The unsteady diffusive mass transfer in doubly connected region bounded by concentric ellipse

Abstract

Investigation of the unsteady mass transfer resulting from diffusion caused by concentration gradient in a region enclosed by two concentric ellipses is explored in this study. Initial deposition of concentration, whose magnitude is C0 assumed to be at the inner ellipse C1 and diffusive mass transfer towards the wall of an outer ellipse C2 is studied. Using conformal mapping, the concentric ellipses in the z-plane are transformed into concentric circles in ζ- plane. Whenever the concentration study in chromatography arises, the concentric ellipses as a doubly connected region provide a better way to separate colors. Hence, confocal ellipses are chosen as doubly connected regions to study diffusion where both surfaces are fixed. As time lapses, in the long run, initial concentration depletes, and this effect on concentration is investigated. It is found that concentration enhances with large mass flux but depletes with an increase in the area of the cross-section of the doubly connected region.

Keywords

• Conformal mapping
• Mass transfer
• Doubly connected region
• Concentric ellipse
• Diffusion