Cox's Theory Research Articles

Mesoscopic simulation of liquid bridge spreading under squeezing of parallel plates

The spreading behavior of a droplet under squeezing between parallel plates is seen in the adhesion of microelectronic components and the lubrication of human joints, which is a process involving complex micro-scale flow behaviors, such as three-phase contact line movement. In this study, a many-body dissipative particle dynamics method is employed to account for this process. The method has been first validated by comparing with Cox's theory of contact lines. Two stages have been identified during the process of squeezing: a contact line retraction state and a symmetrical spreading state, which can also be reflected by the change of the system's surface energy. The combined effects of the squeezing velocity and plate's wettability on the appearance of the first stage have been investigated, showing that a large enough squeezing velocity and a hydrophobic enough substrate will lead to no contraction of the contact line. This study provides a valuable tool to explore the possibility of controlling the droplet squeezing behavior and, thus, is helpful for optimizing the adhesion and lubrication process.

Quantifying the dynamic spreading of a molten sand droplet using multiphase mesoscopic simulations

Molten sand droplets deposited on gas turbine engine components cause severe damage. To better understand the deposition process, we study the wetting dynamics of a highly viscous molten sand droplet on a smooth substrate. A universal contact line spreading, independent of the droplet size, is observed with the characteristic inertial and viscous spreading regimes. It is also shown that the dynamic contact angle is in excellent agreement with Cox's theory.

Transition in a numerical model of contact line dynamics and forced dewetting

We investigate the transition to a Landau–Levich–Derjaguin film in forced dewetting using a quadtree adaptive solution to the Navier–Stokes equations with surface tension. We use a discretization of the capillary forces near the receding contact line that yields an equilibrium for a specified contact angle θΔ, called the numerical contact angle. Despite the well-known contact line singularity, dynamic simulations can proceed without any explicit additional numerical procedure. We investigate angles from 15∘ to 110∘ and capillary numbers from 0.00085 to 0.2 where the mesh size Δ is varied in the range of 0.0035 to 0.06 of the capillary length lc. To interpret the results, we use Cox's theory which involves a microscopic distance rm and a microscopic angle θe. In the numerical case, the equivalent of θe is the angle θΔ and we find that Cox's theory also applies. We introduce the scaling factor or gauge function ϕ so that rm=Δ/ϕ and estimate this gauge function by comparing our numerics to Cox's theory. The comparison provides a direct assessment of the agreement of the numerics with Cox's theory and reveals a critical feature of the numerical treatment of contact line dynamics: agreement is poor at small angles while it is better at large angles. This scaling factor is shown to depend only on θΔ and the viscosity ratio q. In the case of small θe, we use the prediction by Eggers [Phys. Rev. Lett. 93 (2004) 094502] of the critical capillary number for the Landau–Levich–Derjaguin forced dewetting transition. We generalize this prediction to large θe and arbitrary q and express the critical capillary number as a function of θe and rm. This implies also a prediction of the critical capillary number for the numerical case as a function of θΔ and ϕ. The theory involves a logarithmically small parameter ϵ=1/ln⁡(lc/rm) and is thus of moderate accuracy. The numerical results are however in approximate agreement in the general case, while good agreement is reached in the small θΔ and q case. An analogy can be drawn between the numerical contact angle condition and a regularization of the Navier–Stokes equation by a partial Navier-slip model. The analogy leads to a value for the numerical length scale rm proportional to the slip length. Thus the microscopic length found in the simulations is a kind of numerical slip length in the vicinity of the contact line. The knowledge of this microscopic length scale and the associated gauge function can be used to realize grid-independent simulations that could be matched to microscopic physics in the region of validity of Cox's theory.

Dynamic bottleneck elimination in mattress manufacturing line using theory of constraints.

There is a tough competition in the furniture sector like other sectors. Along with the varying product range, production system should also be renewed on a regular basis and the production costs should be kept under control. In this study, spring mattress manufacturing line of a furniture manufacturing company is analyzed. The company wants to increase its production output with new investments. The objective is to find the bottlenecks in production line in order to balance the semi-finished material flow. These bottlenecks are investigated and several different scenarios are tested to improve the current manufacturing system. The problem with a main theme based on the elimination of the bottleneck is solved using Goldratt and Cox’s theory of constraints with a simulation based heuristic method. Near optimal alternatives are determined by system models built in Arena 13.5 simulation software. Results show that approximately 46 % capacity enhancements with 2 buffer stocks have increased average production by 88.8 %.

A renewal model for the emergence of anomalous solute crowding in liposomes.

A fundamental evolutionary step in the onset of living cells is thought to be the spontaneous formation of lipid vesicles (liposomes) in the pre-biotic mixture. Even though it is well known that hydrophobic forces drive spontaneous liposome formation in aqueous solutions, how the components of the earliest biochemical pathways were trapped and concentrated in the forming vesicles is an issue that still needs to be clarified. In recent years, some authors carried out a set of experiments where a unexpectedly high amount of solutes were found in a small number of liposomes, spontaneously formed in aqueous solution. A great number of empty liposomes were found in the same experiments and the global observed behavior was that of a distribution of solute particles into liposomes in agreement with a inverse power-law function rather than with the expected Poisson distribution. The chemical and physical mechanisms leading to the observed "anomalous solute crowding" are still unclear, but the non-Poisson power-law behavior is associated with some cooperative behavior with strong non-linear interactions in the biochemical processes occurring in the solution. For tackling this issue we propose a model grounding on the Cox's theory of renewal point processes, which many authors consider to play a central role in the description of complex cooperative systems. Starting from two very basic hypotheses and the renewal assumption, we derive a model reproducing the behavior outlined above. In particular, we show that the assumption of a "cooperative" interaction between the solute molecules and the forming liposomes is sufficient for the emergence of the observed power-law behavior. Even though our approach does not provide experimental evidences of the chemical and physical bases of the solute crowding, it suggests promising directions for experimental research and it also provide a first theoretical prediction that could possibly be tested in future experimental investigations.

Candidate success in multi-member districts: an investigation of Duverger and Cox

Cox generalizes Duverger's Law to multi-member district elections. He posits that the number of viable candidates in any individual district is limited by an upper bound of M+1 (where M is equal to the district magnitude). I extend Cox's theory to elections held under the single transferable vote in Irish and Tasmanian elections. I do so by examining the re-nomination, vote share and success rates of candidates as compared to each candidate's order of finish in the previous election. The results generally support Cox's hypothesized M+1 boundary.

Effects of fiber length and orientation on elasticity of fiber-reinforced plywood

Short carbon fibers, a reinforced material in wood veneer composites, were used to investigate the effects of fiber length and orientation of fibers on the elasticity of plywood. The technical feasibility, elasticity, and strength of the reinforced plywood with short carbon fiber were evaluated. In a short fiber reinforcement system, the fiber length does not directly influence the reinforcement in Cox's theory when the fiber length exceeded a certain length. When the length of short carbon fiber is beyond 3 mm, the high reinforced result was obtained in the experiment. However, if fiber length was too long, the reinforced result was less owing to the bridge between fibers and the increase of holes. The optimum fiber length must be considered. The orientation of fibers has a strong influence on the reinforcement. Unidirectional, perpendicular, and random orientation displayed different influence on the elasticity. Experimental results were discussed with Cox's method. Reinforced plywood with short carbon fibers in random orientation has a higher shear modulus and bending strength than the controls, in addition to other mechanical properties.

Deduction of an improved formula for coincidence counting and its experimental verification

An improved accurate coincidence correction formula has been deduced on the basis of Cox's theory considering the complex situations of differences in pulse shaping width as well as a relative delay existing between the two channels. The correctness has been examined by experiments.

The Influence of the Adhesion Bond between Matrix and Filler on the Tensile Strength of Particulate-Filled Polymers

A theoretical model for the prediction of tensile strengths of particulate- filled polymers is proposed. According to this model each particle is divided into an in finite number of coaxial cylinders and by applying Cox's theory the mean stress developed in each section of the particle may be calculated. Further a modified rule of mixtures was applied where the degree of adhesion between matrix material and filler particles as well as the degradation of the mechanical behaviour of the matrix due to the existence of the particles is taken into account. Therefore, when tensile strengths of polymer and particles are known, tensile strength of the filled polymer corresponding to specific values of degree of adhesion as well as of the matrix degradation can be estimated by the model. Finally, the model was successfully applied to a series of published data.

The aerodynamic behaviour of cylindrical and spheroidal particles when settling under gravity

A Timbrell Aerosol Spectrometer was used to size-select several types of airborne polydisperse particles: approximately unit density spheres, ‘Fiberfrax’ glass fibres and oblate spheroid shaped Arthrinium fungus spores by virtue of their settling velocities due to gravity. The spores had a much narrower size distribution than the others. The spheres were used as the basic calibrating material. The aerodynamic behaviour of the glass fibres under viscous conditions (1.2 × 10 −2 ≲ V g ≲ 0.75 cm s −1), was shown by experiment to be best described by representing the fibres either as straight cylindrical particles or prolate spheroids sedimenting in a direction perpendicular to their polar (major) axes. The aerodynamic diameter, φ a, of the cylinders is computed by means of Cox's theory, and that of the prolate spheroids by means of either a volume-corrected or a weight-corrected variation of the theory developed by Oseen. In the range 1.2 × 10 −2 ≲ V g ≲ 0.2 cm s −1 (2 ≲ φ a ≲ 8 μm) any one of these theories, as well as the orthodox Oseen theory, was found suitable. The aerodynamic behaviour of the Arthrinium spores tested under the same conditions was shown to be the same as that of oblate spheroids sedimenting in directions parallel to their polar (minor) axes; with φ a derived through the orthodox Oseen theory.

Class, race and ethnicity: A critique of Cox's theory

(1980). Class, race and ethnicity: A critique of Cox's theory. Ethnic and Racial Studies: Vol. 3, No. 2, pp. 169-187.