000 N/m. The optical heads combine a 10 nm sensitivity with a useful range of about 100 µm. The proven range of normal forces is 400 nN–150 mN. The leaf-spring units transduce friction and normal forces independently. Absolute values of normal and friction forces are calibrated. Typical errors are less than 10%. The calibration is partly in situ, for the sensitivity of the optical heads, and partly ex situ for the normal and lateral spring constants of the leaf-spring units. There is minimal coupling between the deflection measurements in the lateral and normal directions. This coupling is also calibrated in situ. It is typically 1% and can be as low as 0.25%. This means that the displacements of the tip can be measured accurately in the sliding direction and normal to the surface. Together, these characteristics make the LFA, well suited for quantitative study of friction dynamics at mesoscopic scales. Furthermore the design of the leaf-spring unit allows exchange of tips which may be fabricated (e.g., etched) from wire material (d0.4 mm) and can have customized shapes, e.g., polished flat squares. The ability of the LFA to study friction dynamics is briefly illustrated by results of stick-slip measurements on soft polymer surfaces

Factorization of the Universal R-matrix for Uq(sl^2)U_q(\hat{sl}_2)

The factorization of the universal R-matrix corresponding to so called Drinfeld Hopf structure is described on the example of quantum affine algebra $U_q(\hat{sl}_2)$. As a result of factorization procedure we deduce certain differential equations on the factors of the universal ${\cal R}$-matrix, which allow to construct uniquely these factors in the integral form.Comment: 28 pages, LaTeX 2.09 using amssym.def and amssym.te

Time-Resolved Studies of Stick-Slip Friction in Sheared Granular Layers

Sensitive and fast force measurements are performed on sheared granular layers undergoing stick-slip motion, along with simultaneous imaging. A full study has been done for spherical particles with a +-20% size distribution. Stick-slip motion due to repetitive fluidization of the layer occurs for low driving velocities. Between major slip events, slight creep occurs that is variable from one event to the next. The effects of changing the stiffness k and velocity V of the driving system are studied in detail. The stick-slip motion is almost periodic for spherical particles over a wide range of parameters, but becomes irregular when k is large and V is relatively small. At larger V, the motion becomes smoother and is affected by the inertia of the upper plate bounding the layer. Measurements of the period T and amplitude A of the relative motion are presented as a function of V. At a critical value Vc, a transition to continuous sliding motion occurs that is discontinuous for k not too large. The time dependence of the instantaneous velocity of the upper plate and the frictional force produced by the granular layer are determined within individual slipping events. The force is a multi-valued function of the instantaneous velocity, with pronounced hysteresis and a sudden drop prior to resticking. Measurements of vertical displacement reveal a small dilation of the material (about one tenth of the mean particle size in a layer 20 particles deep) associated with each slip event. Finally, optical imaging reveals that localized microscopic rearrangements precede (and follow) each slip event. The behavior of smooth particles is contrasted with that of rough particles.Comment: 20, pages, 17 figures, to appear in Phys. Rev.

Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory

Bethe ansatz equations have been proposed for the asymptotic spectral problem of AdS_4/CFT_3. This proposal assumes integrability, but the previous verification of weak-coupling integrability covered only the su(4) sector of the ABJM gauge theory. Here we derive the complete planar two-loop dilatation generator of N=6 superconformal Chern-Simons theory from osp(6|4) superconformal symmetry. For the osp(4|2) sector, we prove integrability through a Yangian construction. We argue that integrability extends to the full planar two-loop dilatation generator, confirming the applicability of the Bethe equations at weak coupling. Further confirmation follows from an analytic computation of the two-loop twist-one spectrum.Comment: 45 pages, v2: typos in (D.9) fixed, reference added, many small change

Polymer Flow Through Porous Media: Numerical Prediction of the Contribution of Slip to the Apparent Viscosity.

The flow of polymer solutions in porous media is often described using Darcy’s law with an apparent viscosity capturing the observed thinning or thickening effects. While the macroscale form is well accepted, the fundamentals of the pore-scale mechanisms, their link with the apparent viscosity, and their relative influence are still a matter of debate. Besides the complex effects associated with the rheology of the bulk fluid, the flow is also deeply influenced by the mechanisms occurring close to the solid/liquid interface, where polymer molecules can arrange and interact in a complex manner. In this paper, we focus on a repulsive mechanism, where polymer molecules are pushed away from the interface, yielding a so-called depletion layer in the vicinity of the wall. This depletion layer acts as a lubricating film that may be represented by an effective slip boundary condition. Here, our goal is to provide a simple mean to evaluate the contribution of this slip effect to the apparent viscosity. To do so, we solve the pore-scale flow numerically in idealized porous media with a slip length evaluated analytically in a tube. Besides its simplicity, the advantage of our approach is also that it captures relatively well the apparent viscosity obtained from core-flood experiments, using only a limited number of inputs. Therefore, it may be useful in many applications to rapidly estimate the influence of the depletion layer effect over the macroscale flow and its relative contribution compared to other phenomena, such as non-Newtonian effects