Solvent casting flow from slot die

Transcription

1 Korea-Australia Rheology Journal, 27(4), (November 2015) DOI: /s x Short Communication Semi Lee and Jaewook Nam* School of Chemical Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Gyeonggi-do , Republic of Korea (Received October 18, 2015; final revision received October 26, 2015; accepted October 27, 2015) A continuous solvent casting method using a slot die can precisely control the film thickness by adjusting the operating conditions, such as the belt speed and pumping rate, not the liquid property. Therefore, it is a suitable method for high precision continuous film production. In this particular method, the dope, or casting solution, is pumped through the feed slot to form a short curtain between the die and the moving belt. Although this method is widely used in producing films for various applications, it is difficult to find indepth analyses of such flow. In this study, we developed a finite element computational model for the steady-state two-dimensional sovent casting flow from the slot die. The effect of die configurations, rheological properties and operating conditions on the behavior and shape of the gas/liquid interfaces and the location of the dynamic contact line, which is the place where the dope meets the moving belt, were investigated. Keywords: solvent casting, shear-thinning fluid, dynamic contact line, slot die 1. Introduction The solvent casting method is one of the most important plastic film manufacturing processes for a long time, and dates back to the development of movie and photographic film industries. The method can be relatively easily expanded to a continuous process. Furthremore, it can produce thermally or mechanically sensitive products because of low stress in the process and is useful in many applications such as optical polarizers for LCD and base materials for flexible printed circuits (Siemann, 2005). To satisfy a recent requirement for high precision film in such applications, a slot die is now widely used as a caster for the film formation step. In this casting method, the film thickness is precisely controlled by the amount of a casting solution, or dope, via pumping mechanism and the production speed determined by a belt speed, which can be considered as the pre-metering method. With a proper design and operating conditions, this slot die casting machine can maintain a high degree of film uniformity. The film thickness uniformity is mainly categorized into two parts: uniformites in transverse and machine directions. The flow inside the internal structure of the die, namely, manifold determines the transverse uniformity, whereas the machine direction uniformity is determined by the solvent casting flow outside the die. The manifold needs to be designed properly under a given operating condition in order to distribute a dope homogeneously in the transverse direction, i.e., cross flow direction inside the feed slot. After the exit of the feed slot, the dope is pulled off and stretched by the moving belt, which drags *Corresponding author; jaewooknam@skku.edu the casted film to create a liquid sheet that is similar to a short-curtain when viewed from the side, as shown in Fig. 1. The thickness in the flow direction, i.e., the machine direction, is strongly controlled by the cross-sectional shape of the sheet. Despite the method s popularity and the importance in the role of the flow outside the die, only limited studies on this short curtain flow have been reported, especially the effect of operating conditions on its cross sectional shape. To the best of our knowledge, there is only one study from Christodoulou et al. (2012), in which a computational analysis was performed on the PET film casting process. They focused on the effect of magnetic field generated by the wire on the shape and wetting of the dope. Here, we analyze a steady-state short curtain-shaped solvent casting flow using the Galerkin/finite element method. The free surface profile, i.e., the shape of the short curtain, and the location of the dynamic contact line, where the dope touches the belt, are examined under different operating conditions including rheological properties of the dope, especially for a shear-thinning fluid. 2. Governing Equations and Solution Methods The two-dimensional steady-state casting flow is governed by the mass and the momentum conservation equations: v = 0, ρv v = T (1) where v is the velocity vector, ρ is the liquid density, and T = PI + 2η()S γ is the stress tensor for a generalized Newtonian liquid with pressure P and viscosity ηγ () at a 2015 The Korean Society of Rheology and Springer pissn X eissn

2 Semi Lee and Jaewook Nam The operating parameters used in this study are lited in Table 1. Like a slot coating method as reported by Koh et al. (2012), the operating conditions including fluid properties and the position and orientation of the slot die can change the shape of the gas/liquid interfaces and eventually DCL location. Consequently, the quality of the pro- given shear rate γ. Here, S = ( 1/2) [ v + ( v) T ] is the strain rate tensor. In this study, the Carreau model is used to describe shear-thinning property of the polymer solution, and the viscosity can be described as ηγ () = η + ( η 0 η )[ 1 + ( λγ ) 2 ] ( n 1)/2 (2) where η, η 0, λ, and n are the infinite shear viscosity, zero shear viscosity, relaxation time and power of the Carreau fluid, respectively (Carreau, 1968). For the twodimensional flow, the shear rate can be represented in terms of the strain rate tensor: 1 γ = -- II (3) 2 S where II S is the second invariant of the strain rate tensor. The boundary conditions are shown in Fig. 1. Because there is no analytical solution of the velocity profile inside a parallel channel for the Carraeu fluid, the inlet pressure value P in is imposed at a fully developed inlet boundary, where n v = 0. To satisfy both the pressure and flow boundary conditions, the traction n T = P in n + η() γ n ( v) T is imposed on the inlet boundary. Using the finite element computation, described later, a flow rate per unit width can be obtained as a function of the inlet pressure P in, and the resulting relationship is shown in the inset of Fig. 1. The relationship is almost linear and the film thickness can be precisely controlled by adjusting the inlet pressure and the belt speed. For the momentum boundary condition for the boundary between the moving belt and the fluid, the Navier-slip condition (Sprittles and Shikhmurzaev, 2012) with slip coefficient β = kg/m 2 s is applied to the boundary. Because of this condition, the velocity of the fluid at the boundary is the same as the belt velocity, except near the region of the dynamic contact line (DCL), where the dope first meet the moving belt. The angle between the gas/liquid interface and the solid/ liquid interface at DCL is set to o. This particular choice (~180 o ) removes the contactline stress singularity, which rises numerical difficulties in the computational analysis for highly viscous flow, as discussed by Benilov and Vynnycky (2013). In this study, the Galerkin/finite element method for the computational analysis is used. The details of the solution method are explained elsewhere (Romero and Carvalho, 2008; Lee and Nam, 2015a). To get a sequence of solutions with different parameters under a certain constraint such as Carreau parameter at a constant final wet film thickness, the direct tracking method is used (Nam et al., 2009; Nam and Carvalho, 2010). 3. Results and Discussions: the effect of operating conditions on the curtain flow shape and the dynamic contact line location Fig. 1. (Color online) A schematic diagram of film casting flow and corresponding boundary conditions. Inset graph is the relationship between the inlet pressure at inflow boundary and the flow rate per unit width. 326 Korea-Australia Rheology J., 27(4), 2015

3 Table 1. Fluid properties, operating conditions and geometry parameters used in this study. Here, polystyrene solution is used (Yasuda et al., 1981). Carrau parameter Zero shear viscosity (Pa s) η Infinite shear viscosity (Pa s) η 0 Relaxation time (s) λ Power law index n Density (g/cm 3 ) ρ 1 Surface tension (dyn/cm) σ 40 Belt velocity (mm/s) V B 10 Wet thickness (μm) h Dynamic contact angle (deg) θ dyn Geometry parameter Height at base point (mm) H 0 3 Die lip length (mm) L u, L d 0.3 Feed gap (mm) H f 0.6 Mounting angle (deg) θ M 45 duced film can get affected. are shown in Fig. 2. Note that P in is continuously changed during the computations to maintain the constant wet film thickness (h 0 = 300 μm), and this can be performed by the direct tracking method (Nam and Carvalho, 2010). Fig. 2a shows the effect of η 0 on x dcl. Inside the feed slot, the fluid viscosity has a distribution. At the center of feed slot, where the shear rate vanishes, ηγ () is almost the same as η 0, but it drops gradually toward the feed slot wall as the rate increases. However, outside the feed slot, where the dope forms a sheet surrounded by the gas/liquid interfaces, the viscosity immediately increases to η 0 everywhere except near the feed slot exit, because of the vanishing shear stress at the interface. The shape of the interface near the feed slot exit is strongly affected by η 0. Furthermore, as η 0 increases, the effect of the viscous drag force by the moving belt becomes stronger, consequently, DCL is pulled toward the moving direction, or x dcl increases. DCL moves toward the die, or x dcl decreases, as λ increases, as shown in Fig. 2b. λ determines the critical shear rate, where the viscosity starts to decrease after the zero shear viscosity plateau. The shear rate near DCL is mainly controlled by the belt speed and the viscosity. At a fixed belt speed, the viscosity near the DCL decreases as λ increases. Therefore, x dcl moves against the direction of the motion, because of the reduced drag force from the belt. The slope of the viscosity with respect to the shear rate is controlled by n in the shear-thinning region. However, under the current operating condition considered in this study, n does not significantly affect the short curtain pro Effect of carreau model parameters First, the effect of shear-thinning properties of polymer solution is investigated by changing the Carreau parameters: the zero shear viscosity η 0, relaxation time λ, and power n. Changes in any of them change the viscosity profile changes in the casting flow, thus changing the interface shapes and shift the DCL location x dcl measured from the projected point of the die lip corner on the belt (Fig. 1). The results of x dcl at different Carreau parameters Fig. 2. (Color online) The location of dynamic contact line with respect to (a) the zero shear viscosity, (b) the relaxation time, and (c) the power of the Carreau fluid. Korea-Australia Rheology J., 27(4),

4 Semi Lee and Jaewook Nam file and x dcl, as shown in Fig. 2c. The shear rate after the feed exit rapidly drops to 1 s 1, when λ is less than 1 s. Note that λ = 1 s stands for the viscosity falls over the 1 s 1. Our results indicate that the rate of viscosity drop with respect to the shear rate does not significantly affect x dcl Effect of die configurations The configuration of the die also affect the interfacial shape and x dcl. As shown in Fig. 3, three different configuration parameters are considered: the mounting angle θ M, the distance between the die and the belt H 0, and the gravity direction angle θ g. The results are summarized in Fig. 3. In the computational model, θ M can be adjusted by fixing the pivot point, which is the upstream corner of the die lip, and tilting the die as depicted in the inset of Fig 3a- 1. When θ M increases, x dcl moves slightly toward downstream, as shown in Fig. 3a-2. However, as discussed in the previous section, the viscosity rapidly increases right after the feed slot exit. Consequently, the shape of the gas/ liquid interfaces, i.e., the free surface profiles, changed dramatically. For θ M =8.68 o, although x dcl is not so different from other angles, the profiles bent severely near the feed slot exit. In this configuration, it may be difficult to maintain transverse directional sheet shape, and hence deteriorate the transverse film thickness uniformity. However, it should be mentioned that this transverse sheet profile cannot be examined in this two-dimensional computation. Fig. 3b shows the effect of H 0 on x dcl. Here, the distance is measured between the pivot point and the belt. As H 0 increases, the fluid escaped from the feed slot has more time to travel until it reaches the belt. Consequently, x dcl moves further downstream. At a given θ M, too small H 0 causes a largely distorted sheet shape near the feed slot exit. However, as H 0 increases, the shape becomes indistinguishable, and x dcl is merely shifted to downstream. The gravity direction can be adjusted by the position of the die to the drum, as shown in the Fig. 3c-1. In this study, θ g represents the angle between the feed slot orientation and the gravity direction. It turns out that θ g has the strongest effect on x dcl than other die configuration parameters. When the gravity direction is normal to the belt (θ g =0 o ), the flow is strongly pulled toward the mov- Fig. 3. (Color online) The effect of die geometry on the shape of free surface and the location of dynamic contact line: (a) Mounting angle of die, (b) height at base point, and (c) gravity direction. 328 Korea-Australia Rheology J., 27(4), 2015

5 Fig. 4. (Color online) (a) The viscosity profile of the solvent casting flow at different belt speed (10 and 40 mm/s), and (b) the location of dynamic contact line as a function of the belt speed. ing belt, thus x dcl is located near the feed exit. However, this effect decreases as the direction becomes close to antiparallel to the moving web (θ g =90 o ), consequently, x dcl increases. This strongly suggests that θ g can be a critical prameter when the location of DCL determines the quality of the film Effect of the belt speed at a given film thickness In this study, the belt speed is the only parameter that can significantly change the magnitude of shear rate near DCL. Since the slot die method is a pre-metered method as mentioned in the introduction, the flow rate need to be decreased to maintain the same wet thickness when the belt speed increases. Consequently, the viscous drag transferred from the belt to the film increases, and the corresponding shear rate increases as well, thus reducing the viscosity near DCL due to the shear thinning behavior. Therefore, the curtain is extended by increasing the belt speed, as shown in Fig. 4a, and x dcl moves to downstream, as shown in Fig. 4b. 4. Final Remark In this study, a computational analysis was performed on the steady-state continuous solvent casting flow using a slot die. The effect of rheological properties, die configurations, and operating condition on the behavior and shape of the short liquid curtain and the movement of dynamic contact line. According to our computational results, the location of DCL is mainly controlled by the die configurations, such as the die mounting position that controls the gravity direction or the distance between the die and the belt, rather than the rheological properties. However, the steady-state results alone do not give us indications for the quality of film, i.e., uniformity. Under the real situation where the continuous casting process is surrounded by various sources of disturbances including pumps, gears and motors, potentially important issues can be the film thickness variation along the flow direction, or the mechanical direction. This aspect is being computationally examined by a frequency response analysis (Lee and Nam, 2015b) and will be reported in the near future. Acknowledgment This study was supported by Samsung Research Fund, Sungkyunkwan University, References Benilov, E.S. and M. Vynnycky, 2013, Contact lines with a 180 contact angle, J. Fluid Mech. 718, Carreau, P.J., 1968, Rheological Equations from Molecular Network Theories, Ph.D Thesis, University of Wisconsin-Madison. Christodoulou, K., S.G. Hatzikiriakos, and E. Mitsoulis, 2012, Numerical simulation of the wire-pinning process in PET film casting: Steady-state results, AIChE J. 58, Koh, H., I. Kwon, H.W. Jung, and J.C. Hyun, 2012, Operability window of slot coating using viscocapillary model for Carreautype coating liquids, Korea-Aust. Rheol. J. 24, Lee, S. and J. Nam, 2015a, Analysis of slot coating flow under tilted die, AIChE J. 61, Lee, S. and J. Nam, 2015b, Response of slot coating flow to gap disturbances: effects of fluid properties, operating conditions, and die configurations, J. Coat. Technol. Res. 12, Nam, J., L.E. Scriven, and M.S. Carvalho, 2009, Tracking birth of vortex in flows, J. Comput. Phys. 228, Nam, J. and M.S. Carvalho, 2010, Flow in tensioned-web-overslot die coating: Effect of die lip design, Chem. Eng. Sci. 65, Romero, O.J. and M.S. Carvalho, 2008, Response of slot coating flows to periodic disturbances, Chem. Eng. Sci. 63, Siemann, U., 2005, Solvent cast technology a versatile tool for thin film production, Progr. Colloid Polym. Sci 130, Sprittles, J.E. and Y.D. Shikhmurzaev, 2012, Finite element framework for describing dynamic wetting phenomena, Int. J. Numer. Meth. Fluids 68, Yasuda, K., R.C. Armstrong, and R.E. Cohen, 1981, Shear flow properties of concentrated solutions of linear and star branched polystyrenes, Rheol. Acta 20, Korea-Australia Rheology J., 27(4),