Winston Lindqwister, Manolis Veveakis, and Martin LesueurDepartment of Civil and Environmental Engineering, Duke University, USATU Delft, Delft, NetherlandsE-mail: winston.lindqwister@duke.eduPhone: +1 919 684 5867AbstractPorous media, while ubiquitous across many engineering disciplines, is inherently difficult to characterize due to their innate stochasticity and heterogeneity. The key for predicting porous material behavior comes down to the structuring of its microstructure, where the linkages of microstructural properties to mesoscale effects remain as one of the key questions in unlocking understanding of this class of materials. One proposed method of linking scales comes down to using Minkowski functionals–geometric morphometers that describe the spatial and topological features of a convex space–to draw connections from icrostructural form to mesoscale features. In this work, chemical equilibrium and kinetics on a microstructure surface were explored, with Minkowski functionals used as the basis for relating microstructural geometry to chemical performance. Using surface CRNs to model chemical behavior–a novel asynchronous cellular automaton– linkages were found between the Minkowski functionals and equilibrium equilibrium constant, as well as properties related to the dynamics of the system’sreaction quotient.
K R eq was selected as the convergence criteria, allowing 14 for steady state solutions to be the sole source of comparison, as seen in Fig. 5. By solely comparing steady-state values, the effects of cell resolution can be investigated on their own. Due to increased resolution, dynamic effects in the unit cell would need to be scaled via the transition rule rate laws, as the increased resolution would effectively increase the distance each set of molecules would need to travel due to the fixed grid nature of surface CRN simulations. Figure 5: Resolution convergence study, varying unit box size. As seen in Fig. 5, Keq values show a clear exponential decrease with increasing resolution, converging at a consistent solution at about N = 200. 15 Figure 6: The effect of diffusion rate on the Keq of the system for each Keq formulation.
id: e545629d2f42bea40c614bd2a8a31f2f - page: 14
Rate Effects According to the work of Boelens et al., 35 the primary discrepancy in Keq values found in interfacial systems compared to well-mixed systems manifests from differing reaction rates, both within the separate phases but also in the transition from one phase to another. In surface CRN simulations, these discrepancies can manifest in the a priori transition rule rates, as well as the assigned diffusion rate for motile species in the simulation space. Fig. 6 demonstrates how an increasing diffusion rate increases Keq consistently across varying methods for Keq calculation. These increases all matched closely to a power law, with consistent power scaling across all three calculation schemes. The primary difference in each curve stems from the order of magnitude of [R] at a consistent linear scaling. A similar class of study was performed comparing the rate of reaction in transition rules.
id: b5025372e77a3f46f5dcba4eb59ad000 - page: 16
As detailed in Eq. 2, the benchmark reaction is a reversible reaction that in its outset favors a forward reaction. For this study, the ratio of the forward reaction kf to the reverse reaction 16 Figure 7: The effect on reaction rate ratio for the forward and reverse reaction on Keq for each Keq formulation. 17 kr was varied, as in Fig. 7. Similar to the behavior exhibited in Fig. 6, Keq calculations varied consistently across the same order power law, modulating by constant orders of magnitude per the Keq formulation. Both rate effect studies shared consistent results in terms of the scalability of Keq calculations across various rate schemes and diffusion rules. The influence of these varying rates points to the validity of Boelens work, as the kinetics of the varying phases of the reaction, both chemically and physically, have a direct influence on the overall steady state behavior of the system.
id: 23f833d86fb7c03306a8f699708e7565 - page: 16
Interface Diffusion Phenomenon as Internal Branching While the kinetics of the system have direct, tangible effects on the overall behavior of the Keq calculation, another important area of consideration is the idiosyncrasies of the simulation medium used in this study. While surface CRNs possess inherent advantages compared to other discrete stochastic simulators in their inherent spatiality and simple solving scheme, secondary behavior may arise depending on the nature of the reaction rules given to the
id: 95fd61e5c7c935d5a2da618903c88448 - page: 18