Flow measurement in porous media is a challenging subject, especially when it comes to performing a three-dimensional (3D) velocimetry at the micro scale. Volumetric flow measurement techniques such as defocusing and tomographic imaging generally involve rigorous procedures, complex experimental setups, and multi-part data processing procedures. However, detailed knowledge of the flow pattern at the pore and subpore scales is important in interpreting the phenomena that occur inside the porous media and understanding the macro-scale behaviors. In this work, the flow of an oil inside a porous medium is measured at the pore and subpore scales using refractive index matching (RIM) and shadowgraph imaging techniques. At the macro scale, flow is measured using the particle image velocimetry (PIV) method in two dimensions (2D) to confirm the volumetric nature of the flow and obtain the overall flow pattern in the vicinity of the flow entrance and at the far field. At the micro scale, the three-dimensional (3D) flow within an arbitrary volume of the porous medium was quantified using 2D particle-tracking velocimetry (PTV) utilizing the law of conservation of mass. Using the shadowgraphy method and a single camera makes the flow measurement much less complex than the approaches using laser light sheets or multiple cameras with multiple viewing angles.

Rising bubble systems are used and investigated in a wide variety of industrial applications. However, the influence of strong confinement in rectangular flow regions has received little attention. An experimental study is undertaken here on a flow channel that allows the passage of bubbles from a region that can be modelled as two parallel plates into a region of rectangular confinement. The effect of a co-flow of a water/glycerol mixture on bubble size and rising velocity in the two confined regions for a wide variety of size ranges is investigated using particle shadow velocimetry. In the parallel plate region, as bubbles become larger in size, their terminal velocity increases due to the relatively higher buoyancy force and negligible effects of the confining geometry, compared to smaller bubble sizes. On entering the rectangular confinement, however, bubbles of relatively large size decelerate to a much lower terminal velocity due to the drag force expressed by the confining walls. Available models in the literature for predicting bubble terminal velocity through circular tubes and parallel plates were evaluated and showed poor predictive performance. To address this gap, a semi-empirical model for the bubble terminal velocity in a rectangular geometry is developed, based on the experimental data, to predict this motion. This model includes the effect of bubble size, fluid medium properties, net co-flow, and confinement geometry. The curious phenomenon of the threshold size of a bubble, which maintains a constant velocity through both geometries, is then predicted using the model.

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