Determining the pressure distribution of a multi-phase flow through a pore space using velocity measurement and shape analysis

Pore-scale velocity measurements can be achieved by using micro particle shadow velocimetry (mu-PSV). Characteristic properties of a flow are, however, best investigated and described by the pressure distribution in the field. At the pore scale, applying direct pressure measurement techniques comes with significant challenges. By detailed measurement of velocity and applying theoretical relations that suit the flow field under study, the pressure field can be determined. This study demonstrates the application of image-based approaches to investigate the multi-phase flow of a single droplet. Experiments based on mu-PSV are used to determine the velocity field in the flow within the droplet as it passes through a single-pore geometry in the presence of a stationary continuous phase. The results are used to determine the pressure field calculated from a simplified Navier-Stokes expression of the flow, discretised using an Eulerian approach. For the dispersed phase, the theory of the Jamin effect allows the capillary pressure to be related to the observed change in radii of the leading and trailing edges of the droplet. To highlight this approach, two sizes of the glycerol droplets passing through a pore geometry in the presence of a stationary canola oil are investigated. The results show that the velocity and pressure distributions are dictated by the deformation properties of the droplet. The same trends are seen in the distribution of pressure and velocity gradients as a function of location along the channel. The larger of the two droplets showed increased levels of velocity and pressure gradients as it flows through the pore geometry. In general, this work demonstrates the use of the deformation behavior of a dispersed phase to determine the velocity and pressure distributions in a multi-phase flow field.