The Lucas-Washburn (L-W) equation is the classical theory to describe the dynamics of spontaneous imbibition in single micro-channels and micro-scale porous media. However, for nanoliter droplets imbibition in nanoporous media, the L-W equation may not be suitable, due to the nanoscale liquid-solid interactions, e.g., contact line pinning and capillary condensation. In addition, for an intrinsically hydrophobic nanoporous substrate, spontaneous imbibition of a nanoliter droplet is hypothesized to occur if capillary condensation had occurred internally already.

A nanoporous carbon scaffold was synthesized and used as a model nanoporous medium. A recently-developed micro-injection technique was used to generate a series of nanoliter water droplets (2.8–34 nL); the entire wetting dynamics (i.e., apparent contact angle and droplet volume as a function of time) were observed inside an environmental scanning electron microscope.

The L-W equation does not describe the wetting dynamics of nanoliter water droplets in nanoporous media. A new theoretical model is developed to characterize the corresponding dynamics. It is demonstrated that, even for an intrinsically hydrophobic nanoporous substrate, spontaneous imbibition of a nanoliter droplet can occur if capillary condensation had occurred internally already.