Sticky Limit Research Articles

An apparatus for the plastic limit and workability of soils

An apparatus is described that replicates Atterberg's rolling technique for the determination of the plastic limit of soils by detecting the brittle–plastic transition. There is much less operator interference, and judgement of the crumbling condition is practically eliminated. In addition, by means of a loading device, stresses are applied during rolling, the diameter is measured for each rolling traverse, and plots of stress against strain are derived. The workability or toughness of the soil is determined as the product of stress and strain, or work/unit volume, for soil threads prepared at moisture contents ranging from near the sticky limit through the workable plastic region to the brittle state. From the results an abrupt brittle–plastic transition is found, allowing the plastic limit to be defined as the moisture content at this transition. Good relationships between toughness and moisture content are obtained, from which the maximum toughness Tmax at the plastic limit can be derived together with other potentially useful properties such as the toughness limit wT, the moisture content at zero toughness, the toughness coefficients TC, the gradients of the relationships, the toughness index, the workability index and the stiffness transition.

Dry and wet granular shock waves

The formation of a shock wave in one-dimensional granular gases is considered, for both the dry and the wet cases, and the results are compared with the analytical shock wave solution in a sticky gas. Numerical simulations show that the behavior of the shock wave in both cases tends asymptotically to the sticky limit. In the inelastic gas (dry case) there is a very close correspondence to the sticky gas, with one big cluster growing in the center of the shock wave, and a step-like stationary velocity profile. In the wet case, the shock wave has a nonzero width which is marked by two symmetric heavy clusters performing breathing oscillations with slowly increasing amplitude. All three models have the same asymptotic energy dissipation law, which is important in the context of the free cooling scenario. For the early stage of the shock formation and asymptotic oscillations we provide analytical results as well.

Influence of Dimensions of UHMW-PE Protuberances on Sliding Resistance and Normal Adhesion of Bangkok Clay Soil to Biomimetic Plates

A number of investigations into application of polymers for macro-morphological modification of tool surface have been carried out. These researches, with extensive stress on convex or domed protuberations as one of the widely used construction units, have tried to harness benefits from using polymers in agriculture. Ultra high molecular weight polyethylene (UHMW-PE) has proved an emerging polymer in its application to reduce soil adhesion. This research was conducted to study the effect of shape (flat, semi-spherical, semi-oblate, semi short-prolate and semi long-prolate) and dimensions (base diameter and dome height) on sliding resistance and normal adhesion of biomimetic plates. To incorporate both shape and size, a dimensionless ratio of height to diameter (HDR) was introduced to characterize the effect of construction unit's physique. Experiments were conducted in Bangkok clay soil with dry (19.8% d.b.), sticky (36.9% d.b.) and flooded (60.1% d.b.) soil conditions respectively. Soil at sticky limit exhibited the highest sliding resistance (77.8 N) and normal adhesion (3 kPa to 7 kPa), whereas these values were 61.7 N and <0.2 kPa in dry, and 53.7 N and 0.5 kPa to 1.5 kPa in flooded soil conditions. Protuberances with HDR ≤ 0.5 lowered sliding resistance by 10%–30% and the same reduced normal adhesion by 10%–60%. The amount of reduction in both sliding resistance and normal adhesion was higher in flooded soil. Lighter normal loads obviously produced lesser resistance and adhesion.

Sewage Sludge to Landfill: Some Pertinent Engineering Properties

More stringent controls on the quality of wastewater discharges have given rise to increasing volumes of sewage sludge for disposal, principally to land, using either land-spreading or sludge-to-landfill operations. Current sludge-to-landfill methods generally involve mixing the concentrated sludge with other solid waste in municipal landfills. However, stricter waste disposal legislation and higher landfill taxes are forcing the water industry to look for more efficient disposal strategies. Landfill operators are also increasingly reluctant to accept sludge material in the slurry state because of construction difficulties and the potential for instability of the landfill slopes. The engineering and drying properties of a municipal sewage sludge are presented and applied, in particular, to the design, construction, and performance of sewage sludge monofills. Sludge handling and landfill construction are most effectively conducted within the water content range of 85% water content, the optimum water content for standard proctor compaction, and 95% water content, the sticky limit of the sludge material. Standard proctor compaction of the sludge within this water content range also achieves the maximum dry density of ∼0.56 tonne/m3, which maximizes the storage capacity and, hence, the operational life of the landfill site. Undrained shear strength-water content data (pertinent to the stability of the landfill body during construction) and effective stress-strength parameters, which take into account the landfill age and the effects of ongoing sludge digestion, are presented. Landfill subsidence, which occurs principally because of creep and decomposition of the solid organic particles, is significant and continues indefinitely but at progressively slower rates.

Pathologies in the sticky limit of hard sphere Yukawa models for colloidal fluids: a possible correction

A known ‘sticky hard sphere’ model, starting from a hard sphere Yukawa potential and taking the limit of infinite amplitude and vanishing range with their product remaining constant, is shown to be ill-defined. This is because its Hamiltonian (which we call SHS2) leads to an exact second virial coefficient which diverges, unlike that of Baxter's original model (SHS1). This deficiency has never been observed so far, since the linearization implicit in the ‘mean spherical approximation’ (MSA), within which the model is analytically solvable, partly masks such a pathology. To overcome this drawback and retain some useful features of SHS2, we propose both a new model (SHS3) and a new closure (‘modified MSA’), whose combination yields an analytical solution formally identical with the SHS2-MSA solution. This mapping allows the recovery of many results derived from SHS2, after a re-interpretation within a correct framework. Possible developments are indicated.

Anomalous clustering and equation-of-state behavior as the adhesive-disk limit is approached

The structure of clusters of two-dimensional particles interacting with a hard-core square-well pair potential is analyzed in order to demonstrate how thermodynamic stability ceases to exist when the system approaches the Baxter’s sticky limit. It is shown that the dependence of the sizes and the radii of gyration of the clusters of two-dimensional sticky disks behave qualitatively differently when the number of particles in the cluster exceeds 6. Cluster sizes with n&amp;lt;7 exhibit smooth transition when the Baxter limit is approached while clusters with seven more disks experience an anomalous transition towards a state of maximal connectedness. The configuration integrals that are needed to describe clusters of seven particles are then used to demonstrate the way in which their contribution to the virial expansion of the equation of state causes it to become pathological. From the results, it is concluded that the system will show the anomalous thermodynamic behavior associated with the approach to instability only for well widths of the order of 10−4 of the hard core diameter or less. The status of using approximate adhesive-particle results as approximate square-well-particle results is then summarized. It is pointed out that there is a fundamental defect in all currently available methods of approximating square-well liquid-gas phase separation using adhesive-sphere results.

The freezing transition as a symmetry breaking phenomenon

A model for the freezing transition where a crystalline seed induces symmetry breakage is discussed. The seed is an array of sticky sites and we have analyzed the case of vanishing sticky potential. We consider a two-dimensional lattice and show that, within the framework of the Yang and Lee theory of phase transitions, the excess free energy of the system is a many valued function of the fugacity. In our simple model one of the branches corresponds to the liquid phase and the other to the solid state. We take first the infinite size limit and then the vanishing sticky limit. We have performed Monte Carlo simulations that indicate clearly that these limits do not commute.

An analytical model of water with sticky spheres of tetrahedral symmetry

A simple potential for the water intermolecular potential, consisting of hard spheres with a point dipole and a narrow attractive potential well with the symmetry of a tetrahedral octupole was proposed sometime ago and studied by Monte Carlo methods. The structure of this very simple model agrees surprisingly well with experimental pair correlation functions. In the sticky potential limit of an infinitely narrow and deep tetrahedral attractive well, this model is solved explicitly in terms of the inverses of three by three matrices. We give full solution of a simplified version without dipole-octupole coupling. We discuss the g oo(r) and compare it with the experimental result obtained from neutron diffraction. The agreement here is very encouraging.

Diverging seventh virial coefficient of sticky discs

The seventh virial coefficient of a two-dimensional system of particles interacting with a hard-core square-well pair potential is studied. The Ree-Hoover type cluster integrals were examined and it was found that a graph in the form of a hexagonal wheel with all the bonds of the attractive square-well type does not allow Baxter's ‘sticky sphere’ limit to be achieved. The value of that particular cluster integral was calculated. It was shown that when approaching the sticky limit the cluster integral corresponding to the hexagonal wheel diverges linearly with the height of the peak in the Mayer f function at the location of the potential square-well. As a consequence, the seventh virial coefficient of the sticky disc system does not have a finite value.