The dissolution of a miscible drop rising or falling in another liquid at low Reynolds number

'A basic and basically unsolved problem in fluid dynamics is to determine the evolution of rising bubbles falling drops one miscible liquid another' [1]. Here, we address this important literature gap present first theory predicting velocity, volume composition such at low Reynolds numbers. For case where diffusion out drop negligible, obtain a universal scaling law. more general occurs into drop, full governed by parameter-free first-order ordinary differential equation, whose closed form solution exists, only depends on initial condition. Our analysis primarily 'drop-scale' effective parameters for diffusivity through interfacial boundary layer. We validate our results against experimental data water suspended syrup, corresponding certain regimes mass exchange ratio between explicitly identify drop-scale theory. [1] Joseph, D.D. Renardy, Y.Y., 2013. Fundamentals two-fluid dynamics: part II: lubricated transport, liquids (Vol. 4). Springer Science & Business Media.