Segregation of a two-phase mixture of incompatible viscous fluids in laminar flow

Investigation of segregation of multiphase fluid sys� tems is of significant scientific and practical interest. In practical terms, the obtained knowledge is in demand in the chemical and oil industries, for which data on the kinetics of the spatial redistribution of the dispersed phase are of considerable applied impor� tance. For example, a change in the specific surface area of emulsions due to coalescence of drops can lead to noticeable variations in chemical reaction rates, including the emulsion polymerization kinetics. This should be taken into account in designing industrial dispersers and mixers. At the same time, in production and transportation of petroleum products containing a certain amount of water, phase separation processes can give rise to discontinuous water domains or con� tinuous water streams along the lower generatrix of pipelines [1, 2]. The presence of dissolved gases, e.g., CO2 and/or H2S, leads to accelerated development of pitting or groove corrosion [3–6], which is fraught with service life reduction and even breakdown of pipelines. In oil pipelines, water dispersions deposit in a flow of a medium. The combination of these processes can change the segregation kinetics of components of the medium in comparison to the deposition kinetics at rest. In particular, this can be caused by variations in the drop collision frequency and drop shape, which, in turn, influence the coalescence conditions and, hence, the deposition velocity. Numerous studies were made of sedimentation of liquid and solid dispersions in flows of air and gases, river streams, ocean currents, and also oil transportation [7–10]. However, this chal� lenge continues to be in the limelight. Specifically, this is highly topical for representative sampling during