Asymptotic and numerical analysis of a simple model for blade coating

Abstract

Motivated by the industrial process of blade coating, the two-dimensional flow of a thin film of Newtonian fluid on a horizontal substrate moving parallel to itself with constant speed under a fixed blade of finite length in which the flows upstream and downstream of the blade are coupled via the flow under the blade is analysed. A combination of asymptotic and numerical methods is used to investigate the number and nature of the steady solutions that exist. Specially, it is found that in the presence of gravity there is always at least one, and (depending on the parameter values) possibly as many as three, steady solutions, and that when multiple solutions occur they are identical under and downstream of the blade, but differ upstream of it. The stability of these solutions is investigated, and their asymptotic behaviour in the limits of large and small flux and weak and strong gravity effects, respectively, determined

Flexible and Patterned Thin Film Polarizer: Photopolymerization of Perylene-based Lyotropic Chromonic Reactive Mesogens

“…For the fabrication of macroscopically oriented DAPDI TFP on the glass and polymer substrates by mechanical shear coating at room temperature, the concentration of DAPDI-H 2 O solution is optimized to be 25 wt %, which is determined based on the POM morphological observations and the degree of polarization (DOP). Additionally, for the subsequent photopolymerization of the macroscopically oriented DAPDI TFP, 1 wt % of water-soluble photoinitiator (2-hydroxy-4′-(2-hydroxyethoxy)-2-methylpropiophenone, Sigma-Aldrich) is added into the 25 wt % aqueous solution before the doctor-blade shear coating process . The detailed fabrication process is described in the Experimental Section of this paper.…”

“…Additionally, for the subsequent photopolymerization 40 of the macroscopically oriented DAPDI TFP, 1 wt % of water-soluble photoinitiator (2-hydroxy-4′-(2-hydroxyethoxy)-2-methylpropiophenone, Sigma-Aldrich) is added into the 25 wt % aqueous solution before the doctor-blade shear coating process. 41 The detailed fabrication process is described in the Experimental Section of this paper. Morphology and molecular orientation of the uniaxially oriented DAPDI TFP are investigated by POM with and without a 530 nm retardation plate after the photopolymerization (Figure 2).…”

A pinned or free-floating rigid plate on a thin viscous film

“…The inset in Figure 5 shows the three solutions in the case δ = 0.005 (< δ * ) and p 0 = 1.232 (< p * 0 ); they are distinguished by their increasing values of α and h ∞ . Although we do not study the stability of such solutions, we conjecture that only the solution that corresponds to the smallest values of α and h ∞ are stable (see Quintans Carou et al 2009 for the stability analysis for the case of a fixed horizontal plate).…”