A homogenised model for flow, transport and sorption in a heterogeneous porous medium

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a novel problem involving cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterised by the local porosity, a local anisotropic flow permeability, an effective local anisotropic solute diffusivity and an effective local adsorption rate. These macroscale properties depend non-trivially on the two degrees of microstructural geometric freedom in our problem: obstacle size and obstacle spacing. We exploit this dependence to construct and compare scenarios where the same porosity profile results from different combinations of obstacle size and spacing. We focus on a simple example geometry comprising circular obstacles on a rectangular lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We investigate scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters or for studying the impact of deformation on transport in soft porous media.

Foam Quality of Foams Formed on Capillaries and Porous Media Systems

Foams are of great importance as a result of their expansive presence in everyday life—they are used in the food, cosmetic, and process industries, and in detergency, oil recovery, and firefighting. There is a little understanding of foam formation using soft porous media in terms of the quality of foam and foam formation. Interaction of foams with porous media has recently been investigated in a study by Arjmandi-Tash et al., where three different regimes of foam drainage in contact with porous media were observed. In this study, the amount of foam generated using porous media with surfactant solutions is investigated. The aim is to understand the quality of foam produced using porous media. The effect of capillary sizes and arrangement of porous in porous media has on the quality of foam is investigated. This is then followed by the use of soft porous media for foam formation to understand how the foam is generated on the surface of the porous media and the effect that different conditions (such as concentration) have on the quality of the foam. The quality of foam is a blanket term for bubble size, liquid volume fraction, and stability of the foam. The liquid volume fraction is calculated using a homemade dynamic foam analyser, which is used to obtain the distribution of liquid volume fraction along with the foam height. Soft porous media does not influence substantially the rate of decay of foam produced, however, it decreases the average diameter of the bubbles, whilst increasing the range of bubble sizes due to the wide range of pore sizes present in the soft porous media. The foam analyser showed the expected behaviour that, as the foam decays and becomes drier, the liquid volume fraction of the foam falls, and therefore the conductivity of foam also decreases, indicating the usefulness of the home-made device for future investigations.

Foam Formation by Compression/Decompression Cycle of Soft Porous Media

A theory of the amount of foam produced by compression/decompression cycles of a soft porous media is developed. The amount of foam produced was found to be dependent on both the amount of surfactant within the media and the minimum separation between the plates of the compression device. The latter is determined by the mechanical properties of the soft media. The theory also shows the importance of the decompression of the media as this is the mechanism of where the air penetrates into the soft porous material. The accumulated air is used during the compression stage for foam formation. The theoretically predicted values of foam mass are found to have good agreement with experimental observations, which validates the theory predictions. The theory also predicts independence of the foam produced in terms of the frequency of compression/decompression cycles, which agrees with our experimental observations.

Foam Formation and Interaction with Porous Media

Foams are a common occurrence in many industries and many of these applications require the foam to interact with porous materials. For the first time interaction of foams with porous media has been investigated both experimentally and theoretically by O. Arjmandi-Tash et al. It was found that there are three different regimes of the drainage process for foams in contact with porous media: rapid, intermediate and slow imbibition. Foam formation using soft porous media has only been investigated recently, the foam was made using a compression device with soft porous media containing surfactant solution. During the investigation, it was found that the maximum amount of foam is produced when the concentration of the foaming agent (dishwashing surfactant) is in the range of 60–80% m/m. The amount of foam produced was independent of the pore size of the media in the investigated range of pore sizes. This study is expanded using sodium dodecyl sulphate (SDS), which has the same critical micelle concentration as the commercial dishwashing surfactant, where the foam is formed using the same porous media and compression device. During the investigation, it was found that 10 times the critical micelle concentration (CMC) is the optimum concentration for a pure SDS surfactant solution to create foam. Any further increase in concentration after that point resulted in no further mass of foam being generated.

Capillarity in Soft Porous Solids

Soft porous solids can change their shapes by absorbing liquids via capillarity. Such poro-elasto-capillary interactions can be seen in the wrinkling of paper, swelling of cellulose sponges, and morphing of resurrection plants. Here, we introduce physical principles relevant to the phenomena and survey recent advances in the understanding of swelling and shrinkage of bulk soft porous media due to wetting and drying. We then consider various morphing modes of porous sheets, which are induced by localized wetting and swelling of soft porous materials. We focus on physical insights with the aim of triggering novel experimental findings and promoting practical applications.