Michael J. Adams

Discrete particle-continuum fluid modelling of gas–solid fluidised beds

Abstract This paper describes a fluidised bed model developed from the DEM-based Aston granular dynamics code in which the solid–solid interaction rules are based on theoretical contact mechanics thereby enabling particles to be directly specified by material properties such as friction, elasticity, elasto-plasticity and auto-adhesion. For the gas phase which is treated as a continuum, the equations of motion are evaluated with a Navier–Stokes solver originally developed for a two-fluid model. The coupling of the discrete particulate phase and the continuous fluid phase equations is an important attribute of such Eulerian–Lagrangian models and two forms of the coupling terms have been examined: one employing the pressure gradient force (PGF model) and the other a buoyancy force based on the fluid density (FDB model). Uniform fluidisation simulations for a superficial gas velocity of 2.5 m s −1 and bed pressure drop-superficial gas velocity simulations for gas flows from 0.3 to 3.0 m s −1 have been carried out in a pseudo-2D bed of 2400 4 mm -diameter spherical particles using the two model formulations. The two formulations yielded minor differences in qualitative fluidisation behaviour with a gas flow of 2.5 m s −1 . However, there were significant differences in the pressure drop-superficial gas velocity profiles in the fixed bed regime and corresponding significant differences in the prediction of minimum fluidisation velocity. The PGF model showed the best agreement with pressure drop-superficial gas velocity trends and minimum fluidisation velocities predicted by empirical correlations. Two new methods for determining the minimum fluidisation velocity have been introduced and found to give predictions in good agreement with those obtained from pressure drop-superficial gas velocity profiles and empirical correlations.

Finger pad friction and its role in grip and touch

Many aspects of both grip function and tactile perception depend on complex frictional interactions occurring in the contact zone of the finger pad, which is the subject of the current review. While it is well established that friction plays a crucial role in grip function, its exact contribution for discriminatory touch involving the sliding of a finger pad is more elusive. For texture discrimination, it is clear that vibrotaction plays an important role in the discriminatory mechanisms. Among other factors, friction impacts the nature of the vibrations generated by the relative movement of the fingertip skin against a probed object. Friction also has a major influence on the perceived tactile pleasantness of a surface. The contact mechanics of a finger pad is governed by the fingerprint ridges and the sweat that is exuded from pores located on these ridges. Counterintuitively, the coefficient of friction can increase by an order of magnitude in a period of tens of seconds when in contact with an impermeably smooth surface, such as glass. In contrast, the value will decrease for a porous surface, such as paper. The increase in friction is attributed to an occlusion mechanism and can be described by first-order kinetics. Surprisingly, the sensitivity of the coefficient of friction to the normal load and sliding velocity is comparatively of second order, yet these dependencies provide the main basis of theoretical models which, to-date, largely ignore the time evolution of the frictional dynamics. One well-known effect on taction is the possibility of inducing stick–slip if the friction decreases with increasing sliding velocity. Moreover, the initial slip of a finger pad occurs by the propagation of an annulus of failure from the perimeter of the contact zone and this phenomenon could be important in tactile perception and grip function.

Influence of ultrasonics on upsetting of a model paste

This paper describes a preliminary study of the influence of ultrasonics on the boundary conditions associated with the equipment walls in a soft solid forming operation using Plasticine as a material model. A detailed finite element analysis is described involving the upsetting of a cylindrical specimen between two parallel rigid dies with kinematics and ultrasonic oscillatory loading conditions. A series of squeeze flow experiments has been conducted to validate the finite element models. The oscillation parameters were measured using a 3D laser Doppler vibrometer to complement the measurement of reaction forces.

An experimental study of the nano-scratch behaviour of poly(methyl methacrylate)

An experimental study of poly(methyl methacrylate) (PMMA) is described with the aim of investigating the potential for the formation of wear particles by the interaction of multiple scratches under plastic ploughing conditions. The work was carried out using a nano-indenter fitted with a Berkovich probe. It was found that orthogonally intersecting scratches produced lumpy protuberances which could act as a precursor for wear particles. However, parallel scratches in close proximity resulted in a self-protective mechanism due to the load carrying capacity of the strain hardened pile-up from neighbouring scratches.

The effect of binder viscosity on particle agglomeration in a low shear mixer/agglomerator

Abstract A study is reported of the effects of changing the binder viscosity in rotating drum granulation of a narrow size fraction of an irregularly shaped sand. Silicone fluids, having viscosities in the range 20–500 mPa s, were used as binders. The size distribution of granules was determined by analysis of microscope images and the granule morphology by examination of sections of granules. The compressive strength of granules was also measured. It was found that the viscosity of the binder affected both the rate of size enlargement and the mechanism of size enlargement. The growth rate increased with increase in binder viscosity up to maximum at a viscosity of about 100 mPa s. Enlargement occurred by a layering mechanism. With binders of viscosity greater than 100 mPa s, layering was not observed and growth was found to be by coalescence. Stokes number analyses of the internal deformation on impact and of the adhesion on impact of surface-wet granules were made and found to account, in part, for the effects of changing binder viscosity.

Discrete element simulations of a high-shear mixer

Abstract Particle motion in a vertical-axis mixer was studied using discrete element method (DEM) simulations and positron emission particle tracking experiments. The mixer was fixed with a circular disk rotating in a horizontal plane or a simple paddle. In the DEM simulations, linear springs, dashpots and frictional sliders were used to model the contact mechanics between the particles and the particles and the walls. Quantitative comparisons were made between the numerical calculations and the experimental measurements. The DEM prediction captures the major features of the flow patterns in the mixer when the mixer was fixed with a disk impeller rotating at 100 r.p.m., although the predicted particle velocities are higher than experimental measurements when using physically reasonable simulation parameters (normal stiffness = 1000 and 10000 N/m; coefficient of restitution = 0.9; internal friction coefficient = 0.2, 0.3 and 0.45; wall friction coefficient = 0.2, 0.25 and 0.3). However, when the mixer was fixed with the paddle impeller, the calculated results using physically reasonable simulation parameters were different from the measurements. The calculated particle velocity was as high as 2 m/s, while the averaged particle velocity from measurement was about 0.1 m/s.

Mechanical properties of alginate hydrogels manufactured using external gelation

Alginate hydrogels are commonly used in biomedical applications such as scaffolds for tissue engineering, drug delivery, and as a medium for cell immobilisation. Multivalent cations are often employed to create physical crosslinks between carboxyl and hydroxyl moieties on neighbouring polysaccharide chains, creating hydrogels with a range of mechanical properties. This work describes the manufacture and characterisation of sodium alginate hydrogels using the divalent cations Mg(2+), Ca(2+) and Sr(2+) to promote gelation via non-covalent crosslinks. Gelation time and Young׳s modulus are characterised as a function of cation and alginate concentrations. The implications of this work towards the use of environmental elasticity to control stem cell differentiation are discussed.

On the squeeze flow of a power-law fluid between rigid spheres

The lubrication solution for the squeeze flow of a power-law fluid between two rigid spherical particles has been investigated. It is shown that the radial pressure distribution converges to zero within the gap between the particles for any value of the flow index, n, provided that the gap separation distance is sufficiently small. However, in the case of the viscous force, it is useful to consider that there are two contributions. The first is developed in the inner region of the gap and corresponds to the lubrication limit. The second is due to an integration of the pressure in the adjacent outer region of the gap. The relative contribution to the force in this outer region increases as n decreases and the separation distance increases. In particular, for flow indices in the range n>1/3, the contribution in the outer region is negligible if the separation distance is sufficiently small. For n⪯1/3, this is the dominant term and an accurate prediction of the viscous force is possible only for discrete liquid bridges. Based on “zero” pressure and lubrication criteria for the upper limits of integration, two closed-form solutions have been derived for the viscous force. Both are accurate for n>0.5 and are in close agreement with a previously published asymptotic solution in the range n>0.6. For smaller values of n, the asymptotic solution over-estimates the viscous force and predicts a singularity when n approaches 1/3. The two closed-form solutions show continuous and monotonic behaviour for all values of n. Moreover, the solution satisfying the lubrication limit is valid in the range n<1/3 provided that it is restricted to liquid bridges.

Effects of wetting hysteresis on pendular liquid bridges between rigid spheres

Abstract The effects of wetting hysteresis on the properties and behaviour of pendular liquid bridges between spherical particles have been investigated both experimentally and theoretically. A thermodynamic analysis shows the existence of metastable states that would account for the observed pinning of the three-phase contact line. The most important findings, with respect to the role of capillary interactions in agglomeration processes, are that (a) some of the kinetic energy of “wet” agglomerates may be dissipated during collisions by such hysteresis, (b) the bridge rupture distance is increased and (c) pinning will result in a maximum in the force–separation characteristics.

On the calibration of rectangular atomic force microscope cantilevers modified by particle attachment and lamination

A simple but effective method for estimating the spring constant of commercially available atomic force microscope (AFM) cantilevers is presented, based on estimating the cantilever thickness from knowledge of its length, width, resonant frequency and the presence or absence of an added mass, such as a colloid probe at the cantilever apex, or a thin film of deposited material. The spring constant of the cantilever can then be estimated using standard equations for cantilever beams. The results are compared to spring constant calibration measurements performed using reference cantilevers. Additionally, the effect of the deposition of Cr and Ti thin films onto rectangular Si cantilevers is investigated.