CAPITULO 3. IMPLEMENTACIÓN DEL MODELO EN UN CASO DE ESTUDIO
3.3 FASE 3: EJECUCIÓN
3.3.2 DESARROLLO DEL PROCESO DE GESTIÓN DE INCIDENTES Y GESTIÓN DE REQUERIMIENTOS
Work carried out by several researchers (Sprow, 1967; Bamea and Mizrahi, 1975;
Calabrese et ai, 1986; Lagisetty et ai, 1986; Kumar et a i, 1991; Boye et al, 1996) has
shown that the viscosity of two-liquid phase dispersions can be approximated to the
viscosity of the continuous phase for low dispersed phase hold-ups. However, as the
structure of the dispersion becomes increasingly complex (with increased phase hold-up)
this assumption is not appropriate in describing the fluid flow properties. Earlier
attempts by Ostwald (1925) to relate the flow properties of a liquid dispersion to its
structural viscosity revealed that in a certain range of shear rate values, most dispersions
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this behaviour was that of extensive flocculation produced by prevailing attraction
between the drops. The Ree-Eyring reaction rate theory (1955) based on this premise
concluded that the dispersion viscosity is simply a sum of the contributions of several
flow units present in the liquids. Although this theory was suitable for describing non-
Newtonian behaviour, it proved difficult in relating the parameters to the structural
properties of the dispersion.
van den Tempel (1963) later proposed the theory of steady state viscosity of dispersions
based on Goodeve's (1939) impulse theory and much later the “immobilized liquid in
aggregate” theory developed by Mooney (1946), Vand (1948) and Albers and Overbeek
(1960) to account for the effects of aggregation on the dispersion flow properties.
According to the impulse theory, the presence of net attractive forces between the drops
resulted in the formation of a “scaffolding structure”, in which neighbouring drops
connected by links were constantly broken and reformed in steady-state flow. It suggested
that the force transmitted from one layer of drops to the next, in the sheared suspension,
depended on the breaking strength of the links between the two layers. The breaking
strength was obtained by assuming the links were broken at a rate proportional to their
concentration. Goodeve (1939) derived an expression for the concentration of the links
(formed by flocculation) under steady-state conditions in terms of drop linkage strength
and system geometry, van den Tempel (1963) was able to show that the rate of drop
aggregation could be obtained from the kinetics of flocculation.
The theory of immobilised liquids later examined the effect of flocculation on the viscosity
due to the apparent increased volume of the dispersed phase entrapped in the aggregates.
Mooney (1946) and Vand (1948) observed that even in the absence of drop interaction,
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liquid. Vand (1948) was able to calculate the amount of liquid immobilised in the
temporary doublets and the increased viscosity resulting from these collision doublets was
found to be in good agreement with experimental observation.
In cases where flocculation occurs as a result of predominant attraction between the
drops, the concentration of aggregated drops was observed to be much higher than those
due to collision only. This effect of drop aggregation on viscosity was described by
assuming that only hydrodynamic interaction occurs between the aggregates (with
immobihsed liquid) and the remaining primary drops. The relation between relative
viscosity, r| and dispersed phase for immobilised liquid dispersions in which only
hydrodynamic interaction occurs at any shear rate was first proposed by Mooney (1946).
Using an empirical relation between the relative viscosity and the effective dispersed
volume, (|)q Mooney showed that:
, = ^ S e x p l - * o
^ 1-25(|)„^ l - * o
(2.21)
Mooney deduced that the viscosity of the dispersion was influenced by the rate of
flocculation of the drops. He observed that the rate of thixotropic recovery immediately
after shearing had ceased resulted in a 40-fold increase in relative viscosity after only 10
seconds with an effective dispersed volume of 0.759 (Fig. 2.14). These results were
explained by assuming that aggregation took place in accordance with Smoluchowski’s
theory of slow coagulation. The rate constant appearing in this theory decreased with
increasing shear stress since collisions led to rather weak binary aggregates disrupted at
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volume of aggregates where the swelling factor depends on the size of the more densely
packed aggregates and the shear stress acting on them.
The non-Newtonian viscosity of water-in-oil dispersions was attributed to the immobilised
liquid in the aggregates. Albers and Overbeek (1960) suggested that at sufficiently high
shear rates the hnk between the water droplets in a doublet will break and the dispersion
will become Newtonian. The link will break if the axial component of the hydrostatic
force (<x shear rate, y ) exerted by the sheared liquid of a doublet exceeds the van der
Waals’ force of attraction (Fig. 2.15).
F ■ t f
I
1
(2 bû2
5 4 3 2 t = a t = 1 sec 1 t = 0 0.2 0.4 0.6 0.8E ffective D isp ersed Phase V olu m e, ((}))
Fig. 2.14. Relation between effective dispersed phase concentration, (j)^ and relative
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van den Tempel (1963) observed that as flocculation led to the formation of aggregates,
the effective dispersed phase concentration, (})o increased as the immobilised liquid volume
increased. At constant shear, the relative viscosity of the dispersion depends on the
effective dispersed phase concentration (Eq 2.21).
+ve Electric Repulsion Steric or Bom forces Theoretical curve (4) Distance Net (3) Potential Secondary (2) Minimum
Van der Waals Attraction
-ve Y
Primary (1) Minimum
Figure 2.15. Potential energy diagram for two colliding drops:
(1) the primary minimum; (2) the secondary minimum; (3) the maximum energy barrier; (4) theoretical interaction curve according to Smoluchowski.
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