An Unreacted Shrinking Core Model Serves for Predicting Combustion Rates of Organic Additives in Clay Bricks

Abstract

The present study investigates the suitability and restrictions of the unreacted shrinking core model to describe the combustion of a fixed organic substance in a clay matrix, as found in the firing process of clay bricks. The model was applied to the experimental data of isothermal measurements and validated by the model prediction of nonisothermal experiments, which were examined by combustion of mixed clay containing several organic additives in a fluidized bed combustor. Besides reactivity measurements, the shrinking core proceeding was also indicated by apparent separated phases within partially reacted clay specimens. The reaction site moves from the surface toward the inner site dividing a reacting solid into two distinct zones with different organic carbon concentrations, which was confirmed by separated analyses. Mass transfer and reactivity parameters of the model were found to be both exponentially related to temperature (Arrhenius law). The apparent chemical activation energies were determined to be 39.8−59.3 kJ/mol and, therefore, relatively small compared to literature data derived from the experimental procedure with low heating rates, but similar to values of experimental data associated with fast warming rates similar to the present investigation. The determined chemical pre-exponential factors seemed to reflect the specific surface of the organic substance incorporated in the clay matrix. The porosity of the clay samples was investigated by means of mercury intrusion porosimetry and found to be dependent on the amount of added organic substance. The porosity of the pure clay sample was 36.4%, while moderately higher values were found for mixed samples (41.0−44.2%). The effective diffusion coefficients appeared to be directly related to the portion of the total porosity generated by the organic additives. The diffusion coefficients found were around 0.002− 0.02 cm 2 /s for a temperature range of 350−650 °C, which is in the same order of magnitude as reported in comparable studies. The presented model provides an important item for the simulation of the firing process of ceramic goods in oxidizing atmospheres and explains mass transfer mechanisms evolving inside ceramic material blended with organic substances under heat exposure.

Considerations on Temperature Dependent Effective Diffusion and Permeability of Natural Clays

“…Temperature dependency of effective diffusion coefficients is frequently assumed to be exponential and described by an Arrhenius equation (e.g. [ 5 , 28 ]). The present results in Figure 10 show that, in porous media, the actual diffusion mechanism can differ from a progressive rise in temperature by the dominant influence of the Knudsen diffusion regime.…”

“…Temperature dependency of effective diffusion coefficients is frequently assumed to be exponential and described by an Arrhenius equation (e.g. [5,28]). The present results in Figure 10 show that, in porous media, the actual diffusion mechanism can differ from a progressive rise in temperature by the dominant influ- Peng et al found a diffusion coefficient of 0.014 cm 2 /s for a clay brick [4], which is very close to the model prediction represented by Figure 10b, revealing an apparent gas-phase diffusion coefficient at an ambient temperature for sample A of 0.011 cm 2 /s.…”

“…It is concluded that transport coefficients for a given heterogeneous system should be determined in the relevant range of process conditions [ 1 ]. However, due to a lack of experimental data, diffusion coefficients are frequently assumed to be a simple function of molecular diffusion coefficients, or are determined together with chemical kinetic parameters from experimental data [ 3 , 5 ]. The permeability of construction materials is usually evaluated by water vapor permeability according to standardized procedures [ 6 , 7 ], whatis not directly comparable with gas permeability.…”

Real-time transport kinetics of drug encapsulated nanoparticles into apoptotic cancer cells inside microchannels

“…Since the variation in the red color intensity directly maps the concentration of M in this system, the concentration of the red dye (C EtBr ) is used to model the entire drug delivery and the reaction for a cancer cell. The concentrations of M at r , s r , cy r , nm and r n are considered as C , s C , cy C , nm C , n respectively [31]. Thus, (i) mass transfer of M through bulk liquid phase, (ii) diffusion of M through cell membrane, (iii) mass transfer of M through cell cytoplasm, (iv) diffusion of M through nuclear membrane, and (v) rate of reaction of cell nucleus (Q) with M can be modeled as…”

“…At steady state, the reaction-diffusion kinetics on the consumption of M from equations (6)-(10) is given by[31],…”