Computational Analysis of Nonuniform Expansion in Polyurethane Foams

This paper computationally investigates heterogeneity in the distribution of foam fraction in chemically expanding blown polyurethane foam. The experimentally observed disparity in the volumes of expanded foam when an equal mass of the foaming mixture was injected into tubes of different dimensions motivated this study. To understand this phenomenon, attributed to local variations in the thermal and rheological properties of the expanding system, we explore available data from free-rise foam-expansion experiments in different geometries. Inspired by the mathematical framework for the microstructure modelling of bubble growth in viscous liquids, we study the reacting mixture as a continuum and formulate appropriate mathematical models that account for spatial inhomogeneity in the foam-expansion process. The nonlinear coupled system of partial differential equations governing flow was numerically solved using finite-volume techniques, and the associated results are presented and discussed with graphical illustrations. The proximity of the foaming-mixture core to the external environment and the thickness of a thermal-diffusion layer formed near the bounding geometry was seen to influence the distribution of the foam fraction. Our simulations showed an average spatial variation of about 1.1% in the distribution of solid foam fraction from the walls to the core, as verified with data from μ CT scan analysis of the expanded foam. This also reflects the distribution of void fraction in the foam matrix. The models were validated with experimental data, and our results favourably compared with the experiment observations.

A patient-specific numerical model of the ankle joint for the analysis of contact pressure distribution

A patient-specific numerical model of the ankle joint has been developed using open-source software with realistic material properties that mimics the physiological movement of the foot during the stance phase of the gait cycle. The patient-specific ankle geometry has been segmented as a castellated surface using 3DSlicer from the computed tomography image scans of a subject with no congenital or acquired pathology; subsequently, the bones are smoothed, and cartilage is included as a uniform thickness extruded layer. A high-resolution Cartesian mesh has been generated using cfMesh. The material properties are assigned in the model based on the CT image Hounsfield intensities and compared to a sandwich-based material model. Gait data of the same subject was obtained and used to relatively position the tibia, talus, and calcaneus bones in the model. The stance phase of the gait cycle is simulated using a cell-centred finite-volume method implemented in open-source software OpenFOAM. The predicted peak contact pressures occur in the range of 4.85-5.53 MPa with average pressures in the range of 1.56-1.95 MPa, and the contact area ranges between 429 and 707.8 mm² for the entire stance phase with the mid-stance phase predicting the maximum contact area. These predictions are in agreement with results from the literature. The effect of arthritis on the contact characteristics of the ankle joint has also been examined. A concentrated increase in pressure was predicted that could be manifested as pain, thereby leading to reduced motion in the ankle. The model, with continued development, has the capability to understand the effect of joint degradation and furthermore, could help provide a tool to predict the efficiency of therapeutic surgical procedures as well as guide the development of next generation ankle prostheses. The work would be made available in the University College Dublin depository (https://github.com/laxmimurali/anklejoint) as well as research gate once the article has been published.