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

Abstract

Pore-scale velocity measurements can be achieved by using micro particle shadow velocimetry (µ-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 µ-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.

Numerical study of drop behavior in a pore space

“…Numerical simulation of a drop falling through a pore due to gravity in an ambient continuous liquid phase is conducted and the results are in qualitatively good agreement compared to the experimental data of Ansari et al (2018Ansari et al ( , 2019. In addition, quantitative verifications confirmed that the pressure distribution inside the deforming drop is consistent with the drop shape as it passes through the pore.…”

“…The results are presented in two parts. First, we consider a drop falling through a pore due to gravity in the ambient continuous liquid phase and compare our results to the experimental data of Ansari et al (2018Ansari et al ( , 2019. This comparison is done for the purpose of qualitatively validating our model.…”

“…4.1 A drop falling through a single pore space due to gravity Ansari et al (2018Ansari et al ( , 2019 carried out an experimental study of a Glycerol drop falling in ambient Canola oil through a pore using micro particle shadow velocimetry (µ-PSV). = 254 where v c and ρ c are the kinematic viscosity and density of continuous phase, respectively).…”

“…The authors considered theoretical solutions and rigorous hydrodynamical simulations for both pore and large scale. 4 Ansari et al (2018Ansari et al ( , 2019 conducted an experimental study of liquid-liquid flow through a pore to determine the pressure field by analysis of the velocity field and shape of the drop obtained by the micro particle shadow velocimetry (µ-PSV). Patel et al (2019) numerically studied the dynamics of a bubble rising in a vertical sinusoidal wavy channel using a dual grid level set method coupled with a finite volume-based discretization of the Navier-Stokes equations.…”

Particle Image Velocimetry of Oil–Water Two-Phase Flow with High Water Cut and Low Flow Velocity in a Horizontal Small-Diameter Pipe

“…Therefore, studying oil–water two-phase flow with high water cut and low flow velocity, particularly in a horizontal small-diameter pipe, is necessary and timely. Velocity measurements of oil–water two-phase flow may be performed by various methods, including the ultrasonic method [9,10,11], the conductance method [12,13], the capacitance method [14,15,16], the electromagnetic method [17], the thermal tracer method, the optical fiber method, the capacitance resistance tomography method [18], the ultraviolet fluorescence [19,20], and particle image velocimetry (PIV) [21,22,23,24]. PIV has become an important research method because of its field visualization capability [25,26].…”