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 single screw and twin screw 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 biomaterials and energetic materials.


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 on-line and off-line adjustable gap slit die rheometers, squeeze flow rheometers, extensional rheometers and novel adaptations of classical rheological analysis methods, including the steady torsional flow and capillary/slit rheometers.

Single and Twin Screw Extrusion

HfMI has been funded continuously since 1985 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 for the optimization of geometry and operating conditions, for structuring of complex fluids, 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 single and twin screw extruders. The mathematical models of the processing of various formulations are also used to design hardware including novel screw and barrel elements.

The twin screw extrusion processes also are used for the fabrication of novel scaffolds (including functionally graded scaffolds) for tissue engineering applications.

Analysis of Microstructural Distributions

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.

Tissue Engineering

HfMI has a number of novel capabilities in the tissue engineering scaffold fabrication area including various hybrid processes that combine twin screw extrusion with electrospinning, spiral winding, and co-extrusion.

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.


Highly Filled Materials Institute
Castle Point on Hudson
Hoboken, NJ 07030
Tel: (201) 216-8225
Fax: (201) 216-8306