Jorge E. Gatica

Reactive Infiltration of Silicon Melt through Microporous Amorphous Carbon Preforms

The kinetics of unidirectional capillary infiltration of silicon melt into microporous carbon preforms has been investigated as a function of the pore morphology and melt temperature. The infiltrated specimens showed alternating bands of dark and bright regions, which corresponded to the unreacted free carbon and free silicon regions, respectively. The decrease in the infiltration front velocity for increasing infiltration distances is in qualitative agreement with the closed-form solution of capillarity-driven fluid flow through constant-cross-section cylindrical pores. However, drastic changes in the thermal response and infiltration front morphologies were observed for minute differences in the preform’s microstructure. This suggests the need for a dynamic percolation model that would account for the exothermic nature of the silicon-carbon chemical reaction and the associated pore-closing phenomenon.

Oxygen Diffusion Through Natural Extracellular Matrices: Implications for Estimating "Critical Thickness" Values in Tendon Tissue Engineering

Oxygen is necessary for maintaining cell proliferation and viability and extracellular matrix (ECM) production in 3-dimensional tissue engineering. Typically, diffusion is the primary mode for oxygen transport in vitro; thus, ensuring an adequate oxygen supply is essential. In this study, we determined the oxygen diffusion coefficients of 3 natural ECMs that are being investigated as construct scaffolds for tendon tissue engineering: small-intestine submucosa (SIS), human dermis (Alloderm), and canine fascia lata. Diffusion coefficients were determined using a standard diffusion cell system. The ranges for each matrix type were: SIS: 7 x 10(-6) - 2 x 10(-5) cm2/s, Alloderm: 1.9 - 3.1 x 10(-5) cm2/s, and canine fascia lata: 1.6 - 4 x 10(-5) cm2/s. We used the experimental oxygen diffusivity data for these natural ECMs in a mathematical model of oxygen diffusion through a cell-seeded scaffold to estimate the critical size of cell-seeded scaffold that can be cultured in vitro.

Interaction between chemical reaction and natural convection in porous media

Abstract Natural convection in porous media has received much attention in the last decades. Most of the work, however, has been devoted to the case of a global driving force resulting from thermal or concentration gradients applied to the boundaries of the system. As changes in the density lead to natural convection, chemical reactions can provide a distributed driving force for secondary flows. The conditions for the onset of natural convection are represented by the critical value of the thermal Rayleigh number. The critical value is found by performing a linear stability analysis of the basic reaction regime. Results are reported for the onset of both oscillatory and monotonic instabilities. The stability of the convective modes is studied by using a variational approach and deriving a set of spectral equations by means of a truncated mode interaction. The initial-value problem is analyzed by continuation routines and bifurcation diagrams are drawn. These diagrams constitute a valuable tool in the design of heterogeneous reacting systems. The numerical solution of the full governing equations serves to corroborate the predictions of the simplified model as well as to illustrate the effects of natural-convection phenomena on systems with chemical reaction.

The biomechanical role of scaffolds in augmented rotator cuff tendon repairs.

BACKGROUND Scaffolds continue to be developed and used for rotator cuff repair augmentation; however, the appropriate scaffold material properties and/or surgical application techniques for achieving optimal biomechanical performance remains unknown. The objectives of the study were to simulate a previously validated spring-network model for clinically relevant scenarios to predict: (1) the manner in which changes to components of the repair influence the biomechanical performance of the repair and (2) the percent load carried by the scaffold augmentation component. MATERIALS AND METHODS The models were parametrically varied to simulate clinically relevant scenarios, namely, changes in tendon quality, altered surgical technique(s), and different scaffold designs. The biomechanical performance of the repair constructs and the percent load carried by the scaffold component were evaluated for each of the simulated scenarios. RESULTS The model predicts that the biomechanical performance of a rotator cuff repair can be modestly increased by augmenting the repair with a scaffold that has tendon-like properties. However, engineering a scaffold with supraphysiologic stiffness may not translate into yet stiffer or stronger repairs. Importantly, the mechanical properties of a repair construct appear to be most influenced by the properties of the tendon-to-bone repair. The model suggests that in the clinical setting of a weak tendon-to-bone repair, scaffold augmentation may significantly off-load the repair and largely mitigate the poor construct properties. CONCLUSIONS The model suggests that future efforts in the field of rotator cuff repair augmentation may be directed toward strategies that strengthen the tendon-to-bone repair and/or toward engineering scaffolds with tendon-like mechanical properties.

Bifurcation analysis of chemically driven convection

Abstract The problem of the progress of an exothermic chemical reaction under conditions apt for the onset of natural convection is considered. The governing partial differential equations are reduced to a set of ordinary differential equations by using a variational approach and a simplified model is obtained. Bifurcation diagrams of the simplified model are presented for various values of the Rayleigh number. Substantial changes in the topology of the solutions space are predicted by the non-linear stability analysis. Qualitatively agreement between predictions and numerical results confirms the validity of the simplified model to represent the behavior of the original equations. Numerical solutions of the full governing equations serve to illustrate the effects of natural convection phenomena in systems with chemical reaction.

Stability analysis of chemical reaction and free convection in porous media

Abstract Stability analysis of an isothermal first order and nonisothermal zero order reaction in the presence of free convection is performed. Critical values of the Rayleigh number for both cases are analytically calculated. The calculated values compare favorably with the numerical simulation of the full governing equations.

Combustion of Metallic Powders: A Phenomenological Model for the Initiation of Combustion

A mathematical model which describes the process when a spherical metallic particle is exposed to an oxidizing atmosphere, has been formulated. We refer to the oxidation process in a generic sense, and the model can be used for the formation of oxides, nitrides and sulphides in general. The oxidation process is modeled for oxides which form n-type semiconductors with the defects in the form of interstitial cations and electrons (e.g., Al2O3) in terms of mass and energy transport phenomena.It accounts for the release of metal cations and electrons at the metal-oxide interface, the transport of these species through the oxide layer due to concentration and eleclric field gradients, and the formation of the metal oxide at the outer interface. As a result a hollow oxide sphere develops as the metal is converted 10 oxide. If the energy released by the oxidation reaction exceeds the heat losses, self-heating will occur. Such a rise in temperature accelerates the release of cations and electrons from the metal i...

An Analytical Model for Rotator Cuff Repairs

BACKGROUND Currently, natural and synthetic scaffolds are being explored as augmentation devices for rotator cuff repair. When used in this manner, these devices are believed to offer some degree of load sharing; however, no studies have quantified this effect. Furthermore, the manner in which loads on an augmented rotator cuff repair are distributed among the various components of the repair is not known, nor is the relative biomechanical importance of each component. The objectives of this study are to (1) develop quasi-static analytical models of simplified rotator cuff repairs, (2) validate the models, and (3) predict the degree of load sharing provided by an augmentation scaffold. METHODS The individual components of the repair constructs were modeled as non-linear springs, and the model equations were formulated based on the physics of springs in series and parallel. The model was validated and used to predict the degree of load sharing provided by a scaffold. Parametric sensitivity analysis was used to identify which of the component(s)/parameter(s) most influenced the mechanical behavior of the augmented repair models. FINDINGS The validated models predict that load will be distributed approximately 70-80% to the tendon repair and approximately 20-30% to the augmentation component. The sensitivity analysis suggests that the greatest improvements in the force carrying capacity of a tendon repair may be achieved by improving the properties of the bone-suture-tendon interface. Future studies will perform parametric simulation to illustrate the manner in which changes to the individual components of the repair, representing different surgical techniques and scaffold devices, may influence the biomechanics of the repair construct.

Permeability of microporous carbon preforms

The permeability of microporous amorphous carbon preforms with varying pore size and pore distributions has been experimentally examined. The porous structures have been characterized by mercury porosimetry and by quantitative metallography of pressure-infiltration-cast metal matrix composites based on the carbon preforms. The permeability shows a linear correlation with the fraction porosity and the square of the pore diameter.

Stability of Non-Adiabatic Solid-Solid Combustion

Abstract In this study, the synthesis of inorganic materials by combustion of solid cylindrical preforms is addressed. The reaction between two solid reactants is analyzed when the reaction proceeds in the combustion regime. This process is characterized by a thin propagating reaction front. The elevated temperature levels reached at the combustion front usually prevent this process from being carried out under ideal adiabatic conditions. The planar model of propagation manifests then as a curved moving front. Previous studies on this subject have followed the approach of lumping the temperature in the radial direction to make the problem more tractable. In this work, such an approach is discarded and a two-dimensional stability analysis is performed. It is shown that planar propagation can become unstable, developing into (i) auto-oscillations, (ii) spinning combustion with a single or multiple heads located near the outer surface, and (iii) multiple-head spinning waves with one or multiple heads near th...