Understanding how a liquid displaces an immiscible fluid in a porous medium is vital to the functioning of a number of processes such as oil recovery, co2 sequestration and ground-water flow. In these flows, which often cannot be observed experimentally as they occur inside a solid, modelling is the only predictive tool available. Our research has considered different classes of such flows, as outlined below.
Pore-scale viscoelastic turbulence
Recent results in Clarke et al, 2012 have shown that the addition of small amounts of polymer to a solution can make a viscoelastic fluid that exhibits pore scale ‘viscoelastic turbulence’, i.e. chaotic flow at low Reynolds numbers. We have been investigating this phenomenon computationally in classical geometries, e.g. cross-slot, as shown below.
Current research is aimed at characterising these fluctuations and determining their influence on trapped interfaces within a porous medium. This work has now been published in [Cooper & Sprittles 2020].
Propagation of wetting fronts through porous media
Standard models for the propagation of a wetting front through a porous medium consider the driving force at the front to be analogous to that of a meniscus through a capillary, resulting in Washburn’s equation. We have extended this approach to consider the effect on the propagation when there are two different modes of motion, the wetting mode (a) in which the liquid meniscus wets the solid and (b) the threshold mode, where liquid meniscus is trapped at a junction.
The new model is outlined in a Journal of Fluid Mechanics publication [Shikhmurzaev & Sprittles, 2012] and was extended in a Physical Review E article [Shikhmurzaev & Sprittles, 2012] to include the influence of random fluctuations on the wetting front, in order to give the first theoretical description to ‘anomalous’ experimental results in [Delker et al, 1996].
Spreading of drops over and into porous substrates
In many cases, drops spread over porous substrates, seeping into them as they do. Understanding the interplay between spreading into and over such solids is a challenging mathematical modelling problem which has been considered in a Journal of Fluid Mechanics article [Shikhmurzaev & Sprittles, 2013].
Often the powders can be pre-wet, and this can significantly affect the drop’s spreading dynamics. In [Marston et al, 2013] we have studied this process both experimentally and theoretically, using simplified models for the spreading process.