Competitive spreading versus imbibition of polymer liquid drops in nanoporous membranes: scaling behavior with viscosity.

The way a liquid drop that is in contact with a nanoporous substrate evolves essentially depends on the competition between imbibition and spreading. Although the scaling behavior of this competitive process with liquid viscosity is important for various applications requiring the filling of nanoporous substrates (template-assisted fabrication, storage, and controlled release of liquids), they appear to be poorly investigated and insufficiently understood. We developed a model study to investigate the wetting and spontaneous imbibition of silicon oil drops of viscosities ranging from 1 to 100 Pa s on nanoporous alumina membranes (pore size of 200 nm). Our results show that the drop radius essentially follows the power law t1/10 time dependence as expected by Tanner's law. However, the scaling of the spreading velocity with the viscosity (approximately eta-n) was found to display an exponent that is comparable on both the reference (impermeable) and nanoporous substrates (n = 0.55) but notably higher than theoretically expected (0.1). More surprisingly, we show that despite the confinement, the rate of imbibition into the nanopores displays a weaker dependence on the viscosity, as compared to the spreading velocity on both the reference and nanoporous substrates. On the basis of Darcy's law for capillary-driven imbibition, this result was discussed in the context of the scaling behavior of the contact angle with the viscosity.