Squeezing of a 40% emulsion through a densely-packed random granular material A snapshot of the drop phase Emulsion flow through a granular material is relevant to oil filtration through underground reservoirs and other applications. We have developed, for the first time, computational methods and codes which allow us to predict such flows by rigorous multiparticle-multidrop simulations, theoretically calculate flow rate-pressure gradient relationships and find the conditions when the emulsion drops are trapped in the pores by capillary forces. In many cases, the average drop-phase velocity is found to exceed that of the continuous case. Scaling for the squeezing time at near-critical conditions was also found.