Commun. Comput. Phys., 6 (2009), pp. 536-552.

Reverse Roll Coating Flow with Non-Newtonian Fluids

Jiin-Yuh Jang 1*, Peng-Yuan Chen 1

1 Department of Mechanical Engineering, National Cheng-Kung University, Tainan, 70101 Taiwan.

Received 4 June 2008; Accepted (in revised version) 6 November 2008
Available online 6 February 2009


In this study an incompressible flow with non-Newtonian fluids in the reverse roll coating process was investigated. Non-Newtonian behavior of the coating fluid was accounted by using power law model with power index, $n$, ranging from 0.8 to 1.2. Effect of roll speed ratio ($V_2/V_1$) of the panel roll to the applicator roll and gap distance on the coating film thickness were also investigated. Numerical results were in good agreement with those of experimental data within 15\%-20\%. Results indicated that the film thickness ratios are function of power-law index, roll speed ration and ratio of roll radius to gap distance. The equations for film thickness ratio were obtained from numerical results as shown below:

\frac{{t_2 }} {{t_1 }} = 0.89n^{0.55} \left( {\frac{{V_2 }} {{V_1 }}} \right)^{ - 0.83} \left( {\frac{{H_0 }} {{R_m }}} \right)^{0.0025},\qquad \frac{{t_3 }} {{t_1 }} = 65.6n^{0.0014} \left( {\frac{{V_2 }} {{V_1 }}} \right)^{ - 0.043} \left( {\frac{{H_0 }} {{R_m }}} \right)^{0.624},

where $t_1$, $t_2$ and $t_3$ are inlet film, transferred film and leakage film thickness, respectively, $n$ is power-law index, $V_1$ and $V_2$ are roll speed of applicator roll and panel roll, $R_m$ is average radius of two rolls and $H_0$ is gap distance. The correlations are accurate within 10\% for $0.8 \le n \le 1.2$, $0.5 \le V_2/V_1 \le 2$, and $7.7 \times 10^{-5} \le H_0/R_m \le 1.54 \times 10^{-4}$.

AMS subject classifications: 76A05

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Key words: Reverse roll coating, non-Newtonian flow, power-law.

*Corresponding author.
Email: (J.-Y. Jang), (P.-Y. Chen)

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