From wicking to anti-wicking: A universal framework for capillary dynamics

Abstract: The dynamics of capillary rise under different geometric and fluid conditions have the common signatures of rapid rise followed by an equilibrium state that describe the underlying competing forces. We present a new interpretation of capillary dynamics using a linear damped system where modulation of damping and forcing characteristics are achieved using axisymmetric channels with sinusoidal variation in radius. The complete axisymmetric design space ranging from hydrophilic channels that enable spontaneous imbibition to hydrophobic channels, that required external pressure mechanisms is modeled and the force dynamics is split into simultaneous damping and forcing characteristics. We introduce the product of damping and forcing terms as the new parameter that effectively characterizes rise dynamics across various geometric and flow conditions, encompassing both flow-enhancing and flow-inhibiting scenarios. The monotonic nature of this parameter enables the development of a stochastic optimization method that can determine optimal channel geometries for controlled capillary rise.