Journal of Coatings Technology and Research

, Volume 16, Issue 6, pp 1653–1661 | Cite as

A process model for slot coating of narrow stripes

  • Ara W. ParsekianEmail author
  • Tae-Joong Jeong
  • Tequila A. L. Harris


Selective deposition of patterned films, without masks or subtractive postprocessing steps, can potentially be achieved by extending the capabilities of traditional slot coating. Realization of a fully additive-only approach of this nature will elevate the viability of slot coating for numerous emerging technologies such as flexible optoelectronic devices, sensors, and wearables. In this study, we develop a process model for slot coating of variable-width narrow stripes, as a fundamental and representative pattern feature for patterned slot coating. Our process model addresses the sensitivity of stripe output to fluid deposition rate, substrate speed, and coating gap for a given coating material. To explain the observed process behavior, we distinguish between separate configurations of contact line pinning of the liquid bridge at the coating tool surface and show experimentally how these configurations relate to regimes in the process model that must be characterized separately. We also demonstrate how the geometry of the liquid bridge and range of intermediate contact angles along its contact line correspond to observed hysteresis of the coated stripe width.


Slot die coating Pattern printing Narrow-stripe coating Polyvinyl alcohol Process modeling 

List of symbols


Substrate velocity


Flow rate


Slot gap


Coating gap

Lu, Ld

Length of upstream and downstream portion of die lip, respectively


Wet film thickness


Width of slot die slot


Width of coating bead and coated narrow stripe

wa, wr

Width of narrow stripe in advancing and receding configurations, respectively

Offset distance between centers of coating bead and slot die outlet


Width/length ratio of the coating bead




Dynamic viscosity


Surface tension

θa, θr

Advancing and receding contact angle, respectively


Dimensionless coating gap


Capillary number


Reynolds number

wa*, wr*

Dimensionless stripe width in advancing and receding configurations, respectively


Average flow velocity at slot die outlet


In recent years, slot die coating of stripe-patterned films has been applied across a range of emerging printed device technologies. These technologies include thin-film solar cells,1, 2, 3, 4 transistors,5,6 batteries,7 and display devices.8, 9, 10 Slot die coating has drawn attention within this ecosystem of applications because it offers a variety of advantages related to manufacturing scale-up. Slot coating offers precise metering of wet thickness, excellent film uniformity, adaptability to new coating materials, low-waste deposition, and wide-area coverage. Slot die coating is therefore a dependable option for high-throughput roll-to-roll (R2R) manufacturing.

For slot die coating of stripe patterns, outflow of coating fluid can be directed using grooves machined into the coating tool or meniscus guides.11 This approach is typically used to deposit continuous stripes at a fixed width. However, the research community has expressed interest in extending the slot coating approach to more ambitious patterning capabilities. Vak et al.4 have developed a 3D printer-based slot die capable of printing curved stripes and patches at fixed width. Lin et al.12 have demonstrated the capability of a narrow slot die to produce a range of stripe widths by varying substrate speed and flow rate. Parsekian and Harris have reported on a slot die coater with on-demand patterning capability comprising independent flow control across local outflow regions.13 These efforts underscore the potential of slot die as an archetype for mask-free, additive-only deposition of sophisticated patterns.

Narrow-stripe deposition, using both conventional slot coating and its various pattern-capable iterations, requires an understanding of pattern morphology with respect to process inputs such as volumetric flow rate (Q), substrate velocity (U), and coating gap (H). Since film thickness (h) and stripe width (w) both depend on similar process conditions, the need arises for sufficient characterization to specify both independently. Physically, process behavior is tied to the mechanics of the coating bead, the liquid bridge between the substrate and slot die outlet. Here, the coating bead cannot be approximated as a two-dimensional phenomenon as is customary for conventional slot die coating.14, 15, 16 Furthermore, the body of literature on liquid bridges focuses primarily elsewhere, on axisymmetric cases under extension and compression,17, 18, 19, 20, 21 although there are relevant insights available regarding shearing,22,23 contact line hysteresis,24, 25, 26 and contact line confinement.27 Thus, direct modeling of the narrow coating bead presents a considerable challenge and would require accurate, extensive characterization of wetting and rheological properties.

In this paper, we develop a process characterization methodology for slot coating of variable-width narrow stripes. These efforts incorporate classification of several key liquid bridge phenomena, each observed in previous studies, as they relate to the slot die coating process. To circumvent extensive characterization of fluid wetting and rheology, the model relies on direct measurement of process output and general knowledge of liquid bridge mechanics. The resulting empirical relationships are validated across a range of coating fluid viscosity, deposition rate, and coating gap. The modeling methodology is then evaluated in terms of the requisite experimental characterizations required to characterize a selected tool geometry, substrate, and coating fluid.

Materials and Methods


Polyvinyl alcohol (PVA), Mowiol® 4-88, was purchased from Sigma Aldrich Corp. Aqueous solutions of PVA at 10% and 15% wt. were prepared by continuous stirring for 30 min at 60°C. Polyethylene terephthalate (PET) film, ES301400, of 100 µm thickness was purchased from Goodfellow Cambridge Ltd. Physical properties of the materials above are organized in Table 1. Density and viscosity values for PVA are taken from the literature.28 Surface tension was measured with the pendant drop method, and contact angle was measured with the volume-add/volume-subtract method, using a Ramé-hart Model 500-U1 goniometer. Contact angle measurements were taken for PVA solutions on PET, the substrate material, in addition to polymethyl methacrylate (PMMA), the slot die material. A value of 0 for θr denotes apparent pinning of the receding contact line on the solid phase.
Table 1

Physical properties of coating fluids at 25°C


ρ (g/mL)

µ (cP)

σ (mN/m)

θa (°)

θr (°)





PVA (10%)








PVA (15%)








Experimental Methods

The deposition of narrow stripes is imaged in-process using the setup shown in Fig. 1a. Coating fluid is deposited by a slot die onto flexible substrate tensioned over a glass platen on a custom roll-to-roll imaging system (R2RIS). Visualization of the coating bead and deposited wet film is accomplished using a Thorlabs DCC3240C digital camera and Edmund Optics 25-mm fixed focal length lens, at an effective pixel size of 21.6 µm.
Fig. 1

(a) Schematic of R2RIS and processing parameters for narrow-stripe slot coating experiments. (b) Programmatic measurement of coating bead and stripe dimensions. Dashed lines overlaid on image (b) indicate the edges of the narrow-stripe film and edges of the slot die lip

Process parameters are illustrated schematically in Fig. 1a. The coating gap (H) is adjusted manually using a linear positioner, flow rate (Q) is set by a syringe pump, and substrate velocity (U) is set by a PID-controlled motor. These process inputs are recorded in software automatically with each captured image, while the remaining geometric parameters are kept fixed at G = 76 µm, w0 = 0.78 mm, Lu = 1.2 mm, and Ld = 1.1 mm for all experiments. Image data such as that shown in Fig. 1b are analyzed ex situ using the MATLAB image processing toolbox to extract pattern morphology (w), and average film thickness (h) is calculated as h = Q/(U·w). For each measurement, the coating bead is qualified as either advancing or receding, and any pinning of the contact line at the coating tool surface is noted.

Empirical modeling approach

We seek a model relating process conditions (U, Q, H) to pattern morphology (w). Previous studies have explored the influence of individual parameters. Lin et al. noted that stripe width correlates positively with Q and negatively with U, as would be expected from continuity.12 In addition, a negative correlation between w and H has been observed in previous studies,12,13 as might be expected from the relationship between gap height and contact radius of a liquid bridge between two plates.25,26 However, a precise explanation for the combined influence of Q, U, and H has been less straightforward. Experimentally, it has been demonstrated that (1) increasing H facilitates the onset of breakup defects in a narrow-stripe pattern at high U and low Q12; (2) the shape of the coating bead relates directly to the final width of the narrow stripe13; (3) the coating bead shape is subject to significant confinement effects at corners and edges of the coating tool12,27; and (4) the proportion of coating bead volume transferred to the substrate is dependent on wettability of the substrate and coating tool, as well as the rate of strain in the bead.20, 21, 22, 23 Together, these published results suggest that the narrow-stripe coating process can be more clearly understood in the context of liquid bridge phenomena. The model constructed for this study incorporates knowledge of these phenomena to improve upon results of previous empirical modeling efforts.

Three possible regimes for pinning of the contact line along the die lip surface are illustrated in Figs. 2a, 2b and 2c. Here, regimes I, II, and III correspond to no pinning of the contact line, pinning at one die lip edge, and pinning at both die lip edges, respectively. To express these confinement phenomena in the process model, the relationships between pattern morphology and other processing parameters are assumed to be piecewise continuous.
Fig. 2

(a)–(c) In-process imaging of three confinement regimes for the advancing narrow-stripe coating bead. (d)–(e) In-process imaging of the (d) advancing and (e) receding coating bead contact line produced by the same value of Q*. (f) Stripe width as a function of flow rate per unit substrate (Q*). Arrows in (f) indicate the progression of time

The empirical process model also assumes hysteresis of the coating bead contact line, a physical consequence of the contact angle hysteresis at the substrate and slot die lip. This effect has been previously noted and studied extensively in liquid bridges of fixed volume subject to tensile and compressive strain.24, 25, 26 The range of intermediate contact angles between θa and θr implies a range of physically permissible liquid bridge volume for a particular stable contact line width. Analogously, in narrow-stripe slot die coating, the coating bead exhibits the hysteresis behavior illustrated in Figs. 2d and 2e. Here, however, the liquid bridge is subject to shear as well as a mass flux condition at two boundaries. The model proposed in this work relies on direct measurement of stripe width for both advancing (wa) and receding (wr) contact line configurations. These correspond to the cases where coating bead size is incrementally increasing or decreasing, respectively, under a quasi-static condition. Separate empirical relationships are constructed for wa and wr, which constitute an upper and lower bound on possible stripe width for a given set of processing parameters.

The transitions between pinning regimes are influenced by the geometry of the die lip (Lu, Ld, and G), the center offset between the coating bead and die slot (), and the length/width ratio of the coating bead (α). The transition between I and II occurs within (Lu/2) ≤ αw ≤ (Lu + Ld + G), and the transition between II and III occurs at αw ≥ (Lu + Ld + G). While parameters and α can be measured directly using the R2RIS in Fig. 1a, it may be impractical to do so on typical R2R systems. Therefore, the process model presented here places the regime pinning transitions based on an initial guess and a data-driven correction.

Previous analysis of the physical quantities relevant to deposition flow suggests several dimensionless groups for formulation of an empirical model.12,13 These consist of a dimensionless length H* ≡ H/(Lu + Ld + G), which expresses the ratio between the coating gap and die lip length; capillary number, Ca ≡ µU/σ, which expresses the ratio of viscous to interfacial forces; Reynolds number, Re ≡ ρu avg 2 /(µU/H), which expresses the ratio of inertial to viscous forces; and a dimensionless stripe width, w* ≡ w/w0, which expresses output pattern morphology. The empirical relationships developed for this process model are based on these dimensionless groups. Here, uavg ≡ Q/(w0·G), the average flow velocity at the slot die outlet, is taken as the velocity scale for inertial forces, while U is used for viscous forces. To distinguish between the advancing and receding contact line configurations, wa* ≡ wa/w0 and wr* ≡ wr/w0 are considered separately in the model formulation.

Results and discussion

Dimensional analysis

To illustrate the influence of input parameters on narrow-stripe width and its hysteresis, w* has previously been examined with respect to flow rate per length unit of substrate (Q/U), or a dimensionless variation thereof (Q*). While this approach provides qualitative insights about the influence of individual process input parameters, it fails to produce any means for predicting stripe width quantitatively. However, if the hysteresis configurations of the coating bead are considered separately, it is possible to construct dimensionless groups that relate to pattern morphology along a unified trend. Two such dimensionless groups are as follows:
$$\Pi_{\text{a}} \equiv Re^{0.5} \cdot Ca^{ - 1} \cdot H^{* - 2} \quad {\text{for}}\;w^{*} = w_{\text{a}}^{*}$$
$$\Pi_{\text{r}} \equiv Re^{0.5} \cdot Ca^{ - 3} \cdot H^{* - 3} \quad {\text{for}}\;w^{*} = w_{\text{r}}^{*} .$$

An evaluation of the goodness of fit for Πa and Πr as defined in Eqs. (1a and 1b), in comparison with alternative dimensionless group selections, is provided in Figure S1 of Supplementary Material.

The effect of this dimensional scaling for 10% wt. PVA across various Q, U, and H is shown in Fig. 3. In Figs. 3a and 3b, distinct trends are apparent across measurements of constant U and H. These correlations between w and Q/U follow from continuity. Additional dimensional scaling is required to arrive at a unified trend, as shown in Figs. 3c and 3d. Here, the influence of the slot die geometry and the relative importance of interfacial forces are encapsulated by H* and Ca, respectively. The influence of flow rate is implicit in Re, which represents the significance of inertial force in the coating bead relative to viscous shear between the slot die and the substrate.
Fig. 3

Results for 10% wt. PVA collected under (a) advancing and (b) receding contact line configurations. Unfilled markers (open triangle, open diamond, open square) denote pinning regimes I and II and filled markers (filled triangle, filled diamond, filled square) denote pinning regime III. Flow rate is 0.017 µL/s for triangles (open triangle, filled triangle), 0.083 µL/s for diamonds (open diamond, filled diamond), and 0.167 µL/s for squares (open square, filled square). Coating gap is denoted by color as indicated in the legend (Color figure online)

As expected, an abrupt feature is present at the boundary between regimes II and III. However, no corresponding feature at the boundary between regimes I and II is easily identifiable. This may be explained by the type of influence that each confinement regime exerts on the liquid bridge, whereas regime II primarily confines the location of the liquid bridge and regime III influences both its location and shape. Thus, in Fig. 3, the presented linear regression fit results have been performed separately over regime III and over the remaining data. It is interesting to note that in all cases, stripe width is significantly less sensitive to other processing parameters within confinement regimes I and II, relative to regime III. This result illustrates the effect of the die lip edge on process sensitivity and suggests that by decreasing the length of the die lip (Lu, Ld), one would be able to achieve a greater range of stripe widths for a given film thickness at the cost of decreased process robustness. It is also notable that pattern output is least sensitive to Q, U, and H near the minimum feature size produced.

Empirical model formulation

The agreement between experimental data and linear regression in Fig. 3 suggests a piecewise empirical model of the following form:
$$w_{\text{a}}^{*} = A_{\text{a}} \ln \left( {\Pi_{\text{a}} } \right) + B_{\text{a}} \quad {\text{for}}\;0 < w_{\text{a}} * \le w_{{{\text{II}} - {\text{III}}}}^{*}$$
$$w_{\text{a}}^{*} = C_{\text{a}} \ln \left( {\Pi_{\text{a}} } \right) + D_{\text{a}} \quad {\text{for}}\;w_{\text{a}}^{*} > w_{{{\text{II}} - {\text{III}}}}^{*}$$
$$w_{\text{r}}^{*} = A_{\text{r}} \ln \left( {\Pi_{\text{r}} } \right) + B_{\text{r}} \quad {\text{for}}\;0 < w_{\text{r}}^{*} \le w_{{{\text{II}} - {\text{III}}}}^{*}$$
$$w_{\text{r}}^{*} = C_{\text{r}} \ln \left( {\Pi_{\text{r}} } \right) + D_{\text{r}} \quad {\text{for}}\;w_{\text{r}}^{*} > w_{{{\text{II}} - {\text{III}}}}^{*} ,$$
where wII−III* is the dimensionless stripe width coinciding with the transition between confinement regimes II and III; Aa, Ba, Ca, Da, Ar, Br, Cr, and Dr are empirical constants; and Πa and Πr are dimensionless groups incorporating process inputs and coating fluid properties, as defined in Eqs. (1a and 1b). For Eqs. (2a, 2b, 2c and 2d), a logarithmic correlation is selected on the basis of agreement with experimental data; the lack of a physical upper bound on stripe width other than the width of the slot die tool, which the model does not consider; and simplicity, to avoid overdetermining the model.
The empirical model must also conform to two additional physical constraints, namely that the transition between confinement regimes occurs at wII−III* and that transitions between any two stripe widths are continuous. These constraints imply a piecewise continuous model with a break point located at wII−III*:
$$A_{\text{a}} \cdot\ln \left( {\Pi_{\text{a}} } \right) + B_{\text{a}} = C_{\text{a}} \cdot\ln \left( {\Pi_{\text{a}} } \right) + D_{\text{a}} \quad {\text{for}}\;w_{\text{a}}^{*} \, = w_{{{\text{II}} - {\text{III}}}}^{*}$$
$$A_{\text{r}} \cdot \ln \left( {\Pi_{\text{r}} } \right) + B_{\text{r}} = C_{\text{r}} \cdot \ln \left( {\Pi_{\text{r}} } \right) + D_{\text{r}} \quad {\text{for}}\;w_{\text{r}}^{*} = w_{{{\text{II}} - {\text{III}}}}^{*} .$$
To assess the consistency of results produced by this approach, the regression slope coefficients, Aa, Ca, Ar, and Cr in Eqs. (2a, 2b, 2c and 2d), are plotted across several data subsets for both 10% and 15% wt. PVA in Fig. 4. The error bars denote the 95% confidence interval for each constant, assuming a normal sampling distribution. The model parameters are consistent within these bounds for each case considered, although the confidence interval is rather large, particularly for the higher-viscosity formulation and lower values of H. The uncertainty in the model fit is most likely a consequence of transient fluctuations in Q or U. Due to hysteresis of the coating bead contact line, the disruption of stripe width due to these transient effects can be expected to persist as long as process inputs are held constant.
Fig. 4

Model uncertainty for (a) advancing coating bead width with 10% wt. PVA, (b) receding coating bead width with 10% wt. PVA, (c) advancing coating bead width with 15% wt. PVA, and (d) receding coating bead width with 15% wt. PVA

To evaluate the influence of viscosity on contact line hysteresis, it may be noted that the results in Fig. 4 exhibit a marginal decrease in model slope for wa, concurrent with a marginal decrease in model slope for wr, for the higher-viscosity solution. From the trends in Fig. 3, hysteresis of the coating bead width becomes more pronounced due to a change in process inputs when wa decreases by a greater amount than wr, or equivalently, when wr increases by a greater amount than wa. Thus, the effect of increased viscosity is to mitigate the severity of contact line hysteresis for relatively wide stripes, near pinning regime III. Intuitively, this may be anticipated from the observation that coating bead hysteresis is an interfacial phenomenon and thus less significant where viscous forces dominate over interfacial ones.

Methodology and demonstration

For a specific combination of coating fluid, substrate, and coating tool geometry, the empirical model is derived by the following three-step process:
  1. 1.

    Narrow-stripe width (w) is sampled across a range of process input parameters (Q, U, H). Each sample point is associated with either advancing or receding coating bead width, based on the history of the sample run (e.g., increasing U from its previous value implies advancing bead width, and vice versa).

  2. 2.

    Regression analysis is used to construct a piecewise model of the form described by Eqs. (2a, 2b, 2c and 2d).

    1. (a)

      Since wII−III* is not known explicitly, wII−III* ≈ (Lu + Ld + G)/w0 is used as an initial estimate.

    2. (b)

      Data are binned into two subsets based on the measurements of w*. One bin contains data where 0 < w* ≤ wII−III*, and the other bin contains data where w* > wII−III*.

  3. 3.

    Binning and regression analysis are updated in order to ensure that the transition between liquid bridge confinement regimes is reflected appropriately, while maintaining continuity of the piecewise model.

    1. (a)

      Uncertainty analysis is performed on model components Ba, Br, Da, and Dr to construct bounds for each piecewise model segment.

    2. (b)

      The uncertainty level where the bounds for the two model segments intersect at wII−III* is determined.

    3. (c)

      The binning process is repeated about Πa(wII−III*) and Πr(wII−III*).

    4. (d)

      Regression analysis and determination of wIIIII* are repeated using the updated binning scheme.

    5. (e)

      Regression analysis is repeated a final time, with the additional constraint imposed by Eqs. (3a and 3b)

Intermediate steps in this process are illustrated in Fig. 5 for narrow stripes of 10% wt. PVA. Plotted against the dimensionless groups from Eqs. (1a and 1b), coating bead width decreases logarithmically, with a transition point corresponding to the boundary between confinement regimes II and III, as shown in Figs. 5a and 5d. Thus, in step 2, data are binned and used to construct separate empirical fits for each confinement regime, as shown in Figs. 5b and 5e. In step 3, the empirical fits are adjusted to ensure model continuity across confinement regimes. The final model is illustrated in Figs. 5c and 5f.
Fig. 5

Steps in the development of the empirical model, illustrated for (a)–(c) advancing coating bead width and (d)–(f) receding coating bead width

In a physical sense, the empirical model provides a range of possible w for each specific combination of U, Q, and H. The piecewise curve fits for wa and wr constitute a stripe width minimum and maximum, respectively. Interestingly, since the models for wa and wr each depend on a different dimensionless group, it follows that process parameters can be chosen to produce a range of wa with wr held constant, and vice versa. This underscores the high degree of variability in stripe width exhibited by the slot coating process. The empirical model provides a clear physical interpretation of this variability where pure correlations between U, Q, H, and w cannot.


Our experimental investigation has highlighted how narrow-stripe slot die coating under steady-state conditions can be described by simple single-input model. Wetting hysteresis and contact line confinement have been illustrated as influential mechanisms in the narrow-stripe slot die coating process, and sharp transitions in observed experimental trends have been related to boundaries between regimes of wetting behavior. The primary outcome of this work has been the development of an empirical modeling methodology for the narrow-stripe slot coating process, validated for a sample aqueous polymer solution. It is of practical significance that the methodology can be applied to other materials without extensive knowledge of their physical properties. Straightforward measurements of pattern morphology and standard R2R process inputs are sufficient for its use.

For future investigations on narrow-stripe slot coating, it will be valuable to consider a wider range of coating material properties to further validate and extend the empirical model. Highly non-Newtonian polymeric fluids, for example, will require the addition of one or more model parameters in order to account for the shear rate dependence of viscosity. Similarly, the viscoelastic effects should be examined. Furthermore, it may be worthwhile to compare results for a non-Newtonian fluid with results from Newtonian fluids over the same viscosity range. In addition to further experimental work, the development of analytical or computational descriptions of the narrow-stripe coating bead will likely provide valuable insights and points of comparison with respect to the empirical model presented here. Such a description could also be used to extend the results of this study to non-steady flow rate conditions and other slot die materials and geometry.

In each of these efforts, the experimental modeling approach developed through this study will be a valuable tool to help isolate the influence of individual process inputs. Even for significantly different tool geometries and material systems, the liquid bridge hysteresis and confinement effects explored in this paper will remain influential and can be considered using the framework developed here.


Supplementary material

11998_2019_233_MOESM1_ESM.docx (164 kb)
Supplementary material 1 (DOCX 164 kb)


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Copyright information

© American Coatings Association 2019

Authors and Affiliations

  1. 1.George W Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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