Injection of calcium phosphate pastes: prediction of injection force and comparison with experiments

Calcium phosphate ceramics suspensions (ICPCS) are used in bone and dental surgery as injectable bone substitutes. This ICPCS biomaterial associates biphasic calcium phosphate (BCP) granules with hydroxypropylmethylcellulose (HPMC) polymer. Different ICPCS were prepared and their rheological properties were evaluated in parallel disks geometry as a function of the BCP weight ratio (35, 40, 45 and 50 %). The suspensions show a strongly increased viscosity as compared to the suspending fluid and the high shear rate part of the flow curve can be fitted with a power law model (Ostwald-de Waele model). The fitting parameters depend on the composition of the suspension. A simple device has been used to characterize extrusion of the paste using a disposable syringe fitted with a needle. The injection pressure of four ICPCS formulations was studied under various conditions (needle length and radius and volumetric flow rate), yielding an important set of data. A theoretical approach based on the capillary flow of non-Newtonian fluids was used to predict the necessary pressure for injection, on the basis of flow curves and extrusion conditions. The extrusion pressure calculated from rheological data shows a quantitative agreement with the experimental one for model fluids (Newtonian and HPMC solution) but also for the suspension, when needles with sufficiently large diameters as compared to the size of particles, are used. Depletion and possibly wall slip is encountered in the suspensions when narrower diameters are used, so that the injection pressure is less than that anticipated. However a constant proportionality factor exists between theory and injection experiments. The approach developed in this study can be used to correlate the rheological parameters to the necessary pressure for injection and defines the pertinent experimental conditions to obtain a quantitative agreement between theory and experiments.

CURING CYCLE OPTIMIZATION OF A THICK-SECTION RUBBER PART

The curing cycle optimization is a first order concern for the rubber industry both to control part quality and to reduce curing times. The curing control of thick parts is very delicate due to low thermal diffusivity of rubber compounds. We present a numerical method for the optimization of the cure cycle of molded parts. The heat equation and vulcanization kinetic equation are solved considering the induction, curing, and reversion phases. We build a conjugate gradient optimization method that estimates an optimum temperature–time couple applied as boundary conditions necessary to obtain a desired homogeneous state of cure. We describe the experimental device including a thermally controlled mold. We also describe the thermal regulation and instrumentation including an original measuring device recording temperatures directly within the molded part while minimizing thermal disturbances during measurement. Then, we present the model validation by comparing the numerical simulation results with those obtained experimentally. We propose a curing cycle optimization method based on the calculation of the sensitivity of the state of cure with boundary condition variations. It is an iterative procedure that allows converging to the boundary conditions necessary to obtain the best compromise between the state of cure homogeneity within the part thickness and the curing time. We define a productivity criterion inversely proportional to the curing time and a quality criterion proportional to the homogeneity of the state of cure. Based on these two criteria, we define a performance index that qualifies the process considering the compromise between quality and productivity.