The simplest model flow which approximates the extrusion (shallow scre
w channels) and lubrication flow is the steady, laminar flow occurring
between two infinitely long parallel plates i.e., the generalized pla
ne Couette flow. Here we develop an analytical model of the generalize
d plane Couette flow of viscoplastic fluids. The deformation and flow
behavior of viscoplastic fluids can be realistically represented with
the Herschel-Bulkley constitutive equation, which we have utilized as
the basis for the development of our analytical model. Furthermore, as
also demonstrated here, the deformation behavior of viscoplastic flui
ds is generally complicated by the presence of wall slip at solid wall
s, which occurs as a function of the wall shear stress. The wall slip
versus the wall shear stress behavior of viscoplastic fluids can be ex
perimentally characterized using viscometric flows, including steady t
orsional and capillary flows. Thus determined Navier's wall slip coeff
icient can then be utilized in modeling of processing flows. In our an
alytical model of the generalized plane Couette flow of viscoplastic f
luids the Navier's wall slip boundary condition was included. This mod
el should be an important engineering tool, which provides design expr
essions for the extrusion and lubrication flows of viscoplastic fluids
, with or without wall slip occurring at the walls.