Operation of a perfusive catalytic membrane with nonlinear kinetics

Operation of a perfusive catalytic curved membrane is systematized into different transport-reaction regimes. The internal viscous permeation improves the catalyst performance, measured here by the effectiveness factor and by its enhancement relative to purely diffusive conditions. A theoretical analysis is presented for nonlinear kinetic expressions, which are suitable to describe the consumption of a reactant in many (bio)catalytic systems. The kinetic and transport parameters required to attain maximum enhancement are related by simple design rules, which depend on the form of the reaction rate law (namely on the order of reaction and dimensionless inhibition constant). For zero-order reactions, these optimum conditions correspond to attaining negligible concentration at a position inside the membrane, while may be interpreted in general as separating situations of severe mass transfer resistance from cases of high effectiveness. It is important to incorporate the correct form of the kinetic expression in the analysis, so that the predictions can be used in a quantitative manner. The results for the different regimes are compiled in enhancement plots and in Peclet–Thiele diagrams. Moreover, the study also yielded new results for the nonlinear reaction–diffusion problem in a curved membrane with its two surfaces exposed to different concentrations, a case of relevance in membrane reactors

Regime mapping and the role of the intermediate region in wall-coated microreactors

Operation of a wall-coated microreactor can occur in several mass transfer-reaction regimes. We define these regimes analytically in several planes of a multi-parametric map, taking into account the different degrees of concentration profile development, as well as the influence of non-unity orders of reaction and reactant inhibition in the kinetic law. It was found that the regions where conversion can be calculated from simplified mass transfer models are not discriminated by common results for entrance-length. We also illustrate the trade-offs that exist across this operating map concerning the catalyst design (costs associated with loading and volume) and overall system performance (evaluated in terms of reactant conversion, flow efficiency and microreactor effectiveness). It is shown that under certain conditions, the existence of moderate mass transfer resistance can be advantageous (even if internal limitations cannot be avoided), clarifying the role of the intermediate transport-reaction region

The Saffman-Taylor problem on a sphere

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.Comment: 26 pages, 4 figures, RevTex, accepted for publication in Phys. Rev.

From chemical gardens to chemobrionics

Chemical gardens in laboratory chemistries ranging from silicates to polyoxometalates, in applications ranging from corrosion products to the hydration of Portland cement, and in natural settings ranging from hydrothermal vents in the ocean depths to brinicles beneath sea ice. In many chemical-garden experiments, the structure forms as a solid seed of a soluble ionic compound dissolves in a solution containing another reactive ion. In general any alkali silicate solution can be used due to their high solubility at high pH. The cation should not precipitate with the counterion of the metal salt used as seed. A main property of seed chemical-garden experiments is that initially, when the fluid is not moving under buoyancy or osmosis, the delivery of the inner reactant is diffusion controlled. Another experimental technique that isolates one aspect of chemical-garden formation is to produce precipitation membranes between different aqueous solutions by introducing the two solutions on either side of an inert carrier matrix. Chemical gardens may be grown upon injection of solutions into a so-called Hele-Shaw cell, a quasi-two-dimensional reactor consisting in two parallel plates separated by a small gap

Internal mass transfer enhancement in flow-through catalytic membranes

Flow-through membrane reactors represent a strategy for process intensification, which benefits from the convective flow that is established due to a transmembrane pressure gradient. The interesting consequence from using these materials is the improved utilization of the catalyst dispersed in the membrane. We propose a theoretical analysis which quantifies the effectiveness factor (η) and the degree of conversion. More importantly, the regime of operation which maximizes the enhancement from convective effects is identified. It corresponds to conditions of not only high internal Peclet number (P), but also of comparable Thiele modulus (ϕ2). We find that these two parameters are related by a simple analytically derived expression: ϕ2C1:26 P. When this relationship holds, an upper limit to the enhancement in the effectiveness factor that can be observed is proportional to P. This result also provides an answer to the effectiveness–conversion trade-off in ‘dead-end’ operation, when both objectives are important. The analytical solutions enable the complete description of the system in Peclet–Thiele diagrams, where the different reaction-transport regimes are identified. Moreover, issues that become particularly relevant in membrane reactors are discussed: curvature, flow direction and the ratio between the concentration distributions at both surfaces. The simplified design rules obtained bridge the gap between materials synthesis (with permeability and thickness as tunable properties) and process design (enhancement of the internal transport and productivity)