Miscible displacements with a chemical reaction in a capillary tube

Abstract

in Wiley InterScience (www.interscience.wiley.com).Miscible displacement of a more-viscous liquid by a less-viscous one with a chemical reaction in a capillary tube was investigated experimentally and theoretically. In such a flow field, the less-viscous liquid continuously leaks from the tip of the fingershaped boundary between the two liquids to form another thin finger depending on flow condition. This is called a ''spike.'' Experimental results show that in the spike product is clearly or scarcely observed when the initial reactant concentration in the less-viscous liquid is sufficiently larger or smaller than the stoichiometry, respectively. On the basis of theoretical results, a model is proposed in which the difference in the reaction plane's location in either the less-viscous liquid or in the boundary (determined by the variation in the initial reactant concentrations) results in a significant difference between the locations of the boundary and the reaction plane, this difference being affected by the spike configuration of the boundary.

Investigation of reacting flow fields in miscible viscous fingering by a novel experimental method

“…These analytical results were essentially similar to those in the previous analyses, 15,17 although there was a difference in that when u v ! 1, the reaction plane was located in the boundary region in Nagatsu et al, 20 whereas it was located in the more-viscous liquid region in Nagatsu and Ueda. 15,17 Physical model of reacting flow fields in the cell's gap direction…”

“…Comparing the depth of the blood-red color by u v , we find it to be deeper as u v is smaller, which shows that the product concentration is higher as u v is smaller, although the initial reactant concentrations are set as c pr is theoretically identical when a 5 2 or they are set as c pr theoretically increases with u v when a 5 1 (this indicates that the product concentration will still increase with a decrease in u v if c pr is set to be identical for various u v under the condition where the stoichiometric ratio is 1) in the previous steady convection-diffusion-reaction analysis. 20 Since the reaction time is independent of u v , the difference in the product concentration is caused by the difference in the overall reaction rate (the quantity of the product produced per unit time and per unit volume). In other words, the overall reaction rate in the region from the trough to the inside near the trough of the fingers is higher as u v is smaller under the condition in which c pr is constant.…”

“…In Nagatsu et al, 20 we conducted a steady convection-diffusion-reaction analysis that was considered to be an improved version of the previous analyses performed by Nagatsu and Ueda 15,17 where a distinct interface between two miscible fluids was assumed. In other words, the analysis in Nagatsu et al 20 took miscibility into account.…”

“…In other words, the analysis in Nagatsu et al 20 took miscibility into account. The analytical results showed that when the convective effect was weak, the reaction plane was located relatively far from the boundary in the less-viscous liquid for u v ( 1, whereas it was located in the boundary for u v % 1 and u v ) 1.…”

“…In the present study, for the reactant concentration conditions shown in Figures 1a-c, we denote u v ( 1, u v % 1, and u v ) 1, respectively. In Nagatsu et al, 20 the product concentration at the reaction plane, c pr , was theoretically obtained as follows:…”