Entropic Analysis of Color Homogeneity

We propose an entropic measure to assess color homogeneity as well as deviations from a standard/ideal color. We illustrate the concept by analyzing samples obtained in a single screw extruder by mixing blue and yellow polymer pellets. Alternatively the proposed technique can be employed to assess the efficiency and degree of distributive mixing attained in polymer processing equipment

Color Mixing in the Metering Zone of A Single Screw Extruder: Numerical Simulations and Experimental Validation

We present numerical simulations for an acrylonitrile-butadiene-styrene copolymer (ABS) resin extrusion in an industrial conventional single-screw extruder. Based upon the flow field patterns obtained in the simulations, a particle tracking procedure was employed to obtain information about the spatial distribution of particle tracers of two colors. Results of the simulation were compared with experimental data obtained under similar extrusion conditions. To evaluate the degree of color mixing and color homogeneity for the system, we employ a specific index calculated based upon the Shannon entropy for two species populations

Entropic Analysis of Color Homogeneity

We propose an entropic measure to assess color homogeneity as well as deviations from a standard/ideal color. We illustrate the concept by analyzing samples obtained in a single screw extruder by mixing blue and yellow polymer pellets. Alternatively the proposed technique can be employed to assess the efficiency and degree of distributive mixing attained in polymer processing equipment

Statistical mechanics characterization of spatio-compositional inhomogeneity

On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the actual configurational macrostate and the theoretical reference one that maximizes entropy. Two kinds of disorder compete: i) the spatial one connected with possible positions of pillars inside a cell (the first component of the measure), ii) the compositional one linked to compositions of each local sum of their integer heights into a number of pillars occupying the cell (the second component). As both the number of pillars and sum of their heights are conserved, the upper limit for a pillar height hmax occurs. If due to a further constraint there is the more demanding limit h <= h* < hmax, the exact number of restricted compositions can be then obtained only through the generating function. However, at least for systems with exclusively composition degrees of freedom, we show that the neglecting of the h* is not destructive yet for a nice correlation of the h*-constrained entropic measure and its less demanding counterpart, which is much easier to compute. Given examples illustrate a broad applicability of the measure and its ability to quantify some of the subtleties of a fractional Brownian motion, time evolution of a quasipattern [28,29] and reconstruction of a laser-speckle pattern [2], which are hardly to discern or even missed.Comment: 17 pages, 5 figure

Quantifying Fluid Mixing with The Shannon Entropy

We introduce a methodology to quantify the quality of mixing in various systems, including polymeric ones, by adapting the Shannon information entropy. For illustrative purposes we use particle advection of two species in a two-dimensional cavity flow. We compute the entropy by using the probability of finding a suitable chosen group/complex of particles of a given species, at a given location. By choosing the size of the group to be in direct proportion to the overall concentration of the components in the mixture we ensure that the entropic measure is maximized for the case of perfect mixing, that is, when at each location the component concentration is equal to the corresponding overall component concentrations. The scale of observation role in evaluating mixing is analyzed using the entropic methodology. We also illustrate the effect of initial conditions on mixing in a laminar system, typical in operations involving polymers

Flow complexity in open systems: interlacing complexity index based on mutual information

Flow complexity is related to a number of phenomena in science and engineering and has been approached from the perspective of chaotic dynamical systems, ergodic processes or mixing of fluids, just to name a few. To the best of our knowledge, all existing methods to quantify flow complexity are only valid for infinite time evolution, for closed systems or for mixing of two substances. We introduce an index of flow complexity coined interlacing complexity index (ICI), valid for a single-phase flow in an open system with inlet and outlet regions, involving finite times. ICI is based on Shannon’s mutual information (MI), and inspired by an analogy between inlet–outlet open flow systems and communication systems in communication theory. The roles of transmitter, receiver and communication channel are played, respectively, by the inlet, the outlet and the flow transport between them. A perfectly laminar flow in a straight tube can be compared to an ideal communication channel where the transmitted and received messages are identical and hence the MI between input and output is maximal. For more complex flows, generated by more intricate conditions or geometries, the ability to discriminate the outlet position by knowing the inlet position is decreased, reducing the corresponding MI. The behaviour of the ICI has been tested with numerical experiments on diverse flows cases. The results indicate that the ICI provides a sensitive complexity measure with intuitive interpretation in a diversity of conditions and in agreement with other observations, such as Dean vortices and subjective visual assessments. As a crucial component of the ICI formulation, we also introduce the natural distribution of streamlines and the natural distribution of world-lines, with invariance properties with respect to the cross-section used to parameterize them, valid for any type of mass-preserving flow

Color Mixing in the Metering Zone of A Single Screw Extruder: Numerical Simulations and Experimental Validation

We present numerical simulations for an acrylonitrile-butadiene-styrene copolymer (ABS) resin extrusion in an industrial conventional single-screw extruder. Based upon the flow field patterns obtained in the simulations, a particle tracking procedure was employed to obtain information about the spatial distribution of particle tracers of two colors. Results of the simulation were compared with experimental data obtained under similar extrusion conditions. To evaluate the degree of color mixing and color homogeneity for the system, we employ a specific index calculated based upon the Shannon entropy for two species populations

Color Mixing in Single Screw Extruder: Simulation &Amp; Experimental Validation

We present numerical simulations for an ABS resin extrusion in an industrial conventional single screw extruder. Based upon the flow field patterns obtained in the simulations, a particle tracking procedure was employed to obtain information about the spatial distribution of particle tracers of two colors. Results of the simulation were compared with experimental data obtained under similar extrusion conditions. To evaluate the degree of color mixing and color homogeneity for the system, we employ a specific index calculated based upon the Shannon entropy for two species populations

Simultaneous Characterization of Dispersive and Distributive Mixing in a Single Screw Extruder

Simultaneous characterization of dispersive and distributive mixing in a single screw extruder was discussed. A mixing index based on the calculation of Shannon entropy for different size fractions of the minor component present in the system was developed. It was found that operating the extruder at negative throttle ratio improved mixing efficiency