Kinetics of Spreading over Porous Substrates

Abstract

The spreading of small liquid drops over thin and thick porous layers (dry or saturated with the same liquid) is discussed in the case of both complete wetting (silicone oils of different viscosities over nitrocellulose membranes and blood over a filter paper) and partial wetting (aqueous SDS (Sodium dodecyl sulfate) solutions of different concentrations and blood over partially wetted substrates). Filter paper and nitrocellulose membranes of different porosity and different average pore size were used as a model of thin porous layers, sponges, glass and metal filters were used as a model of thick porous substrates. Spreading of both Newtonian and non-Newtonian liquid are considered below. In the case of complete wetting, two spreading regimes were found (i) the fast spreading regime, when imbibition is not important and (ii) the second slow regime when imbibition dominates. As a result of these two competing processes, the radius of the drop goes through a maximum value over time. A system of two differential equations was derived in the case of complete wetting for both Newtonian and non-Newtonian liquids to describe the evolution with time of radii of both the drop base and the wetted region inside the porous layer. The deduced system of differential equations does not include any fitting parameter. Experiments were carried out by the spreading of silicone oil drops over various dry microfiltration membranes (permeable in both normal and tangential directions) and blood over dry filter paper. The time evolution of the radii of both the drop base and the wetted region inside the porous layer were monitored. All experimental data fell on two universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and of the wetted region inside the porous layer on dimensionless time. The predicted theoretical relationships are two universal curves accounting quite satisfactorily for the experimental data. According to the theory prediction, (i) the dynamic contact angle dependence on the same dimensionless time as before should be a universal function and (ii) the dynamic contact angle should change rapidly over an initial short stage of spreading and should remain a constant value over the duration of the rest of the spreading process. The constancy of the contact angle on this stage has nothing to do with hysteresis of the contact angle: there is no hysteresis in the system under investigation in the case of complete wetting. These conclusions again are in good agreement with experimental observations in the case of complete wetting for both Newtonian and non-Newtonian liquids. Addition of surfactant to aqueous solutions, as expected, improve spreading over porous substrates and, in some cases, results in switching from partial to complete wetting. It was shown that for the spreading of surfactant solutions on thick porous substrates there is a minimum contact angle after which the droplet rapidly absorbs into the substrate. Unfortunately, a theory of spreading/imbibition over thick porous substrates is still to be developed. However, it was shown that the dimensionless time dependences of both contact angle and spreading radius of the droplet on thick porous material fall on to a universal curve in the case of complete wetting.