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Capillary Flows with Forming Interfaces explores numerous theoretical problems that arise in the mathematical description of capillary flows. It focuses on developing a unified approach to a variety of seemingly very different capillary flows of practical importance where classical fluid mechanics leads to nonphysical results. The book begins with a review of the conceptual framework of fluid mechanics and then proceeds to analyze the roots of singularities, such as the moving contact-line problem and the capillary breakup problem. The author then examines how different singular flows can be described as particular cases of a general physical phenomenon of interface formation. He illustrates the developed mathematical models and experimentally verifies them through a number of example problems relevant to engineering applications. The conceptual framework provided in this reference enables further progress in developing mathematical models of capillary flows. The book also allows readers to make informed strategic choices regarding available numerical codes and the in-house development of these codes.