title: Stokes problems for moving half-planes.
abstract: New exact solutions of the Navier-Stokes equations are obtained for the unbounded and bounded oscillatory and impulsive tangential edgewise motion of touching half-infinite plates in their own plane.  In contrast to Stokes classical solutions for the harmonic and impulsive motion of an infinite plane wall, where the solutions are separable or have a simple similarity form, the present solutions have a two-dimensional structure in the near region of the contact between the half-infinite plates.  Nevertheless, it is possible to obtain relatively simple closed-form solutions for the flow field in each case by defining new variables which greatly simplify the r- and theta- dependence of the solutions in the vicinity of the contact region.  These solutions for flow in a half-infinite space are then extended to bounded flows in a channel using an image superposition technique.  The impulsive motion has application to the motion near geophysical faults, whereas the oscillatory motion has arisen in the design of a novel oscillating half-plate flow chamber for examining the effect of fluid shear stress on cultured cell monolayers.
authors.affiliation: Department of Mechanical Engineering, The City College of the City University of New York 10031, USA.
authors.forename: Y
authors.initials: Y
authors.lastname: Zeng
authors.forename: S
authors.initials: S
authors.lastname: Weinbaum
mesh_terms: D000818:Animals; D001696:Biomechanical Phenomena; D018929:Cell Culture Techniques / Q000379:methods; D008433:Mathematics; D019563:Mechanics; D008962:Models, Theoretical; D010011:Osteocytes / Q000502:physiology*; D055585:Physical Phenomena; D010825:Physics; D013314:Stress, Mechanical