Summary
The observed energy dissipation in coagulated sols subjected to a shear flow can be explained by assuming that the basic units of flow are elastic flocs which are slightly deformed during collisions because of the stretching of the particle bonds within a floc by a few tenths of a nanometer. Liquid inside perforated structures is generally considered immobile, but during the deformation of the flocs some internal liquid movement occurs. Although the amount of internal liquid movement is rather small, of the order of 1%, it is sufficient to account for the observed energy dissipation.
Zusammenfassung
Die beobachtete Energiedissipation in koagulierten Sollösungen, die einer Scherströmung ausgesetzt werden, kann durch die Annahme erklärt werden, daß die zugrundeliegenden Fließeinheiten elastische Flocken sind, die während der Zusammenstöße geringfügig deformiert werden, da die Bindungen zwischen den Teilchen in einer Flocke um einige Zehntel eines Nanometers gestreckt werden können. Die Flüssigkeit innerhalb perforierter Strukturen wird im allgemeinen zwar als bewegungslos betrachtet, aber während der Deformation der Flocken findet eine geringe innere Flüssigkeitsbewegung statt. Obwohl diese innere Flüssigkeitsbewegung ziemlich gering, nämlich in der Größenordnung von einem Prozent ist, genügt sie bereits zur Erklärung der wahrgenommenen Energiedissipation.
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Abbreviations
- a, ā; a 1,a f :
-
floc size, average value; average size of a flocculus, of a floc (excluding flocculi).
- A; A i :
-
Hamaker constant of system;\(\prod\limits_{j = 1}^{i - 1} {Kj,} \) K j,j=1 (A 1 = 1)
- B(d 1):
-
function introduced in [5b]
- C FP :
-
φ F/φ p
- d 0,d 1 :
-
distance of closest approach between two spheres, distance at which the attraction forces are maximum.
- D; D 0;\(D_{C_{FP} } \) :
-
rate of shear; rate of shear above which no permanent floc aggregates exist; highest shear rate the system ever experienced.
- E e,E S,E f,E L :
-
energy dissipation during collision due to elastic stretching of bonds, stretching of floc, internal fluid movement in floc, movement of liquid into gap of separating spheres.
- E fS :
-
energy dissipation due to internal fluid movement in a single floc.
- E DR;E V;E tot :
-
energy dissipation due to rupture of floc doublets; to single flocs; total dissipation.
- E i,F i,E h,F h :
-
energy and force associated with spherei, at distanceh from floc center.
- h :
-
distance from floc center
- i, n :
-
integers
- K i :
-
equilibrium constants, associated with floc dynamics.
- n C,n F :
-
number of chains in a floc crossing a unit area in a given direction, number of links per unit area between two flocs forming a floc doublet.
- n S,n b :
-
number of spheres, of bonds in a floc.
- n f,n n :
-
number of flocs, number of flocs consisting ofn flocculi.
- p :
-
volume fraction at close packing.
- Q :
-
force parameter, defined by [5b].
- r :
-
particle radius.
- \(\bar t\) :
-
average lifetime of a floc
- V i,V h :
-
velocity of spherei, at distanceh from floc center.
- v 3 :
-
undisturbed fluid velocity.
- V, ΔV; V *,ΔV * :
-
volume of liquid inside a floc, volume of mobile liquid in a floc; volume of floc, volume of shaded region in fig. 3.
- X i,x i :
-
Cartesian axes and coordinates
- α 0 :
-
orthokinetic capture efficiency
- β :
-
constant (54/10)
- γ, γ * :
-
constant (27/40), corrected forφ p dependence.
- τ δ i :
-
distance of stretching the bonds in a floc; displacement of sphere from floc center.
- Δ (%):
-
percentage difference between exact and approximate ratio of spheres to bonds in a floc.
- ζ :
-
ζ-potential of individual spheres.
- η, η PL;[η] :
-
suspending medium viscosity, plastic viscosity; intrinsic viscosity.
- λ :
-
correction factor to Stoke's law.
- ρ :
-
sphere density in a floc.
- τ; τ B :
-
shear stress; Bingham yield stress.
- φ F,φ p :
-
volume fraction of flocs, of particles.
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van de Ven, T.G.M., Hunter, R.J. The energy dissipation in sheared coagulated sols. Rheol Acta 16, 534–543 (1977). https://doi.org/10.1007/BF01525653
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DOI: https://doi.org/10.1007/BF01525653