Mathematical Modeling

Mathematical modeling at HfMI starts with the simulation of the particle formation processes and goes all the way to the mixing and processing occurring in continuous processors in very complex geometries. For example, in the area of mathematical modeling of the processing operations HfMI has the ability to solve the coupled conservation equations to accurately determine the temperature, stress, residence time and velocity distributions for various extruder and die combinations. Such unique capabilities provide realistic solutions to the industry and Department of Defense organizations for the outcome-certain processing of various complex materials, including energetic materials.

Crystallization

Particle formation upon crystallization from solution and the deposition of nanoparticles from the vapor phase are some of the particle formation processes which we work on. Our research in this area covers first the force-field based calculations of solvent/antisolvent interactions during crystallization to determine the optimum recipes for crystallization to arrive at the desired crystal polymorph and particle shape/size distributions. Micro scale equipment is used for validation, followed by the characterization of the crystal polymorphs using powder diffraction patterns and the particle size shape using SEM. Upon validation, the scale up of the crystallization process is carried out under the guidance of mathematical models of the crystallization process. These mathematical models are also used as the basis for model predictive control at the plant level.

Rheology

HfMI has developed a series of technologies and mathematical models for the characterization of the rheological behavior of suspensions and dispersions (especially in the relatively high solid concentration regime) and their continuous and batch processing. The rheological methods include new on-line and squeeze flow rheometers, extensional rheometers and novel adaptations of classical rheological analysis methods, including the steady torsional flow and capillary/slit rheometers.

Extrusion

Over the last 13 years HfMI has been funded by DOD and industry to develop mathematical models of the flow and heat transfer occurring in various continuous processors including single and twin-screw extruders and the dies used in shaping of the grains. The mathematical models are used to weed out the conditions, which are precarious to safety, including those, which generate temperature hot spots and stagnant zones.

The mathematical models of the process and the determined parameters of constitutive equations are tested in-house using well-instrumented industrial scale extruders. The mathematical models of the processing of various formulations are also used to design hardware including novel screw and barrel elements.

Analysis of Microstructural Distributions

During the last 13 years HfMI has developed proprietary techniques for the quantitative characterization of the statistics of the spatial distributions of the ingredients of complex formulations "degree of mixedness", the particle size and orientation distributions of the crystalline solid phase.

Ultimate Properties

HfMI has the capabilities and experience in the characterization of various electrical, magnetic and mechanical properties.

Die and Tool Design and Manufacture

Through its partnerships with various companies HfMI has the capability to design and manufacture specialized dies, screws, mixing elements and sensors; all tailored to a specific material and application.