Non-Newtonian fluids v frictional resistance of discs and cones rotating in power-law non-Newtonian fluids

Summary Relations have been derived for the frictional resistance of finite discs and cones rotating in Ostwald-de Waele (power-law) type non-Newtonian fluids. The obtained equations can be formulated as dimensionless relations between the dimensionless moment coefficient and the generalized Reynolds number; the flow-behaviour index n enters the equations as a parameter. The relations derived for cones contain the apex angle 2₀ as an additional parameter in the form of A=sin ₀. The validity of the theoretically derived relations has been verified by measurements of the torque of discs and cones for a number of pseudoplastic power-law fluids.Nomenclature A sin ₀ parameter - b exponent in regression equation (16) - C coefficient in regression equation (16) - c_Mi dimensionless moment coefficient, for bodies wetted on one side (i=1) and for completely wetted bodies (i=2), equations (8) and (9b) - d diameter of turntable - F, G velocity functions of exact solution, equation (4) - K consistency coefficient of non-Newtonian fluids - M_Ki torque of rotating bodies, i=1 for bodies wetted on one side, i=2 for completely wetted bodies - n flow-behaviour index of non-Newtonian fluids - N=K/ kinematic consistency coefficient - P tangential force - r(y) perpendicular distance of point on cone surface from axis - R radius of disc or of base of cone - modified Reynolds number defined by equation (14) - Re_ow generalized Reynolds number defined by equation (10) - S, S area - u, v components of velocity vector - x, y, z coordinates according to fig. 1 - ₀ half the apex angle of cone - coefficient of frictional resistance defined by equation (11) - thickness of boundary layer - independent variable in exact solution, defined by equation (5) - density of fluid - _zx, _zy tangential stresses - angular velocity of rotationIndices T theoretical value - E experimental value - 0 refers to surface of rotating body