Dimensional analysis of a planetary mixer for homogenizing of free flowing powders: Mixing time and power consumption

International audiencePowder mixing is crucial to the processing stages in many industries. However, there is still a paucity of information about the effects of process parameters on mixing efficiency. This paper investigates the homogenization of free flowing granular materials with a planetary mixer, TRIAXE (R), examining the effect of the ratio of impeller rotational speeds (N-R/N-G) on the mixing process. First, a dimensional analysis carried out with mixing time and power consumption as target variables, established that both a Froude number and N-R/N-G controlled the process for the given free flowing powder mixture and planetary mixer. A further theoretical approach also suggested that these two dimensionless ratios which control hydrodynamics can be reduced to a modified Froude number providing that the maximum linear velocity achieved (mu(ch)) by the planetary mixer is introduced, replacing the dual impeller rotational speeds (N-R and N-G). Mixing time and power experiments validated the above hypothesis. Homogeneity tests performed in a granular media showed that the length of path achieved by the impeller governs the obtained mixing level. Finally, this work reflected that (i) dimensional analysis was also well suited to model powder homogenization with a planetary mixer. (ii) A concise set of dimensionless numbers governing mixing phenomena can be deduced through the introduction of the maximum linear velocity as obtained in previous studies on gas/liquid and miscible liquids mixing processes

Derivation of dimensionless relationships for the agitation of powders of different flow behaviours in a planetary mixer

International audienceThis study investigates the bulk agitation of free flowing or nearly cohesive granular materials in a pilot-scale planetary mixer equipped with a torque measurement system. Our major aim is to investigate the effect of the flow properties of several powders, as well as that of the set of experimental conditions (engine speeds N-R and N-G), on the power consumption of such a mixer. Thanks to a previous dimensional analysis of the system, this influence is studied through the variations of the power P with a characteristic speed rich, defined from engine speeds and geometrical considerations. Two relationships involving dimensionless numbers are derived to describe the agitation process: N-pG = f (F-rG, Nu(R)/Nu(G) )and N-pM = f(Fr-M). For free flowing powders, a linear relationship is observed when plotting P against u(ch), and he resulting process relationship linking dimensionless numbers is Np-M = 15Fr(M)(-1). In the more cohesive case, power values vary around an average value (P = 54W) and the resulting process relationship is Np-M = 1.8072Fr(M)(-1.467). It is argued that the exponent in the representation of N-pM against Fr-M may be a useful parameter for powder classification, and should be linked to powder rheometrical considerations

Improving the rheometry of rubberized bitumen: experimental and computation fluid dynamics studies

Multi-phase materials are common in several fields of engineering and rheological measurements are intensively adopted for their development and quality control. Unfortunately, due to the complexity of these materials, accurate measurements can be challenging. This is the case of bitumen-rubber blends used in civil engineering as binders for several applications such as asphalt concrete for road pavements but recently also for roofing membranes. These materials can be considered as heterogeneous blends of fluid and particles with different densities. Due to this nature the two components tends to separate and this phenomenon can be enhanced with inappropriate design and mixing. This is the reason behind the need of efficient dispersion and distribution during their manufacturing and it also explains while realtime viscosity measurements could provide misleading results. To overcome this problem, in a previous research effort, a Dual Helical Impeller (DHI) for a Brookfield viscometer was specifically designed, calibrated and manufactured. The DHI showed to provide a more stable trend of measurements and these were identified as being ‘‘more realistic” when compared with those obtained with standard concentric cylinder testing geometries, over a wide range of viscosities. However, a fundamental understanding of the reasons behind this improvement is lacking and this paper aims at filling these gaps. Hence, in this study a tailored experimental programme resembling the bitumen-rubber system together with a bespoke Computational Fluid Dynamics (CFD) model are used to provide insights into DHI applicability to perform viscosity measurements with multiphase fluids as well as to validate its empirical calibration procedure. A qualitative comparison between the laboratory results and CFD simulations proved encouraging and this was enhanced with quantitative estimations of the mixing efficiency of both systems. The results proved that CFD model is capable of simulating these systems and the obtained simulations gave insights into the flow fields created by the DHI. It is now clear that DHI uses its inner screw to create a vertical dragging of particles within a fluid of lower density, while the outer screw transports the suspended particles down. This induced flow helps keeping the test sample less heterogeneous and this in turns allows recording more stable viscosity measurements

Width distribution of contact lines on a disordered substrate

We have studied the roughness of a contact line of a liquid meniscus on a disordered substrate by measuring its width distribution. The comparison between the measured width distribution and the width distribution calculated in previous works, extended here to the case of open boundary conditions, confirms that the Joanny-de Gennes model is not sufficient to describe the dynamics of contact lines at the depinning threshold. This conclusion is in agreement with recent measurements which determine the roughness exponent by extrapolation to large system sizes.Comment: 4 pages, 3 figure

2-loop Functional Renormalization Group Theory of the Depinning Transition

We construct the field theory which describes the universal properties of the quasi-static isotropic depinning transition for interfaces and elastic periodic systems at zero temperature, taking properly into account the non-analytic form of the dynamical action. This cures the inability of the 1-loop flow-equations to distinguish between statics and quasi-static depinning, and thus to account for the irreversibility of the latter. We prove two-loop renormalizability, obtain the 2-loop beta-function and show the generation of "irreversible" anomalous terms, originating from the non-analytic nature of the theory, which cause the statics and driven dynamics to differ at 2-loop order. We obtain the roughness exponent zeta and dynamical exponent z to order epsilon^2. This allows to test several previous conjectures made on the basis of the 1-loop result. First it demonstrates that random-field disorder does indeed attract all disorder of shorter range. It also shows that the conjecture zeta=epsilon/3 is incorrect, and allows to compute the violations, as zeta=epsilon/3 (1 + 0.14331 epsilon), epsilon=4-d. This solves a longstanding discrepancy with simulations. For long-range elasticity it yields zeta=epsilon/3 (1 + 0.39735 epsilon), epsilon=2-d (vs. the standard prediction zeta=1/3 for d=1), in reasonable agreement with the most recent simulations. The high value of zeta approximately 0.5 found in experiments both on the contact line depinning of liquid Helium and on slow crack fronts is discussed.Comment: 32 pages, 17 figures, revtex

Bursts in a fiber bundle model with continuous damage

We study the constitutive behaviour, the damage process, and the properties of bursts in the continuous damage fiber bundle model introduced recently. Depending on its two parameters, the model provides various types of constitutive behaviours including also macroscopic plasticity. Analytic results are obtained to characterize the damage process along the plastic plateau under strain controlled loading, furthermore, for stress controlled experiments we develop a simulation technique and explore numerically the distribution of bursts of fiber breaks assuming infinite range of interaction. Simulations revealed that under certain conditions power law distribution of bursts arises with an exponent significantly different from the mean field exponent 5/2. A phase diagram of the model characterizing the possible burst distributions is constructed.Comment: 9 pages, 11 figures, APS style, submitted for publicatio

On the complexity of acyclic modules in automata networks

Modules were introduced as an extension of Boolean automata networks. They have inputs which are used in the computation said modules perform, and can be used to wire modules with each other. In the present paper we extend this new formalism and study the specific case of acyclic modules. These modules prove to be well described in their limit behavior by functions called output functions. We provide other results that offer an upper bound on the number of attractors in an acyclic module when wired recursively into an automata network, alongside a diversity of complexity results around the difficulty of deciding the existence of cycles depending on the number of inputs and the size of said cycle.Comment: 21 page

Matrix-Bound PAI-1 Supports Cell Blebbing via RhoA/ROCK1 Signaling

The microenvironment of a tumor can influence both the morphology and the behavior of cancer cells which, in turn, can rapidly adapt to environmental changes. Increasing evidence points to the involvement of amoeboid cell migration and thus of cell blebbing in the metastatic process; however, the cues that promote amoeboid cell behavior in physiological and pathological conditions have not yet been clearly identified. Plasminogen Activator Inhibitor type-1 (PAI-1) is found in high amount in the microenvironment of aggressive tumors and is considered as an independent marker of bad prognosis. Here we show by immunoblotting, activity assay and immunofluorescence that, in SW620 human colorectal cancer cells, matrix-associated PAI-1 plays a role in the cell behavior needed for amoeboid migration by maintaining cell blebbing, localizing PDK1 and ROCK1 at the cell membrane and maintaining the RhoA/ROCK1/MLC-P pathway activation. The results obtained by modeling PAI-1 deposition around tumors indicate that matrix-bound PAI-1 is heterogeneously distributed at the tumor periphery and that, at certain spots, the elevated concentrations of matrix-bound PAI-1 needed for cancer cells to undergo the mesenchymal-amoeboid transition can be observed. Matrix-bound PAI-1, as a matricellular protein, could thus represent one of the physiopathological requirements to support metastatic formation