p
0 40 80 120
0 1000 2000 3000 4000
Time (s) Good with Heptane
Good with Decane Bad with Heptane
Bad with Decane h
2(cm
2)
48
CHAPTER 3
surface properties, rather than an average value. As real powders may be heterogeneous with a distribution of surface energies, this is the key advantage of this technique. Figure 3.11 shows an example of the distribution of surface energy of coal particles measured by the powder immersion technique.
The critical surface energy may also be determined from the variation of sediment height with the surface tension of the solvent (Vargha-Butler, 1989).
Figure 3.11. Distribution of Critical Solid Surface Energy for a Coal Sample Based on Penetration Tests with Aqueous Methanol Solutions (Fuerstenau et al., 1991)
Chemical Probing of the Powder Surface. Vapour adsorption techniques (organic sorption balance and inverse gas chromatography (IGC)) can be used to give information about powder surface properties without wetting the powder with any liquid. By probing the powder with different solvents, the dispersive and polar contributions of the powder surface energy are extracted.
The IGC technique uses standard gas chromatography equipment with the powder of interest as the packing. The retention time is measured for a number of non-polar and polar vapours. For each probe, the free energy of desorption is:
VN
RT G= ln
Δ (3-13)
This free energy is related to the work of adhesion which is further broken up into dispersive and polar interactions (eqn. 3-4a):
P lv P sv D lv D sv a
N W
V RT
G= ∝ = γ γ + γ γ
Δ ln (3-14)
50
WETTING, NUCLEATION AND BINDER DISTRIBUTION
For an alkane (non-polar) probe, the dispersive surface energy will be given by:
c G∝ svD lvD +
Δ γ γ (3-15)
A plot of ΔGagainst γlv for series of alkane probes will give a straight line. The dispersive component is calculated from the slope of the line using eqn. 3-15. If polar probes are used, the measured ΔG will fall above the reference line for alkanes and distance above the line is the polar free energy contribution. Thus, the polar contribution to the solid surface energy is calculated as:
P lv P sv D
P G G
G =Δ −Δ ∝ γ γ
Δ (3-16)
Figure 3.12 gives an example of calculating the dispersive and polar surface energy components for a glass powder using IGC. Having calculated γ svD and γsvP , the contact angle and solid-liquid surface energy for the powder with any other solvent can be calculated from eqns. 3-4a and 3-5.
This technique is potentially very powerful in matching powders and binders. It does rely heavily on the mixing rule for the polar and non-polar interactions (eqns. 4a and 3-14). The non-polar term has a fundamental basis. However, the polar interaction is entirely empirical. Nevertheless, the work of adhesion with standard polar and non-polar probes provides a fast and reproducible method of ranking powders and identifying batch to batch variability in surface properties.
The polar and non-polar surface energies can also be obtained from a series of Washburn tests using a variety of polar and non-polar solvents (Zisman, 1964). This approach is much more tedious, however, and cannot be used if the powder dissolves in some of the reference solvents.
Charges may also exist at interfaces. In the case of solid-fluid interfaces, these may be characterized by electrokinetic studies (Shaw, 1983).
51
CHAPTER 3
Figure 3.12. Measurement of Interfacial Properties of a Glass Powder by IGC
3.2. Wetting and Nucleation Regimes for Granulation
Section 3.1 established techniques for characterizing the wetting behaviour of powders. To use this information for our granulation processes, we must first identify conditions that will ensure good nucleation. Consider the nucleation process described at the start of the chapter and illustrated in figure 3.1. We arbitrarily break down the nucleation possibilities into three regimes:
1. Droplet controlled: Each individual drop wets completely and quickly into the powder bed to form a single nuclei granule. The nuclei size distribution is essentially controlled by the drop size distribution.
2. Shear controlled: Liquid pooling or caking occurs where the spray meets the bed.
Binder distribution occurs only by breakage of lumps or granules due to shear forces Dispersive Surface Energy of Glass
(T = 40°C)
0 5 10 15 20
0 100 200 300 400
MeO THF Aceton
B Chl
C1 C3
C7
C10 C9
C8
C5 2N(γs
D)1/2
Δ
G = RT Ln(V
N
) [kJ/mol]
a(γL
D)1/2 [Å2mJ1/2 /m]
γs
D = 24.4 dyn/cm ΔGP for Acetone
{
γ γD γP α A DN Polar
Liqui Notatio 2 Character
Pentan C 16.0 16.0 0 46. -
-Heptan C 20. 20. 0 5 -
-Octan C 21.6 21.6 0 62. - - Neutra
Nonan C 22. 22. 0 68. -
-Decan C1 23.8 23.8 0 75. -
-Benzen B 28. 26. 2. 4 8. 0. Acid
Chloroform Chl 28. 26. 1. 4 8. 0
THF THF 26. 22. 4 4 8 2 Bas
Methano MeO 22.4 1 4.4 26. 41. 1 Amphoteric
Aceton Ac 2 2 4 28. 12. 1
2 (Å) (-
(-(mJ/m ) (mJ/m ) 2 (mJ/m ) 2 ) )
52
WETTING, NUCLEATION AND BINDER DISTRIBUTION
within the powder bed and the “nuclei” size distribution is independent of the drop size distribution.
3. Intermediate: This regime is intermediate between droplet controlled and shear controlled. Some agglomeration does occur in or near the spray zone without complete caking or pooling. The nuclei size distribution will be sensitive to many formulation properties and operating parameters.
Wetting thermodynamics, wetting kinetics and the ratio of powder to liquid fluxes in the spray zone will all influence the nucleation regime. Ideally, we would like to operate in the drop controlled regime. It is much easier to control the size (and size distribution) of drops from a spray nozzle than it is to mechanically disperse the liquid through the bed.
Only mixer granulators have any chance of achieving good mechanical dispersion.
To achieve drop controlled nucleation, two conditions are required:
1. Drops penetrate into the bed quickly and do not roll on the bed surface and contact other drops.
2. Drops overall on the powder surface is minimal.
Drop penetration rate is set by wetting thermodynamics and kinetics and primarily influenced by formulation properties. Drop overlap is related to the flux of drops hitting the powder surface and is set by operating parameters. We will consider each of these phenomena in turn.
3.2.1. Drop penetration into powder beds
Theoretical prediction of drop penetration time. Consider a drop hitting the loosely packed, moving powder bed surface in a tumbling or mixer granulator. How long will this drop take to penetrate into the powder bed and what is the effect of formulation properties on penetration time?
We can imagine the porous powder bed as consisting of a series of capillary pores. For a drop to penetrate the pores, the contact angle between the liquid and the powder must be less than 90º (wetting thermodynamics). If this is so, drop penetration is driven by capillary suction and the rate at which liquid penetrates the pore is given by the Washburn equation (see eqns. 3-7 to 3-9 and figure 3.8).
Consider a drop of volume Vd hitting the powder surface. The drop will have a circular footprint on the surface of radius:
3 / 1
4 3 ¸
¹
¨ ·
©
=§ πd
d
r V (3-16)
The rate at which the liquid flows from the drop is:
v dt r
Q= dV =πd2ε (3-17)
53
CHAPTER 3
where İ is the powder bed voidage. The average velocity in the pore
v
is given by the differential form of the Washburn equation:t
Combining eqns. 3-17 and 3-18 and integrating gives the penetration time ie. the time for the total volume of drop to penetrate the bed:
θ
This equation was derived separately by Middleman (1995) and Denesuk et al. (1993).
There are many assumptions made in this derivation but the key one is assuming the total voidage of the loosely packed powder bed is present as uniform cylindrical pores. With this assumption, the pore radius can be the bed voidage and the specific surface mean particle size:
This Kozeny model for the bed voidage is reasonable for a tapped powder bed in random close packing. However, a loosely packed bed of fine powder has very heterogeneous voidage distribution. Hapgood et al. (2003) divided the voidage into two parts: micropores and macrovoids (see figure 3.13). Liquid will flow through the micropores, but there is no capillary driving force for the liquid to flow into the expanding macrovoids. In effect, the liquid does not see the macrovoids. Using the Kozeny approach will overestimate both the voidage and the pore size seen by the penetrating fluid.
Hapgood introduced an effective voidage İeff. If we assume all the voidage above the tapped bed voidage is present as macrovoids, then the effective bed voidage for capillary driven flow is:
)
The effective pore size seen by the liquid is the average micropore size:
eff
WETTING, NUCLEATION AND BINDER DISTRIBUTION
and the drop penetration time is:
θ γ
μ
ε cos
35 .
1 2
3 / 2
eff lv eff
d
p R
t = V (3-23)
Eqns. 3-21, 3-22 and 3-23 allow us to calculate the drop penetration time from measurable properties of the powder and liquid binder.
Figure 3.13. Heterogeneous packing of particles in a loose powder bed.
A drop on the powder surface will penetrate the micropores by capillary action but stops where the pore expands into a macrorvoid
Experimental measurement of drop penetration time. Hapgood et al. (2002) did an extensive study of drop penetration into loosely packed powder beds. It is a relatively easy experiment to perform, similar to the contact angle goniometry (figure 3.6). A carefully metered single drop is placed on a carefully prepared powder surface and the time for complete penetration of the drop is measured (see figure 3.14).