Increase In Size Ratio Research Articles

Molar isopycnicity in heterogeneous binary mixtures

Heterogeneous mixtures are said to be in molar isopycnic phase equilibrium when – at least – two of the constituent phases exhibit the same molar volume v or, equivalently, the same molar density ρ. Consequently, the molar densities of the constituent phases experiment inversion (or molar barotropy), thus yielding an interesting singularity that may be observed in both super- and sub-critical equilibrium conditions.This contribution aims to theoretically characterize the molar isopycnic behavior observed in binary mixtures. Accordingly, theoretical predictions and strategically guided molecular simulations of the Lennard–Jones fluid are performed to describe the phase behavior and the interfacial properties of mixtures characterized by molar density inversions. Necessary and sufficient conditions are then deduced to detect molar isopycnicity in binary mixtures and, finally, these limiting conditions are related to the various classes of global phase behavior.Our results indicate that molar isopycnicity is present in mixtures exhibiting Types II, III, IV and V behavior. It follows then that molar density inversions seem to be more common than previously believed and that liquid phase immiscibility provides a natural condition for its existence. It is also observed that the phenomenon is controlled by differences in molecular size and critical properties. Particularly, molar isopycnicity becomes observable in ranges where stable fluid phases can be observed as the constituents’ molecular size ratio increases. Differences in critical properties, in turn, promote wider temperature ranges of molar density inversions. The main classes and mechanisms that constraint molar isopycnic equilibria are illustrated and exemplified by considering binary van der Waals mixtures.

DEM simulation of polydisperse systems of particles in a fluidized bed

Numerical simulations based on three-dimensional discrete element model (DEM) are conducted for mono-disperse, binary and ternary systems of particles in a fluidized bed. Fluid drag force acting on each particle depending on its size and relative velocity is assigned. The drag coefficient corresponding to Ergun’s correlation is applied to the system of fluidized bed with particle size ratios of 1:1 for the mono-disperse system, 1:1.2, 1:1.4 and 1:2 for the binary system and 1:1.33:2 for the ternary system by keeping total volume and surface area of the particles constant. Results indicated that a reasonable estimation of drag force based on individual particle diameters as compared to that of the mean diameter of the particles is achieved in the fluid cells. The total translational kinetic energy of the particles is found to increase as the particle size ratio increases, suggesting an enhanced momentum transfer in polydisperse particle systems. Systems with wide particle size distribution exhibited higher particle velocities around bubbles, resulting in faster bubble growth and its subsequent rise through the fluidized bed.

Depletion interactions in two-dimensional colloid–polymer mixtures: molecular dynamicssimulations

The depletion interactions acting between two hard colloids immersed in a bath ofpolymers, in which the interaction potentials include the soft repulsion/attraction, areextensively studied by using the molecular dynamics simulations. The collision frequenciesand collision angle distributions for both incidental and reflection conditions are computedto study the dynamic properties of the colloidal mixtures. The depletion effect induced bythe polymer–polymer and colloid–polymer interactions are investigated as well as thesize ratio of the colloid and polymer. The simulated results show that the strongdepletion interaction between two hard colloids appears for the highly asymmetrichard-disc mixtures. The attractive depletion force at contact becomes deeper and therepulsive barrier becomes wider as the asymmetry in size ratio increases. The strongpolymer–polymer attraction leads to the purely attractive depletion interaction betweentwo hard colloids, whereas the purely repulsive depletion interaction is induced by thestrong colloid–polymer attraction.

Inviscid behaviour of fines-rich pyroclastic flows inferred from experiments on gas–particle mixtures

Abstract Experiments were carried out on granular flows generated by instantaneous release of gas-fluidised, bidisperse mixtures and propagating into a horizontal channel. The mixture consists of fine ( 100 μm) particles of same density, with corresponding grain size ratios of ∼ 2 to 9. Initial fluidisation of the mixture destroys the interparticle frictional contacts, and the flow behaviour then depends on the initial bed packing and on the timescale required to re-establish strong frictional contacts. At a fines mass fraction ( α ) below that of optimal packing (∼ 40%), the initial mixtures consist of a continuous network of coarse particles with fines in interstitial voids. Strong frictional contacts between the coarse particles are probably rapidly re-established and the flows steadily decelerate. Some internal friction reduction appears to occur as α and the grain size ratio increases, possibly due to particle rolling and the lower roughness of internal shear surfaces. Segregation only occurs at large grain size ratio due to dynamical sieving with fines concentrated at the flow base. In contrast, at α above that for optimal packing, the initial mixtures consist of coarse particles embedded in a matrix of fines. Flow velocities and run-outs are similar to that of the monodisperse fine end-member, thus showing that the coarse particles are transported passively within the matrix whatever their amount and grain size are. These flows propagate at constant height and velocity as inviscid fluid gravity currents, thus suggesting negligible interparticle friction. We have determined a Froude number of 2.61 ± 0.08 consistent with the dam-break model for fluid flows, and with no significant variation as a function of α , the grain size ratio, and the initial bed expansion. Very little segregation occurs, which suggests low intensity particle interactions during flow propagation and that active fluidisation is not taking place. Strong frictional contacts are only re-established in the final stages of emplacement and stop the flow motion. We infer that fines-rich (i.e. matrix-supported) pyroclastic flows propagate as inviscid fluid gravity currents for most of their emplacement, and this is consistent with some field data.

An Innovative Device for Quantification of Percolation and Sieving Segregation Patterns–Single Component and Multiple Size Fractions

ABSTRACT Segregation occurs during most particulate materials-related unit operations including mixing, conveying, discharging, filling, and compaction. A redesigned second-generation primary segregation shear cell (PSSC-II) was fabricated to simulate and quantify percolation and sieving mechanisms-based segregation. Several binary mixtures were tested to quantify the effect of size ratios and absolute size. The constituents of binary mixtures studied were spherical glass beads. Three binary size ratios, 4:1, 6:1, and 8:1, were tested. For a given size ratio, three different absolute coarse (710–850, 1000–1200, and 1400–1700 μm) to fine particle sizes were studied. The experimental results showed that the PSSC-II was capable of quantifying segregation potential for various materials. Several physical parameters such as segregation rate (SR), phase of segregation rate (PSR), distribution of segregation rate (DSR), maximum segregation rate (MSR), and normalized segregation rate (NSR) were created to describe the quantity of segregation to a certain level. It was concluded that: (1) Generally, the segregation rates increase with the increase in size ratio. A linear relationship between NSR and size ratio exists for glass beads (R2 = 0.99). (2) Segregation rate also increases with absolute size. NSR increases linearly with absolute size for glass beads (R2 = 0.99). Furthermore, a quantitative relationship exists between certain size ratios and segregation rates, i.e., while size ratio increased two-fold from 4:1 to 8:1, the NSR increased approximately six-fold. (3) The largest magnitude of the NSR occurred where both absolute size and size ratio were at their largest values. (4) The DSR for the binary mixture of glass beads was mainly concentrated in the center region of the shear box for larger size ratios such as 8:1 and 6:1, whereas, for smaller size ratios such as 4:1, the DSR is approximately uniformly distributed. (5) Both duration of lag phase (DLP) and duration of acceleration phase (DAP) decrease with increase in size ratios and in absolute sizes. The smaller the DLP and DAP, the larger the MSR.

Cannibalism within Mating Pairs of the Parasitic Isopod, Ichthyoxenus Fushanensis

Two types of sexual cannibalism, differing in the sex of the victim, were found among heterosexual pairs of the parasitic isopod Ichthyoxenus fushanensis Tsai and Dai, 1999, residing in the body cavity of the freshwater fish Varicorhinus bacbatulus (Pellegrin, 1908). In one type, categorized as sexual cannibalism, the male was consumed by the female before or after mating. In the other, reversed type, the female was eaten by her mate during or after breeding. Both types of cannibalism occurred during the breeding season from April to November, with female-on-male cannibalism occurring earlier on, and the reversed type later. Both types of cannibalism occurred in pairs inhabiting smaller hosts (<10 cm in body length), which suggests that resource limitation is an important factor triggering the cannibalism. Cannibalism may lead to rapid growth or sex change of the cannibal. The availability of free-living mancas during the breeding season enables a mating pair to be re-formed after cannibalism has occurred. Both types of cannibalism occurred in mating pairs with a low size ratio (below 1.6, female to male), and both resulted in a greater discrepancy between female and male sizes in the re-formed pairs. This increase in size ratio between paired individuals may ultimately lead to an increase in clutch size. Because an individual of I. fushanensis undergoes protandrous sex change, the cannibalistic behavior could not have evolved in response to selection on either the male or female sexuality. Rather, both types of cannibalism may be regarded as the result of competition between paired individuals, which appears to be a by-product in the evolution of a reproductive strategy rather than a consequence of sexual selection.

Competitive diffusion into two reactive spheres of different reactivity and size.

Exact series solutions for the reaction rates of two reactive spheres of different reactivity and size are presented. The reaction rates are explicitly expressed in terms of the interparticle distance from reaction- to diffusion-limited conditions. The competitive diffusion favors the larger particle and the reaction rate of the smaller one is significantly reduced as the size ratio increases. For interactions between a diffusion-limited sink and a reaction-limited one, the diffusive interaction favors the reaction rate of the former and hinders that of the latter. Several approximate expressions have been proposed and compared with the exact results. The monopole approximation always underestimates the rate of the smaller sink for diffusion-limited reaction. The asymptotic limit of large size ratio is also analyzed. The asymptotic expression gives a quite accurate result if the smaller particle is regarded as a point sink plus a point dipole.

Perception of two-body center of mass.

Participants estimated the perceptual center of mass between two horizontally oriented black dots varying in size and distance. Experiment 1 showed that estimates, measured as distance from the larger dot's center, decreased with an increase in size ratio between the dots and a decrease in the distance between them, as predicted by the physical center-of-mass equation. The results were replicated and extended in further experiments with different ratios and distances. In all experiments, the true center was consistently overestimated, either because the stimuli were perceived in a low dimensionality or because of a hesitancy to place estimates near the larger dot's edge. In Experiment 4, the center was deliberately placed near this edge for one- and two-dimensional solutions. Participants still overestimated, indicating an "edge effect" as responsible.

An empirical model predicting the viscosity of highly concentrated, bimodal dispersions with colloidal interactions

The relationship between particle size distribution and viscosity of concentrated dispersions is of great industrial importance, since it is the key to get high solids dispersions or suspensions. The problem is treated here experimentally as well as theoretically for the special case of strongly interacting colloidal particles. An empirical model based on a generalized Quemada equation is used to describe η as a function of volume fraction for mono- as well as multimodal dispersions. The pre-factor η˜ accounts for the shear rate dependence of η and does not affect the shape of the η vs φ curves. It is shown here for the first time that colloidal interactions do not show up in the maximum packing parameter and φmax can be calculated from the particle size distribution without further knowledge of the interactions among the suspended particles. On the other hand, the exponent ɛ is controlled by the interactions among the particles. Starting from a limiting value of 2 for non-interacting either colloidal or non-colloidal particles, ɛ generally increases strongly with decreasing particle size. For a given particle system it then can be expressed as a function of the number average particle diameter. As a consequence, the viscosity of bimodal dispersions varies not only with the size ratio of large to small particles, but also depends on the absolute particle size going through a minimum as the size ratio increases. Furthermore, the well-known viscosity minimum for bimodal dispersions with volumetric mixing ratios of around 30/70 of small to large particles is shown to vanish if colloidal interactions contribute significantly.

Scaling relations for granular flow in quasi-two-dimensional rotating cylinders.

An experimental study of the flow of different materials (steel balls, glass beads, and sand) in quasi-two-dimensional rotating cylinders is carried out using flow visualization. The flow in the rotating cylinder comprises of a thin-flowing surface layer with the remaining particles rotating as a fixed bed. Experimental results indicate that the scaled layer thickness increases with increasing Froude number (Fr=omega(2)R/g, where omega is the angular speed, R is the cylinder radius, and g the acceleration due to gravity) and with increase in size ratio (s=d/R, where d is the particle diameter). The free surface profile, is nearly flat at low Fr and becomes increasingly S shaped with increasing Fr. The layer thickness profiles, which are symmetric at low Fr become skewed at high values of Fr and small s. The dynamic angles of repose for all the materials studied show a near-linear increase with rotational speed (omega). Scaling analysis of the experimental data shows that the shape of the scaled surface profiles and the scaled layer thickness profiles are nearly identical when Froude number and size ratio are held constant, for each material. The surface profiles and layer thickness profiles are also found to be nearly independent of the material used. The dynamic angle of repose (beta), however, does not scale with Fr and s and depends on the particle properties. The experimental results are compared to continuum models for flow in the layer. The models of Elperin and Vikhansky [Europhys. Lett. 42, 619 (1998)] and Makse [Phys. Rev. Lett. 83, 3186 (1999)] show good agreement at low Fr while that of Khakhar et al. [Phys. Fluids, 9, 31 (1997)] gives good predictions over the entire range of parameters considered. An analysis of the data indicate that the velocity gradient (gamma;) is nearly constant along the layer at low Fr, and the value calculated at the layer midpoint varies as gamma;(0)~[g sin(beta(0)-beta(s))/d cos beta(s)](1/2) for all the experimental data, where beta(s) is the static angle of repose and beta(0) is the interface angle at the layer midpoint. An extension of "heap" models (BCRE, BRdG) is used to predict the interface angle profiles, which are in reasonable agreement with experimental measurements.

Sintering of unequal grains

This theory shows that, as the ratio of the grain sizes increases, the boundary between the grains becomes more highly curved and the smaller grain becomes more deeply embedded in the larger one. At a ratio of only 1.57, the exposed portion of the small grain is too small to allow it to bond to a third, larger grain, and it cannot effectively connect to a chain of grains. For equal grains the theory reduces to the earlier theory but, as the size ratio increases, the stress gradient in the grain boundary decreases and the grain boundary becomes more tightly curved. These two factors decrease the rate of bonding, which decreases as either the ratio of the sizes, or their absolute sizes, increase.

Analysis of a crack in a disclinated cylinder

In this paper, the stress intensity factors and the opening displacement of a crack loaded by a negative wedge disclination in an isotropic cylinder are numerically determined. The disclination axis coincides with the long axis of the cylinder, and one end of the crack coincides with the disclination location. The cylinder may also be subjected to equal and opposite line loads on its surface. An exact formulation leads to a pair of decoupled singular integral equations of the Cauchy type. Numerical solutions show that if the cylinder represents a grain in a polycrystal, (i) unstable submicroscopic cracks 10-5 to 10-1 times the grain size and stable microscopic cracks of the order of the grain size, are predicted, (ii) the submicroscopic crack length to grain size ratio decreases, while the microscopic crack length to grain size ratio increases, as the grain size increases, (iii) significant differences exist, even in the case of the submicroscopic cracks, between the predictions of the exact theory and the approximate theory which ignores stress redistribution, and (iv) the opening displacement is independent of the elastic constants and the crack profile is wedge-shaped.

Separation of Fine Particles from Nonaqueous Media: Free Energy Analysis and Oil Loss Estimation

Abstract In industrial processes for the separation of fine particles from oil to produce clean liquid fuels, a significant portion of oil is entrained by the solids and is lost, A semi-empirical model is proposed to explain the mechanism of oil loss and floe carryunder. The favorability of the transfer of fine particles from oil to water was determined by conducting a free energy analysis of the process. The ratio of the water drop to particle radius (size ratio) and the contact angle were found to be important parameters affecting the free energy change. The oil loss was found to increase with an increase in size ratio. To verify the model, experiments to determine oil loss in a practical system were conducted for two different surfactants. The model was found to fit experimental data for oil loss very well. The results show that by choosing a suitable surfactant and demulsifier, it is possible to decrease the oil loss considerably. Hence, the proposed model is useful for evaluating the efficiency of th...

A test of the mean density approximation for Lennard-Jones mixtures with large size ratios

The mean density approximation for mixture radial distribution functions plays a central role in modern corresponding-states theories. This approximation is reasonably accurate for systems that do not differ widely in size and energy ratios and which are nearly equimolar. As the size ratio increases, however, or if one approaches an infinite dilution of one of the components, the approximation becomes progressively worse, especially for the small molecule pair. In an attempt to better understand and improve this approximation, isothermal molecular dynamics simulations have been performed on a series of Lennard-Jones mixtures. Thermodynamic properties, including the mixture radial distribution functions, have been obtained at seven compositions ranging from 5 to 95 mol%. In all cases the size ratio was fixed at two and three energy ratios were investigated, ɛ22/ɛ11=0.5, 1.0, and 1.5. The results of the simulations are compared with the mean density approximation and a modification to integrals evaluated with the mean density approximation is proposed.

The role of predator‐prey size ratio in determining the efficiency of capture by Anthocoris nemorum and the escape reactions of its prey, Acyrthosiphon pisum

Abstract Laboratory experiments are described which give the efficiency of Anthocoris nemorum in capturing its aphid prey Acyrthosiphon pisum. The efficiency of capture increases as the predator‐prey size ratio increases. The relationship holds through all the anthocorid developmental stages. Aphid escape reactions are made up of three basic components; kicking, walking or dropping off the plant. These reactions are all related to the predator‐prey size ratio. Kicking is most successful at small ratios while dropping is most successful at high ratios. Walking occupies an intermediate position but has a generally lower probability of success.