Abstract
An unusual stress controlled turbulent flow phenomenon observed in aqueous solutions of some derivatives of an unsaturated 18 carbon atom fatty acidis described. Some other unusual viscometric and rheogoniometric properties of these solutions are also discussed.
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Abbreviations
- D :
-
tube diameter
- f :
-
friction factor
- J 0 :
-
observed pressure gradient for soap-free solution
- J p :
-
observed pressure gradient for soap solution
- K :
-
parameter in eq. [9]
- L :
-
tube length
- M :
-
thrust
- n :
-
parameter in eq. [9]
- P 11,P 22 :
-
components of the deviatoric normal stresses parallel to the streamlines and normal to the shearing surfaces, respectively
- Q :
-
volumetric flow rate
- r :
-
radial coordinate
- R :
-
tube radius
- Re :
-
Reynolds number =DV/v
- s :
-
slip velocity, defined by eq. [6]
- u z(r):
-
velocity component
- V :
-
bulk average velocity
- z :
-
distance along axial coordinate
- γ :
-
local shear rate
- ζ(Τw):
-
slip coefficient, defined by eq. [6]
- θ :
-
parameter in eq. [10]
- v :
-
kinematic viscosity of soap-free solution
- ξ :
-
reduced radius defined byξ = r/Rπ = 3.1416
- ϱ :
-
fluid density
- σ :
-
parameter in eq. [10]
- Τ,Τ 12 :
-
local shear stress
- Τ w :
-
shear stress evaluated at tube wall
- (Τ w)c :
-
critical shear stress corresponding to maximum drag reduction
- Τ 11,Τ 22 :
-
total normal stress components parallel to the streamlines and normal to the shearing surfaces, respectively
- ψ 1 :
-
function defined by eq. [13]
- ψ 2 :
-
function defined by eq. [14]
References
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Savins, J.G. A stress-controlled drag-reduction phenomenon. Rheol Acta 6, 323–330 (1967). https://doi.org/10.1007/BF01984629
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DOI: https://doi.org/10.1007/BF01984629