Abstract
Near the mouth of a liquid—filled hole in a rigid wall over which liquid undergoes shear flow, the stream surfaces are curved, appearing convex when viewed from the hole base (Fig. 11.1). For the particular case of creeping flow of a Newtonian liquid past the mouth of a transverse slot,1 the local stream surfaces are symmetric with respect to reflection in the hole center plane (Figs. 11.1, 11.6(a)). As the Reynolds number Re is increased from zero, asymmetry develops,3 with the stream surfaces being deflected in the flow direction in the sense shown in Fig. 11.6(b). For non—Newtonian liquids, 2,3 similar stream surface patterns are found, but there is, in addition, a tendency for the asymmetry to develop in the opposite direction, presumably due in some way to the elasticity of the liquid, or to the shear rate dependence of viscosity. Near the hole mouth, there is a dividing stream surface separating the liquid into two zones; between this surface and the hole base, one or more vortices occur, and the fluid velocities are very small.
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Abbreviations
- a(T) :
-
time temperature shift function
- b :
-
hole diameter or slit width parallel to main flow direction
- h 2 i :
-
diagonal components of metric tensor for the coordinate system y i of Fig. 11.6
- h, w :
-
height and width of slit die cross-section
- L*:
-
defined by eqn (11.40)
- n :
-
d log P*e/d log σ
- N 3, ß:
-
N1 + 2N2, N2/N1
- P 1, av P 2, P 3 :
-
pressures measured with flush-mounted and two hole-mounted transducers
- P*:
-
P 1, av P 2 (‘hole pressure’)
- P*f :
-
contribution to P* from finite width effects in flush mounted transducer
- P*i, P*e :
-
inertial and elastic contributions to P*
- P*N :
-
value of P* — P*ffor a Newtonian liquid
- p ij (i = 1, 2, 3):
-
physical components of stress for the orthogonal coordinate system yi
- r, R :
-
distance from axis, and gap radius in cone-plate rheometer
- Re:
-
ρbhγ/ (4η) (Reynolds number)
- T :
-
absolute temperature
- X r :
-
ρ。T。X/(ρT) (X = (σ, σp, N i, P *e‘reduced stress’)
- z :
-
distance between holes
- γa :
-
approximate wall shear rate in slit die rheometer
- γr :
-
γa(T)(‘reduced shear rate’)
- η, η s :
-
solution or melt viscosity, solvent viscosity
- ηrel :
-
η/ η s (relative viscosity)
- ρij :
-
principal radii of curvature for the γi coordinate surfaces of Fig. 11.6
- ρ, ρ。 :
-
densities at temperatures T, T 。
- σ, γ, N1, N2 :
-
shear stress, shear rate, 1st and 2nd normal stress differences in unidirectional shear flow
- σp :
-
σ — ηsγ (polymer contribution to shear stress)
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© 1993 Springer Science+Business Media Dordrecht
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Lodge, A.S. (1993). Normal Stress Differences from Hole Pressure Measurements. In: Collyer, A.A., Clegg, D.W. (eds) Rheological Measurement. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2898-0_11
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