The paper presents the longitudinal dispersion of passive tracer molecules released in a steady laminar flow through an annular pipe with heterogeneous reaction at the outer wall, which causes a depletion of contaminant in the flow. A finite‐difference implicit scheme has been adopted to solve the unsteady advection‐diffusion equation for all time period. Here, it is shown how the spreading of tracers is influenced by the shear flow, the aspect ratio (the ratio of the inner radius to the outer radius of the annular pipe), and the absorption parameter at the outer wall. The solute disperses in the annular region due to the interaction between advection and transverse diffusion. Three stages of longitudinal dispersion with time, named as diffusive regime, anomalous regime, and Taylor's regime observed for Poiseuille flow, are discussed for an annular pipe with absorption boundary. The axial distributions of mean concentration are determined from the first four central moments using Hermite polynomial representation. The results of this study are likely to be of interest for understanding the interaction between flow and dispersion in a catheterized artery with conductive walls.
The effects of tapering fabricated air-silica photonic crystal fibers (PCFs) by tailoring the key modal and nonlinear properties of PCFs have been studied by analyzing the tapered structure using a finite difference mode calculation algorithm. The process of tapering is simulated through repeatedly redefining the geometry of the fiber cross section in a progressively tapered dimension preserving the shape. We tested the performance of the analysis by evaluating the modal characteristics, namely, the mode-effective area, birefringence, dispersion, nonlinearity, and supercontinuum properties of some well-known PCF examples under successive tapered conditions. Tapering, as an additional parameter, is seen to improve birefringence of a typical high-birefringence PCF by 1 order of magnitude. The analysis also estimates the extent of tapering that is required to achieve a target amount of evanescent field that has potential applications in an evanescent field sensor. Our investigation with tapered PCF structures includes tailoring dispersion properties and increasing nonlinearity, which leads to broader and lower threshold supercontinuum generation. The analysis should, therefore, be useful as a ready technique for taper analysis of any arbitrary structure PCF and also in PCF-preform (stacking structure) analysis, which can provide preestimates of properties in a targeted dimension of the final PCF before drawing.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.