Fragmentation and coalescence dynamics of non-wetting blobs during immiscible two-phase flows in porous media

We study experimentally the dynamics of non-wetting blobs flowing simultaneously with a wetting fluid in a quasi-two-dimensional porous medium consisting of random obstacles. The blobs continuously merge, forming larger ones (coalescence), and break up into smaller ones (fragmentation), leading to an overall dynamic equilibrium between the two processes. We develop a clustering algorithm for the identification of fragmentation and coalescence events that records the size of the blobs prior to and immediately after each event from high-resolution videos of the immiscible flow experiments. The results provide significant insight into the main physical features of these two processes, such as blob size distributions, breakup and coalescence frequency as a function of total flow rate, and the size distributions of the blobs formed by either the fragmentation or coalescence of other ones. One of the salient features of the fragmentation process in our study is that blobs that are smaller than the typical pore size exhibit a higher probability of producing two almost identical children (in size), whereas larger blobs break up into two children of different sizes. In the latter case, one of the children is found to have a dimension that is practically equal to the typical pore size. Our experimental results are also interpreted in the framework of a mean-field approach, where the dynamics of the blob sizes is expressed through an integro-differential population balance equation that comprises terms for the description of the rates of size gains and losses by either fragmentation or coalescence. We recover appropriate expressions for the relevant coalescence and fragmentation kernels, as functions of the blob sizes that participate in each event. A rather surprising result is that for a given blob size population, we obtain an equilibrium between the gains by fragmentation and the losses by coalescence. Furthermore, the opposite is also true, as the population gains by coalescence are found to be equal to the losses by fragmentation.