Mechanical mixing of fluids interpreted as deformation of contact interfaces between materials or originally designated material surfaces, can be described by continuum mechanical arguments. The idea is developed at two levels. Part I: Exact kinematical description of mixing of fluids with negligible interfacial tension. Part II: Description of mixing of fluids with negligible interfacial tension in terms of intermaterial area density. The approach provides a unified mathematical description of the mechanical mixing of fluids.