Deformable roll coating flows: steady state and linear perturbation analysis
Deformable roll coating flows: steady state and linear perturbation analysis
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DOI：
10.1017/s0022112097005090
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发表时间：
1997-05
影响因子：
3.7
通讯作者：
M. Carvalho;L. Scriven
中科院分区：
文献类型：
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作者：
M. Carvalho;L. Scriven
辊涂的特点是使用旋转滚筒之间的一个或多个间隙来计量连续液体层并将其施加到连续柔性基材上。在形成正向或反向辊涂间隙的两个辊中，其中一个通常被一层或多或少可变形的弹性体覆盖。进入压区会聚侧的液体可以产生足够高的压力，使弹性盖变形，从而改变压区轮廓，从而改变速度和压力场。这种弹性流体动力学耦合作用尚未得到很好的理解。理论建模必须考虑粘性流、滚动变形和自由表面效应，以便预测流动行为。在这项工作中，共享相同角速度的刚性和可变形反向旋转辊之间的流动通过润滑近似以及基于膜流方程的粘毛细管模型来描述，用于膜分裂区域。弹性体层的变形由径向定向的胡克弹簧建模，构成一维模型。通过检查对无穷小扰动的时间相关响应来分析系统对横向扰动的稳定性，以便识别那些增长最快的扰动。相应的方程组采用一阶连续牛顿法求解。报告了涂层厚度、操作参数（加载力、间隙设置、辊速度等）、液体特性和覆盖层特性之间的关系，以及数学模型预测的罗纹开始的临界毛细管数和罗纹图案的波长。结果表明如何使用可变形覆盖层来延迟肋纹的出现以获得所需的涂层厚度。为了验证粘毛细管/胡克弹簧模型的理论预测，还对一对刚性辊和一对由可变形辊和刚性辊组成的对称薄膜分裂流进行了实验分析。
Roll coating is distinguished by the use of one or more gaps between rotating cylinders to meter a continuous liquid layer and to apply it to a continuous flexible substrate. Of the two rolls that make a forward or reverse roll coating gap, one is often covered by a layer of more-or-less deformable elastomer. Liquid carried into the converging side of the nip can develop high enough pressure to deform the resilient cover, which changes the nip profile and thus alters the velocity and pressure field. This elastohydrodynamic coupled action is not yet well understood. Theoretical modelling has to take into account the viscous flow, the roll deformation and the free-surface effects in order to predict the flow behaviour. In this work the flow between a rigid and a deformable counter-rotating roll that shares the same angular speed is described by the lubrication approximation together with a viscocapillary model, based in the film-flow equation, for the film-split region. The deformation of the elastomer layer is modelled by Hookean springs oriented radially, which constitute a one-dimensional model. The stability of the system to transverse perturbation is analysed by examining the time-dependent response to infinitesimal disturbances in order to identify those that grow fastest. The corresponding system of equations is solved by Newton's method with first-order continuation. The relationship between coating thickness, operational parameters (loading force, gap setting, roll velocities, etc.), liquid properties and the properties of the cover is reported, as well as the critical capillary number for onset of ribbing and wavelengths of the ribbing pattern predicted by the mathematical model. The results indicate how a deformable cover may be used in order to delay the onset of ribbing for a desired coating thickness. In order to validate the theoretical predictions of the viscocapillary/Hookean spring model, the symmetric film-split flows between a pair of rigid rolls and a pair consisting of a deformable roll and a rigid one were also analysed experimentally.