Capillary rise in pipes with variable cross section

This work proposes an ODE model for a capillary rise in pipes with variable cross section, and compares it to the lubrication theory model. Two key assumptions are made: (1) radius of the pipe varies with axial coordinate, and (2) pipe’s convergence angle is small. The model reduction process involves the identification of critical parameters and simplifies the governing equations by neglecting higher-order terms. Under appropriate scaling, it is shown that generalized Washburn’s equation for capillary rise in pipes with variable cross section reduces to the lubrication theory model [1] , [2] . • A model for capillary rise in pipes with variable cross section is derived. • Derivation is based upon first principles – mass and momentum balance laws used in local and global form. • The model generalizes Washburn’s equation for capillary flow. • Approximate model is derived for the pipes with slowly varying cross section. • When inertial term is neglected, the model is reduced to the one derived using lubrication theory.