When two solid spheres collide in a liquid, the dynamic collision process is slowed by viscous dissipation and the increased pressure in the interparticle gap as compared with dry collisions. This paper investigates liquid-immersed head-on and oblique collisions, which complements previously investigated particle-on-wall immersed collisions. By defining the normal from the line of centers at contact, the experimental findings support the decomposition of an oblique collision into its normal and tangential components of motion. The normal relative particle motion is characterized by an effective coefficient of restitution and a binary Stokes number with a correlation that follows the particle-wall results. The tangential motion is described by a collision model using a normal coefficient of restitution and a friction coefficient that are modified for the liquid effects.
Based on the dramatic accelerating effect of 2-aminophenol, three ligands derived from 2-aminophenol were developed. Copper-catalyzed coupling reaction of nitrogen-containing nucleophiles with aryl bromides was efficiently carried out under mild conditions using 1,2,3,4-tetrahydro-8-hydroxyquinoline as a novel, simple, and versatile ligand.
We propose a constitutive model to describe the nonlocality, hysteresis, and several flow features of dry granular materials. Taking the well-known inertial number I as a measure of sheared-induced local fluidization, we derive a relaxation model for I according to the evolution of microstructure during avalanche and dissipation processes. The model yields a nonmonotonic flow law for a homogeneous flow, accounting for hysteretic solid-fluid transition and intermittency in quasistatic flows. For an inhomogeneous flow, the model predicts a generalized Bagnold shear stress revealing the interplay of two microscopic nonlocal mechanisms: collisions among correlated structures and the diffusion of fluidization within the structures. In describing a uniform flow down an incline, the model reproduces the hysteretic starting and stopping heights and the Pouliquen flow rule for mean velocity. Moreover, a dimensionless parameter reflecting the nonlocal effect on the flow is discovered, which controls the transition between Bagnold and creeping flow dynamics.
Coumarins are synthesised via Pechmann condensation of phenols with ethyl acetoacetate catalysed by montmorillonite clay in satisfactory yields; the scope and limitation of the method have been investigated.
Experimental evidence shows that the presence of an ambient liquid can greatly modify the collision process between two solid surfaces. Interactions between the solid surfaces and the surrounding liquid result in energy dissipation at the particle level, which leads to solid-liquid mixture rheology deviating from dry granular flow behaviour. The present work investigates how the surrounding liquid modifies the impact and rebound of solid spheres. Existing collision models use elastohydrodynamic lubrication (EHL) theory to address the surface deformation under the developing lubrication pressure, thereby coupling the motion of the liquid and solid. With EHL theory, idealized smooth particles are made to rebound from a lubrication film. Modified EHL models, however, allow particles to rebound from mutual contacts of surface asperities, assuming negligible liquid effects. In this work, a new contact mechanism, 'mixed contact', is formulated, which considers the interplay between the asperities and the interstitial liquid as part of a hybrid rebound scheme. A recovery factor is further proposed to characterize the additional energy loss due to asperity-liquid interactions. The resulting collision model is evaluated through comparisons with experimental data, exhibiting a better performance than the existing models. In addition to the three non-dimensional numbers that result from the EHL analysis-the wet coefficient of restitution, the particle Stokes number and the elasticity parameter-a fourth parameter is introduced to correlate particle impact momentum to the EHL deformation impulse. This generalized collision model covers a wide range of impact conditions and could be employed in numerical codes to simulate the bulk motion of solid particles with non-negligible liquid effects.
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