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Analytical determination of process windows for bilayer slot die coating.

Abstract Slot die coating is a film casting process with a highly diverse variety of everyday applications. As a pre-metered process it not only guarantees excellent film uniformity, but is also suitable for simultaneously applied multilayer coatings. Characteristic singularities like the behavior of the liquid-liquid interface and the impact of the additional mid-lip on film uniformity were already investigated before. However, the effect of an altered gap pressure regime on commonly used coating windows has not yet been discussed. In this work, we therefore extended available single-layer coating windows for Newtonian and power-law liquids to the bilayer case. Here, the emphasis was laid on the air entrainment limit. Subsequently, the theoretical results were compared to experimental data. It was found that the onset of air entrainment strongly depends on the top to bottom film thickness ratio for bilayer coatings. A critical film thickness ratio which delivers similar coating limits as those for single-layer coatings was derived and confirmed by experimentally gained results.

Keywords Multilayer, Bilayer slot die coating, Process window, Non-newtonian flow, Lithium-ion batteries


Slot die coating is a widely used coating method for the application of uniform films. (1,2) Since many film shaped products consist of a stack of several layers, it is reasonable to produce them simultaneously to increase economic rationality. (3) Slot die coating offers this possibility of coating multiple layers with different involved fluids at the same time, as it is a pre-metered process. (1)

Regarding the coating of complex lithium-ion battery (LIB) slurries, the advantages of subdivided layers are broadly scattered. On the one hand, it is conceivable to pre-distribute additives and binder components by the combination of different slurries. In doing so, a decreased weight and an improvement of the cell performance could be obtained. On the other hand, even different active materials could be combined in only one electrode which also could enhance the performance of the final battery (see Fig. 1; right).

Concerning pre-distributed film morphologies, the different layers are not expected to mix during their application. Due to always prevalent laminar conditions, a convective mixing in the coating gap only appears for exceptional cases. Here, disturbing vortices and fluctuations of the liquid separation line could emerge during a mid-gap invasion. (3) Nevertheless, the transport mechanisms of the film-drying step on polymeric components and sub-pm particles should not be neglected. Experiments showed a re-distribution of those components for multilayer LIB-coatings which will be described elsewhere.

Homogeneous coatings can only be obtained within certain coating limits. (4) For economic reasons the most interesting limits are the maximum possible coating speed for a given film thickness and vice versa a minimum film thickness for a given speed. Nonetheless, these limits cannot simply be transferred from a single layer to a bilayer process. All characteristics of the changed flow field have to be taken into consideration.

In previous studies, it was shown that two-layer LIB coatings offer a smaller process window compared to single-layer films. (5,6) In both cases, single-layer and bilayer coatings, air entrainment from the upstream direction occurred as the dominating coating limit, which is strongly related to the coating bead stability. This stability is given when the bead pressure regime in the gap equals the applied outer pressure conditions. (1) Available publications in the field of bilayer slot die coatings include numerical investigations and complex models to describe the flow inside the coating bead. (7,8) Further publications are additionally focusing on the movement of the separation line. (3) However, the impact of subdivided coatings on the limiting onset of air entrainment has not yet been discussed. Thus, the main goal of this work is the development of a model which is capable of comparing the coating windows of single-layer applications with those of the bilayer case. To this end, the liquid pressure field was simplified by reducing it to a 1-dimensional problem. Furthermore, it is desirable to expand this model to shear thinning liquids such as LIB slurries in order to explain the previous observations with a special regard to the air entrainment limit.

Calculation of the single-layer coating bead pressure

For introducing a 1-dimensional analytical pressure model inside the coating gap of a slot die, some simplifications have to be made. Initially only a pressure gradient into the x or length direction is assumed. This excludes any liquid-liquid interactions into the z or height direction in the bilayer case. For the area beneath the feed slot, we also neglect any change in pressure. Moreover, a completely wetted downstream gap (the area beneath the downstream lip) and planar gap geometries were presumed.

In a first step the derivation will be applied to the well-known single-layer coating. Thus, a schematic sketch of a single-layer slot die gap with all relevant parameters is shown in Fig. 2.

As described in literature, the feed slot divides a single-layer coating gap into a downstream and an upstream gap. Within the downstream gap there is a superposition of the web-driven Couette flow and the pressure-induced Poiseuille flow. Thus, the overall coating bead pressure gradient [DELTA][p.sub.DU] shall be composed by the single sections including the capillary pressure at the interfaces.

[p.sub.D] - [p.sub.U] = [DELTA][p.sub.DU] = [DELTA][p.sub.D1] + [DELTA][p.sub.12] + [DELTA][p.sub.23] + [DELTA][p.sub.3U] (1)

The variable shape of the upstream meniscus and its two fixed locations results in four discrete cases for equation (1). In Fig. 3 a schematic drawing of the four upstream coating bead variation is presented.

Hence, literature delivers the following four expressions for Newtonian single-layer coatings (1,9,10):



Case 3 [DELTA][p.sub.3U] = 1.34[Ca.sup.3./4] [sigma]/h + (1 - 2h/[h.sub.G])(6[eta][u.sub.w][l.sub.D]/[h.sup.2.sub.G]) + 2[sigma]/[h.sub.G] (4)

Case 4 [DELTA][p.sub.DU] = 1.34[Ca.sup.2./3] [sigma]/h + (1 - 2h/[h.sub.G])(6[eta][u.sub.w][l.sub.D]/[h.sup.2.sub.G]) + 2[sigma]/[h.sub.G] (5)

For the liquid-gas interface at the downstream edge, the expression for the capillary pressure within a film forming surface of Ruschak (11) was applied. At the upstream meniscus a simple capillary pressure gradient in dependence to the gap height was assumed. Since the meniscus could be formed convex or concave this term is either positive or negative. Higgins (10) developed for both interfaces more detailed models. Since their deviation may be small and they require more information about the liquid-gas interaction we retained the simplified expressions.

For Cases 1 and 2, respectively, the equations (2) and (3) define limits for a stable located coating bead, where the upstream gap is wetted and the upstream meniscus is pinned at the upstream edge (shown in Fig. 3). If the resulting bead pressure gradient increases above equation (2), the liquid gets pushed out at the upstream lip. If it decreases beneath (3), the meniscus is no longer pinned at the upstream corner and starts moving toward the feed slot. Within the Cases 3 and 4, respectively, the equations (4) and (5), the upstream meniscus is pinned at the upstream corner of the feed slot. If the pressure gradient decreases below equation (5) the upstream meniscus can no longer bridge the gap and air entrainment occurs. Beyond this limit the coated film will be enforced by defects. For a pressure gradient increasing beyond equation (4), the meniscus again starts moving toward the outer edge of the upstream lip. For a pressure gradient in between equations (3) and (4), the upstream meniscus has no fixed point on which to be pinned. Here, the meniscus is susceptible to external disturbances, which might affect film uniformity. However, homogenous coatings are possible in this region until the process is limited by the low-flow mechanism which is described elsewhere. (12-14)

In industrial production there are many coating liquids with a non-Newtonian viscosity behavior, such as polymeric solutions or dispersions. In previous works on LIB coatings, we showed their monotonic shear thinning character in the relevant range of shear rates. (15-17) This behavior can be described very precisely by a power-law approach

[eta] = [kappa][[??].sup.[epsilon]-1] (6)

where the shear rate could approximately be described by:

[??] = [u.sub.W]/[h.sub.G] (7)

Tsuda (18) and Lee (19) solved the resulting complex equation of motion of fluids following the power-law approach. For the single-layer coating bead Lee describes two expressions for the downstream pressure gradient (19):



As in equations (2)-(5), the wet film thickness in the downstream pressure drop represents the net flow in the considered area. For the upstream gap, the net flow of zero again results in a differing expression to:

[DELTA][p.sub.23] = [l.sub.U] x [kappa] x [(([epsilon] + 1)(2[epsilon] + 1)/[epsilon]).sup.[epsilon]] [h.sup.- ([epsilon]+1]).sub.G] x [u.sup.[epsilon].sub.W] (10)

Describing the capillary pressure for the downstream meniscus, the capillary number is now a function of the shear rate (20):

Ca = [kappa] [u.sup.[epsilon].sub.w]/[sigma] x [h.sup.[epsilon]-1].sub.G] (11)

Although Ruschak's expression was derived for Newtonian liquids, we assume only minor deviations, due to relatively high wet film thickness h.

For film stability reasons the wet film thickness in coating LIB electrodes is mostly selected close to the gap height. Thus, equation (8) represents the pressure difference beneath the downstream lip in the following calculations. Combining equations (8)-(11) with (1) the four stability cases of a power-law coating bead and h>[h.sub.G]/2 are:





Calculation of the bilayer coating bead pressure

Deriving the four stability cases for bilayer coatings, all its singularities have to be taken into account. In Fig. 4 a schematic sketch of a bilayer slot die gap with all relevant parameters is plotted.

Due to the pre-metered nature of this process, the wet film thickness has to equal the specific feed volume. For the bilayer slot die coating the resulting wet film thickness consequently arises from the combination of top and bottom layer feed and thus their film heights:

h = [q.sub.B] + [q.sub.T]/[u.sub.W] = [h.sub.B] + [h.sub.T] (16)

To substitute the individual film heights we introduce a ratio:

m = [h.sub.T]/[h.sub.B] (17)

Describing the coating bead pressure [DELTA][p'.sub.DU] for bilayer applications, there is a new pressure gradient [DELTA][p'.sub.23] beneath the mid-lip. Here, the net flow is reduced to the specific bottom layer flow rate [q.sub.B]. With a substitution of the flow rate by (16) and (17), the pressure difference becomes:

[DELTA][p'.sub.23] = (1 - 2h/[h.sub.G] 1/(1 + m))(6[eta][u.sub.w][l.sub.M])/[h.sup.2.sub.G]) (18)

Compared to the single-layer application in equation (1), the summarized pressure drop for bilayer slot die coatings has to be extended to:

[DELTA][p'.sub.DU] = [DELTA][p'.sub.D1] + [DELTA][p'.sub.12] + [DELTA][p'.sub.23] + [DELTA][p'.sub.34] + [DELTA][p'.sub.4U] (19)

Similar to equations (2)-(5) the two pairs of stability limits are:





Similar to the Newtonian calculation there is an additional mid-lip pressure gradient [DELTA][p'.sub.23] for bilayer coatings. By a substitution of the bottom layer film height via (16) into (9), the mid-lip pressure gradient for [h.sub.B] < [h.sub.G]/2 is expressed as:


whereas for [h.sub.B] > [h.sub.G]/2 the equation can be derived similar via (16) and (8).

Combining (24) with equations (12)-(15) describes the four limiting cases for power-law bilayer coatings with h > [h.sub.G]/2 and [h.sub.B] < [h.sub.G]/2:






In order to compare the coating windows of Newtonian and power-law liquids as well as single-layer and bilayer coatings, we applied the values in Table 1 to the equations (2)-(5), (20)-(23), (12)-(15), and (25)-(28).

Based on the above set of standard parameters, the Newtonian viscosity [[eta].sub.1], was selected to compare with the power-law data measured for a typical LIB anode slurry ([u.sub.w] = 5m/min; [??] [approximately equal to] 650 1/s; [eta]([??]) [approximately equal to] 0.45mPas). (5) Due to this assumption the comparison between Newtonian and power-law calculations for various speeds is mostly valid close to 5 m/min. The Newtonian calculations themselves were compared with coating results of an available Newtonian silicone oil (Rotitherm[R] M 220) with a viscosity [[eta].sub.2] and [h.sub.G,2]

For the validation of the calculations, an available experimental set-up (15) was applied. For one, respectively, two highly precise syringe pumps (CHEMYX, Nexus 6000) fed the slot dies with coating widths [w.sub.Die] of 60 mm. For both, the single-layer and the bilayer slot dies were self-constructed with the dimensions plotted in Table 1. During the experiments they were arranged in 8 o'clock position against a stainless steel roller with a diameter of 350 mm. For their optical characterization the films were applied directly onto the roller and bladed off again within one turnaround.

Results and discussion

In Fig. 5 the resulting set of four coating windows, each with the four limiting pressure cases, are plotted.

The coating window for Newtonian single-layer applications in Fig. 5 upper left, describes a typical form for high viscosities and gap to film height ratios [h.sub.G]/h close to unity.

Concluding from equations (2)-(5), the viscosity describes the spreading of the side warded triangle which would be smaller for lower viscosities. In contrast to that, the gap ratio effects the whole orientation of the triangle, which would be turned toward positive pressure gradients for smaller film heights or higher gaps.

As mentioned above, the areas where the upstream meniscus is stable pinned are between Case 1 and 2, respectively, and Case 3 and 4. Since the group of linear pairs is describing an opening triangle by departing from each other, the upstream meniscus is not steadily pinned in the area between Case 2 and 3.

In concrete terms, for [DELTA][p.sub.DU] = 0 the upstream meniscus is only pinned at the outer edge of the upstream lip until 2-3 m/min at all calculations. Again, beyond these speeds the coating bead is fragile against external disturbances but only limited by other mechanisms like the low flow limit. (12-14) Nevertheless, it was shown that it is possible to coat LIB electrodes films far in this "unpinned" area even at higher speeds. (15,16) Remarkably, the most interesting Case 4, representing air entrainment, is orientated in a negative direction. Thus, air entrainment will not appear for this gap ratio at ambient conditions ([DELTA][p.sub.DU] = 0), even toward higher coating speeds.

In Fig. 5 upper right, the same coating window is plotted for a bilayer application where the film is equally split into the top and bottom layer. Due to the small amount of [DELTA][p'.sub.23] for m = 1 in equations (20)-(23) the coating window does not differ much from the single-layer case. In the following paragraphs the influence of m for this case will be discussed in detail.

The orientation of the pairs of limits is slightly turned toward positive pressure gradients. This leads to an earlier air entrainment for decreasing pressure gradients at a given coating speed.

In comparison to the Newtonian calculations, the single and the bilayer power-law coating bead describe similar but non-linear coating limits (see Fig. 5 bottom). For smaller coating speeds there is a strong curvature at all cases. This can be related to the bigger portion of [DELTA][p.sub.D1], respectively, [DELTA][p'.sub.D1] in this region. Due to a smaller exponent set for the speed in the power-law calculations, the impact of this pressure gradient decreases for increasing speeds.

Again the coating window for multilayer coatings is slightly more orientated toward positive pressure gradients.

In previous works, the limiting mechanism of air entrainment occurred for decreasing wet film thicknesses at given speeds. (5,6,15) To characterize its onset, we calculated Case 4 again for a single-layer power-law coating bead (see equation (12)) and certain film heights. The results are plotted for various coating speeds in Fig. 6.

As mentioned above, the orientation of the whole coating window turns toward positive pressure gradients with decreasing film heights. With special regard to Case 4, this results in a crossing of the zero level at a certain coating speed as seen in Fig. 6. Rewording, the upstream meniscus moves beyond its final position at the feed slot for decreasing film heights from 120 to 60 [micro]m where air entrainment occurs.

Thus, being interested in the minimum film thickness at a certain pressure gradient, we have to calculate Case 4 implicitly. To compare our calculation with previous experimental results made without a vacuum chamber, we set the pressure gradients [DELTA][p.sub.DU] = [DELTA][p.sub.DU] = 0. A solver computed the minimum film thickness in dependence to the coating speed. The results for the Newtonian calculations are plotted in Fig. 7.

The results for the Newtonian coating bead (see Fig. 7) show a horizontal gradient beyond speeds of [u.sub.w] [congruent to] 5m/min. Thus, it is not limited by air entrainment for higher film thicknesses.

Without the contributions of the menisci, the minimum film thickness would be h = [h.sub.G]/2 for the single-layer case, to fulfill [DELTA][p.sub.DU] = 0. Nevertheless, for speeds higher than 5 m/min, where [DELTA][p.sub.3U] is small, the motional pressure gradient [DELTA][p.sub.12] has to eliminate the downstream capillary pressure [DELTA][p.sub.D1]. Here, the limit is calculated to [h.sub.Minimum] [approximately equal to] 65 [micro]m. At speeds lower than 5 m/min the contribution of the motional pressure gradient decreases in comparison to the capillary upstream pressure [DELTA][p.sub.3U]. Thus, the limit develops a curvature toward the zero point and smaller film heights are possible in this area.

For bilayer coatings with m = 1, [DELTA][p'.sub.12] and the additional pressure gradient [DELTA][p'.sub.DU] differ in sign in equation (19) for the given conditions. Now [DELTA][p'.sub.12] has to eliminate both [DELTA][p'.sub.D1] and [DELTA][p'.sub.12], for which the minimum film thickness increases further to approximately [h.sub.Minimum] [approximately equals] 78 [micro]m. Remarkably, this effect of an additional pressure term switches the results for coating speeds lower than lm/min. Here, the bilayer calculations allow for smaller film thicknesses than the single-layer application. This shows the importance of the ratio m for bilayer coatings.

In Fig. 8 we plotted a graphical representation of the single-layer and bilayer pressure gradients as a pressure distribution within the coating gap including different feed ratios m.

The pressure distributions plotted in Fig. 8 represent the conditions of the standard parameters in Table 1 where the upstream gap is partly wetted. This enables a more vivid illustration of the impact of m.

In comparison to the single-layer pressure distribution, the bilayer gradients [DELTA][p'.sub.D1], [DELTA][p'.sub.12], [DELTA][p'.sub.4U] and the slope of [DELTA][p'.sub.34] compared to [DELTA][p.sub.23] are not changed. Only the slope of the mid-lip gradient [DELTA][p'.sub.23] shifts the pressure level beneath the feed slot and thus the starting point [DELTA][p'.sub.34], representing the wetted upstream area. At the given ratio of ho/h the critical [m.sub.crit] with a sign turnaround in [DELTA][p'.sub.23] is reached for Newtonian liquids at m = 0.875 which is shown in equation (29).

[m.sub.crit] = 2h = [h.sub.G]/[h.sub.G] = 0.875 (29)

If m [right arrow] 0, representing a dominant bottom layer, the value of [DELTA][p'.sub.23] approaches [DELTA][p'.sub.12]. The pressure level beneath the bottom layer slot then would be doubled compared to the top layer slot. Thus, the upstream meniscus would move outside the gap and die swelling occurs. If m [right arrow] [infinity] the slope of [DELTA][p'.sub.23] approaches the one of [DELTA][p'.sub.34] and the upstream meniscus moves toward the feed slot. Thus, Case 4, representing air entrainment, could appear for bilayer coatings earlier than for single-layer coatings if m > [m.sub.crit].

Nevertheless, a bilayer and a single-layer application could have the same coating window if m < [m.sub.crit] chosen, leading to smaller possible film heights before air entrainment occurs. This results from a higher bead pressure beneath the upstream feed slot. For single-layer coatings this result may be reached by an extended downstream gap.

In Fig. 9 the theoretical and experimental observed impact of the feed ratio on the minimum film thickness is plotted.

The calculated and experimental results confirm the expected impact of the feed ratio m. For the bilayer calculations, the minimum film thickness decreases from ~ 103 [micro]m for m = 5 to ~ 77 [micro]m for m = 0.1. The latter approaches the single-layer calculation with only 2 [micro]m deviation. Remarkably, the slope at smaller coating speeds is much steeper and the film height higher compared to Fig. 7. This is a result of the higher viscosity [[eta].sub.2] and gap height [h.sub.G,2] in Fig. 9. In contrast to the calculations the impact of m decreases for the experimental results. While there is no observable difference between the minimum thicknesses of m = 0.875 and m = 5 they are smaller for m = 0.1. Yet they are at least 10 [micro]m thicker than for the single-layer experiments. These deviations may be related to inaccurate adjustments which decrease the impact of m, such as the gap beneath the mid-lip. Unlike the calculations the experiments additionally show a slightly rising trend toward higher coating speeds. This may be related to the assumptions, which for example neglect a speed dependence of [DELTA][p'.sub.4U] and [DELTA][p.sub.3U] Nevertheless, the predicted trend of smaller minimum film thicknesses for small feed ratios could be shown.

For liquids following the power-law approach, Case 4, respectively, equations (15) and (28) were again calculated implicitly. The minimum wet film thicknesses are plotted for several speeds together with previous experimental results in Fig. 10.

For both applications, single layer and bilayer, the minimal film thickness reaches its horizontal gradient beneath 0.5 m/min. This is due to the higher value of the speed-dependent pressure gradients at lower speeds compared to the capillary upstream pressure.

Furthermore, the difference of the minimum film thickness in single-layer and bilayer applications is higher than for the Newtonian calculations. The value for single layer coatings remains at [h.sub.Minimum] [approximately equal to] 65 [micro]m while the bilayer limit increases compared to the Newtonian calculations to [h.sub.Minimum] [approximately equal to] 86 [micro]m. This can also be related to the relatively higher values of the pressure gradients close to the limit. Nevertheless, if the film thickness increases, the gradients get higher for the Newtonian calculation, due to the recessive exponent in the power-law equations.

Hereby, the pressure distributions, plotted in Fig. 11, do not reach the higher Newtonian levels plotted in Fig. 8.

Similar to the Newtonian calculations, a change in the film height ratio m affects the slope of [DELTA][p'.sub.23] and thus the location of the upstream meniscus. Due to a flatter distribution, the shift of the pressure level beneath the bottom layer slot results in a higher impact to the length axis and hence the minimum film thickness.

To fulfill [DELTA][p'.sub.23] = 0 for liquids following the power-law approach, the critical ratio m can be calculated similar to equation (29) leading to the same value.

Similar to the calculations, the experimental results plotted in Fig. 10 show a diverging minimum film thickness between single-layer and bilayer coatings. Here, the value of the difference matches quite well to those calculated.

In contrast, both experimental series indicate a clear rising trend for the limiting film thickness regarding higher coating speeds. This was also visible for the Newtonian results in Fig. 9. As described above, the calculations remain on a constant value. Apparently a coating speed influenced factor was underestimated or neglected in the calculations.

Previous works, including pressure measurements for power-law liquids, confirm the accuracy of the downstream pressure gradient [DELTA][p'.sub.D1] in equation (8) and (9). (17)

This may confirm that the designated deviation might be caused by the simplified capillary pressures.

As mentioned above, [DELTA][p'.sub.D1] was derived for Newtonian liquids and may not be suitable for describing a power-law flow. A less recessive exponent to the capillary number and thus the speed sets an increasing trend to the minimal film thickness.

Nevertheless, the observation of differing minimal film thickness for single-layer and bilayer power-law coatings can be explained with the presented model.


In this work, we investigated the major differences of single layer and bilayer coated Newtonian and power-law fluids. We therefore extended available 1-dimensional models describing only single-layer slot die coating beads to bilayer coatings.

It was shown that relatively thick films with gap ratios close to unity are not limited by air entrainment at ambient conditions. Thus, we computed the minimal possible film thickness for each case in dependence of the coating speed. Here, the bilayer coating shows a higher minimal film thickness for both Newtonian and power-law liquids.

To characterize the impact of the additional mid-lip pressure gradient, a top to bottom film height ratio m was introduced. This ratio is able to switch the signs of the additional pressure gradient beneath the mid-lip.

Confirming the experimental results, the additional pressure gradient increases the minimal film thickness at a top to bottom feed ratio about unity and beyond.

Nevertheless, by choosing a critical ratio [m.sub.crit] this effect can be eliminated. Calculations and experiments showed its capability to shift the onset of air entrainment to smaller possible film heights for bilayer coatings with m [right arrow] 0.



h            Height (z-axis) ([micro]m)
l            Length (x-axis) (mm)
p            Pressure (mbar)
u            Speed (m/min)

Greek letters

[??]         Shear rate (1/s)
[epsilon]    Power law exponent
[kappa]      Consistency factor (Pa [s.sup.n])
[eta]        Newtonian viscosity (Pa s)


crit         Critical
D            Downstream
G            Gap
M            Mid-lip
U            Upstream
W            Web

DOI 10.1007/s11998-015-9701-4

M. Schmitt ([mail]), S. Raupp, D. Wagner, P. Scharfer, W. Schabel

Institute of Thermal Process Engineering, Thin Film Technology, Karlsruhe Institute of Technology, Karlsruhe, Germany



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Table 1: Table with the standard coating parameters
and slot die dimensions applied to the above calculations

Parameter        Value           Unit

[h.sub.G,1]      128     [micro]m
[h.sub.G,2]      148     [micro]m
h                120     [micro]m
[l.sub.D]        1000    [micro]m
[l.sub.M]        500     [micro]m
[l.sub.U]        1000    [micro]m
m                1       --
[u.sub.w]        5       m/min
[[eta].sub.1]    0.45    Pa s
[[eta].sub.2]    1       Pa s
K                1.27    Pa [s.sup.[epsilon]]
[epsilon]        0.7     --
[sigma]          0.066   N/m


Please note: Some tables or figures were omitted from this article.
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Date:Sep 1, 2015
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