M³ RESEARCH GROUP

AREAS OF RESEARCH

Modeling

Dispersion

Simulation

Granulation/Binding

We study the fundamentals governing processes related to agglomeration and de-agglomeration (dispersion) of powder clusters on lab systems which enable precise control of key parameters. We attempt to model these processes so as to transfer the information obtained on the lab scale to a larger and more complex scale via simulations.

In this scenario, modeling becomes the link between lab scale and real scale systems. Moreover, modeling allows a more in-depth and precise understanding of the process, with a more fundamental emphasis on the properties of the system which determine the dynamics of the process under study.

We start from fundamental concepts and equations to develop quantitative models. Experimental investigations are used to gain insight into the factors which govern the phenomena, and our models are further validated against experimental data.

Because our research is rather fundamental, the knowledge gained through modeling is applicable to a wide variety of fields, spanning from polymer processing to powder technology, including the food and pharmaceutical industries.

Our ongoing efforts involve modeling very complex phenomena to expand current understanding of dispersion and granulation theories. By combining this knowledge with models and analyses of distributive mixing, we also aim to enable improved polymer processing simulations and optimization studies.

Modeling is employed to clarify many of the phenomena that play key roles in the dispersion of powder agglomerates in polymeric media. Our work includes modeling of fluid infiltration into powder media and its effect on powder dispersibility, and modeling of dispersion of spherical agglomerates in simple shear flows, incorporating both the rupture and erosion phenomena.

Current work incorporates modeling of binder effects via interparticle forces and their modification due to the presence of interstitial fluid.

Dispersion is generated by a simple force balance between hydrodynamic forces acting to pull the minor component apart versus cohesive forces acting to hold the minor component together. The systems studied here involve fine particle clusters as the minor component and polymer fluids as the major one.

In such systems the hydrodynamic forces are generally dependent upon the strength and geometry of the flow field, whereas the cohesive strength of powder agglomerates is dependent upon the physical nature of the powder, the density and morphology of the agglomerate, and the presence of any binder or surface modifier. Matrix infiltration is another factor that needs to be taken into account when mixing powders in liquids. The presence of fluid within a porous powder agglomerate will alter both the hydrodynamic forces transferred to the agglomerate as well as its overall cohesivity.

Experiments in our lab involve single agglomerates subjected to well defined flow fields. There are two types of flow devices used in these experiments. The first is a constant shear device with a cone and plate configuration. The second flow device is an oscillatory shear device with a stationary plate and an oscillating plate that generates a time dependent shear flow field.

There are several mechanisms of dispersion that have been observed. Typically dispersion proceeds by erosion, a phenomenon that is characterized by the removal of small fragments from the surface of the parent agglomerate, or by rupture, when the agglomerate is split into relatively large fragments (Figure 1). In some cases the presence of fluid within a powder agglomerate leads to a different type of dispersion in some systems. This dispersion involves the removal of the infiltrated layer of powder from the outside of the agglomerate (Figure 2).

Figure 1. - Two most common types of powder dispersion for dry and partially infiltrated systems: (a) erosion - a phenomenon characterized by the removal of small powder fragments from the surface of the parent agglomerate. (b) rupture - a phenomenon characterized by the fragmentation of a powder agglomerate into a few relatively large agglomerates. Both types are seen when the hydrodynamic forces applied to the agglomerate are larger than the cohesive forces holding the agglomerate together.

Figure 2. - Powder dispersion seen only in certain partially infiltrated powder systems. This type of dispersion has been classified as adhesive failure. A partially infiltrated agglomerate has an infiltrated ‘skin’ surrounding a dry core. In some systems the infiltration process produces a mechanically weak point at the interface between the wet region and the dry core. The removal of the infiltrated ‘skin’ occurs at levels of hydrodynamic stress lower than the measured cohesive stress of the powder agglomerate.

Simulation is a method of solving a real problem on a computer using the laws of physics. As the computational facilities are being developed, more and more complex processes can be simulated.

In our lab we use Computational Fluid Dynamics Packages (CFD), such as FIDAP and Polyflow, based on the Finite Element Method (FEM) to simulate the polymer fluid motion in industrial mixing equipment. The complexity of the simulation varies based on the type of simulated process (steady state / transient flow, isothermal / non-isothermal, etc.), and the rheological properties of the polymer melt (Newtonian, non-Newtonian, viscoelastic, etc.).

The flow field obtained in the simulation (Fig. 1) can be used to evaluate the overall mixing efficiency of the device using sets of tracers placed in the field (Fig. 2).

Figure 1. Contour of Vz component of velocity in a four-pitch single screw extruder

The distribution of tracers can be analyzed to get information about distributive mixing efficiency. To obtain information about dispersive mixing efficiency, an agglomerate dispersion algorithm can be used along the tracer trajectories.

Figure 2. Particle tracers in the flow field of the extruder

This process allows for virtual manufacturing targeting mixing equipment optimization and scale-up free of costly experiments.

Particle-binder and particle-particle interactions govern the processes of dispersion and wet agglomeration. Hence, understanding these interactions is key to understanding and controlling these processes.

Both dispersion and binder-induced agglomeration, a commonly employed granulation technique, involve direct contact between particles (with or without surface modification) as well as the formation of liquid bridges between particles. Liquid bridges introduce viscous forces and the capillary forces of surface tension and the hydrodynamic Laplace pressure between the particles. Ongoing research work involves probing the impact of modifiers and liquid bridges on both the macroscopic and microscopic scales.

A general understanding of the impact of modifiers and binders is developed through studies involving the controlled dispersion of spherical, millimeter-size powder agglomerates modified to incorporate a secondary material, such as a surfactant or a binding fluid. The dispersion behavior of these agglomerates is quantified, and comparisons are made to determine changes in particle-particle and particle-dispersant interactions in the presence of the modifiers. Analyses of overall agglomerate properties (such as density, porosity, modifier content, etc.) are undertaken to identify the factors with the greatest impact on the dispersion behavior.

A counter-balance between dispersion and agglomeration provides only a bird’s-eye view of the counteracting hydrodynamic and cohesive forces acting over the whole agglomerate. The effect of interactions at the level of individual aggregates, caused by the liquid bridges between them, is explicitly taken into consideration in studies probing the forces of interaction for model unit systems, consisting of a pair of particles bound together by a liquid bridge. Going down to the level of individual aggregates/particles, entails additional considerations of the effects of surface chemistry, and modification for better wetting of binder on particle surface.

The capillary (or static) component of the force arises on account of surface tension effects, partly due to change in the liquid-vapor interface and partly due to change in the bulk pressure differential, as the bridge evolves. This pressure differential, estimated as the Laplace pressure, is given as:

Where

g - interfacial tension

R₁, R₂ - primary and secondary radii of curvature, respectively

Figure1. A liquid bridge extended between two equi-spherical particles of radius, R. From the position of the contact line on both spheres, an accurate numerical estimation for the half-filling angle, b, on both upper (b₁) and lower (b₂) spheres. The separation distance is represented as h and the upper sphere is submerged in the liquid to a depth of l, as shown. The radii of curvature are R₁, in the plane of the meridian and R₂, in the plane orthogonal to the meridian, within the bridge, such that it’s center of curvature lies on the axis of symmetry of the bridge.

The viscous (or dynamic) component of the force arises due to the dynamics of the system, relative velocity of motion of particles concerned, flow field parameters, etc. Thus material parameters such as the binder viscosity and surface tension assume importance in “wet” processes. Modeling of the same is based on a lubrication regime approximation stemming from a solution of the Reynolds’ equation relating pressure in the fluid to the separation between the confining surfaces.

Ongoing experimentation and modeling aims to clarify the effect of flow geometry and surface chemistry on the forces of interaction. This is being implemented by imposing a range of flow conditions (constant velocity or constant deformation rate), using different fluid viscosities, scaling particle sizes and changing the wetting behavior of the binder on the particle.

The impetus behind this thrust on characterizing these modifier/binder-induced particle interactions is the development of analytical solutions for the interaction force incorporating dynamics relevant to specific flow fields, enabling extrapolation of the same results to the real-world inter-aggregate scenario.