6 SURFACE TREATMENT OF PAPER 6,1 Why coat paper?
6.3 Rheology .1 Steady shear
As stated above, coating rheology is of utmost impor-tance for runnability. It will, to a large extent, deter-mine pressure changes and forces at the blade/roll, and the relaxation of the colour after its brief residence in the coating head. Moreover, we can use rheologi-cal measurements as a tool to investigate interactions in coating suspensions and thus engineer desired out-comes. From a rheological point of view, coating colours are highly non-trivial in nature, displaying a compli-cated rheological response to external stresses, as is
typical of highly concentrated particulate suspensions.
An excellent reference for those new to the rheology of complex fluids is the text by Larson (37).
The nature of shear stresses in the coating process, including the delivery to the coating head, application at the nip, and the drying stage, are extremely complex.
Laboratory methods must be judiciously chosen in order to either mimic these conditions as best as possible so as to evaluate performance in a controlled manner, or alternatively provide other information regarding coat-ing microstructure which can then be "fine-tuned". In the latter category are low shear-rate measurements in laboratory rheometers based on cell geometries such as the cone-plate, plate-plate or concentric cylinders, employing controlled shear or controlled stress mecha-nisms, and also capillary viscometers. The latter in turn are also used to make high-shear-rate devices, where the suspension is driven into the capillary under pres-sure. Alternatively, some pressure-driven devices use slit geometries in order to simulate the blade coater.
Coating colours, as one would expect from their com-position, are in general non-Newtonian fluids, so that the steady-shear viscosity r\(y) is shear rate-dependent, for a given shear stress a\
T](y) = ay (7.10) This is not simply because of the presence of rheology modifiers or other polymers; a simple NaPA-stabilized GCC suspension will also show a plastic-like behaviour.
Typically, this involves the suspension behaving like a solid at low shear rates and stresses, and only "yielding"
to liquid-like behaviour above a certain yield stress ay. This behaviour can be modelled in various ways, with two common ones being the Bingham:
o=oy + r)vxY (7.11) and the Casson:
«r'/2 = ff>/2 + ^ . / 2 ( l l 2 )
models, where r)v\ is the plastic viscosity.
For such materials, the steady-shear viscosity decreases with increasing shear rate, y. This is known as "shear-thinning" and is in itself a vitally important feature for the coating process: without shear thinning, coating colours would be difficult to handle at low shear (i.e. pouring or pumping) and would have severe runnability problems at the high shear rates present at the coater. Shear thinning can be understood in terms of the formation of layers of particles (layered in the flow direction) in the sheared suspension; in other words, shearing induces a suspension structure which reduces resistance to further shearing. An elegant example of this was in fact shown with clay particles sheared in a cuvette cell and examined by neutron scattering, whereby the suspension microstructure can be inferred (38), as shown in Figure 7.29. Indeed, increasing shear rate indicated the breakdown of clay particle "domains" and the formation of conveniently oriented layers as y was increased. While this is conceptually appealing for plate-like clays, it also occurs for other particles (such as GCC). An important quantity in the consideration of phenomena such as shear thinning is the Peclet number, Pe = a2y/Do, where a is the mean particle radius and DQ the diffusion constant. Essentially, the shear rate must be such that the particles do not have time to diffuse back to their equilibrium mean positions, so that shear thinning is expected when Pe > 1. The opposite effect, shear thickening, is speculated to be, conversely, the result of the induction of an increasingly unfavourable suspension structure with increasing shear rate. This may occur, for example, when the layers induced through shear thinning are broken up at higher shear rates. Clearly, shear thickening can cause severe runnability problems in the coating process if it occurs at unfavourable shear rates. The characteristic behaviour of non-Newtonian fluids is illustrated in Figure 7.30. Indeed, similar particles, but with different size distributions, can behave very differently in the same shear-rate interval (the appearance of the radius a in the expression for Pe
Figure 7.29. Schematic representation of shear thinning of clay particles. (Taken from ref. (38))
v v
Y
Figure 7.30. Generic Theological behaviour of non-Newtonian fluids - shear stress versus shear rate
could indicate why). However, this might be used to advantage: Alince and Lepoutre (39) showed how two GCC populations, one shear thickening and the other shear thinning, might be combined to give, remarkably, a nearly Newtonian suspension of relatively low viscosity.
(It should be remarked, however, that this may not be a general phenomenon, and also difficult to implement in practice.)
An important property from both a bulk rheological and microstructural point of view is the relative plastic viscosity:
r]r = r]pi/r]o (7.13) where T]0 is the viscosity of the liquid phase, which depends on the volume fraction of solids 0. A num-ber of semi-empirical models exist, one being the Krieger'-Dougherty (KG) equation, which accounts for viscosity increases with 0 through a mean-field approx-imation, while accounting for the divergence in T]x at the maximum packing fraction rjm empirically, as follows:
V 0m/
where [rj] is the intrinsic viscosity (or shape factor) of the particles. An example of such a plot is given in Figure 7.31. Not only do plots of rjr against 0 give important information about viscosity increases with solids content, but they can also be used to investigate structure formation in particulate suspensions. If floccu-lation has been induced in the system, such as through the introduction of salt or through a polymeric mecha-nism, then the impact upon the viscosity of these floes may be inferred by the replacement 0 —• 0f in the KG
o
Figure 7.31. Volume-fraction dependence of relative viscosity for a suspension of calcium carbonate dispersed with NaPA
equation, where 0f is the volume fraction of floes. This leads to the definition of aflocculation index, as follows:
Ct = <k/4> (7.15) which characterizes the extent of flocculation in the system.
6.3.2 Viscoelasticity
An alternative to a steady-shear measurement is oscilla-tory shear, described in the linear regime by the follow-ing:
o(t) = Yo [G'((o) sin(<»0 + G"(co) cos(<wf)] (7.16) where the sample is sheared at an oscillatory frequency a) and strain amplitude yo, and the storage modulus G' and loss modulus G" respectively indicate the degree of elastic response to, and viscous dissipation of, the time-dependent shear stress o(t). This type of measurement is useful because it can indicate the nature of relaxation processes acting with the suspension, through the Deborah number, given by the following:
De = TO) (7.17) where r is a characteristic relaxation time. As a>
is increased, the elastic nature of suspensions often decreases and the viscous nature increases. The suspensions start to behave more like fluids. Note that increasing o) is akin to reducing an "impulse time". If G' and G" cross over at a given o), then that may indicate a value of r, the shortest time-scale on which restoring forces act in the system.
Coating colours do indeed show viscoelastic behaviour; however, estimating z for such materials is CTy
Bingham plastic
^r
Shear
thickening Newtonian
Shear thinning
not straightforward, as relaxation processes appear to occur on many time-scales, and the G' and G" moduli rarely cross over. Triantafillopoulos (40) has reviewed viscoelasticity in paper coatings. He suggested that a more straightforward method may be to determine the time it takes for the shear modulus to drop to a predetermined value. Such measurements by several authors indicate that 0.1 < r < 1 ms, and since in practice the impulse time at the nip is of the order of 10~5 s, we can assume that for coating colours, De ^> 1. The consequence of this is that coatings may behave more like elastic solids than fluids at the blade.
Furthermore, large values of G' indicate that there may be insufficient time for the colour to relax at the nip, so that coating thickness is affected by elasticity; in addition, partial recovery before drying may preserve non-uniformities and defects.
A useful manner in which to quantify the relative contributions of elastic and viscous effects is through the loss angle 8, as follows:
tan<5 = G' IG" (7.18) with larger values of 8 indicating a relatively more viscous, as opposed to elastic, material. One neat conclusion that can be drawn from such an analysis (40) is that GCC coatings are generally more viscous in character than their relatively elastic clay counterparts;
this again may well be an indication of the role of particle morphology in determining the rheological properties. The elastic nature of clay suspensions could be related to the domain formation alluded to previously, or indeed the often-postulated "house-of-cards" structure which may form at low pH values. In practice, this viscoelastic information may well indicate why clay and carbonate-based coatings can have quite different responses to the impulse at the coating nip under the same mechanical conditions.