Computational methods have been extended recently to allow for the presence of moving contact lines in simulated two-phase flows. The predictive capability offered by these methods is potentially large, joining theoretical and experimental methods. Several challenges rather unique to this area need to be overcome, however, notably regarding the conditions near a moving contact line and the very large separation of length scales in these flows. We first summarize the main models for moving contact lines and follow with an overview of computational methods that includes direct continuum approaches and macroscale models that resolve only the large-scale flow by modeling the effects of the conditions near the contact line using theory. Results are presented for contact-line motion on ideal as well as patterned and grooved surfaces and for extensions to account for complexities such as thermocapillarity and phase change.

Numerical Simulations of Flows with Moving Contact Lines

Numerical simulations of 3D flows with moving contact lines

Slot die coating is a pre-metered process commonly used for producing thin and uniform films. It is an important film fabrication method for applications where precise coating is required. A major concern in slot die coating processes is how to determine the operating limits to set the appropriate range of operating parameters, including coating speed, flow rate, vacuum pressure, coating gap, liquid viscosity and surface tension, etc. Operating limits directly determine the effectiveness and efficiency of the process. In this article, the current state of academic research on operating limits in slot die coating processes is reviewed. Specifically, the theories, mechanisms, and empirical conclusions related to the limits on vacuum pressure, the low-flow limit, the limit of wet thickness for zero-vacuum-pressure cases, the limit of dynamic wetting failure, and the limits of coating speed for a specific flow rate are reviewed. The article concludes with some recommendations for future work. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2508–2524, 2016

A review of the operating limits in slot die coating processes

Time and length scales as well as the magnitude of individual contributions to eddy dispersion in chromatographic beds are resolved. We address this issue by a high-resolution numerical analysis of flow and mass transport in computer-generated bulk (unconfined) packings of monosized, nonporous, incompressible, spherical particles and complementary confined cylindrical packings with a cylinder-to-particle diameter ratio of d(c)/d(p) = 20. The transient behavior of longitudinal and transverse dispersion is analyzed and correlated with the spatial scales of heterogeneity in the bulk and confined packings. Simulations were carried out until complete transcolumn equilibration in the confined packings was achieved to facilitate a quantitative study of the geometrical wall effect. Longitudinal plate height data calculated over a wide range of reduced velocities (0.1 < or = nu < or = 500) were fitted to the comprehensive Giddings equation. The determined transition velocities for individual contributions to eddy dispersion were found to be widely disparate. As a consequence, the total effect of eddy dispersion on the plate height curves can be approximated in the practical range of chromatographic operational velocities (5 < or = nu < or = 20) by a composite expression in which only the short-range interchannel contribution retains its coupling characteristics, while transchannel and transcolumn contributions appear as simple mass transfer velocity-proportional terms.

Time and Length Scales of Eddy Dispersion in Chromatographic Beds

From random sphere packings to regular pillar arrays: effect of the macroscopic confinement on hydrodynamic dispersion.

Dynamic wetting is crucial to processes where liquid displaces another fluid along a solid surface, such as the deposition of a coating liquid onto a moving substrate. Numerous studies report the failure of dynamic wetting past some critical process speed. However, the hydrodynamic factors that influence the transition to wetting failure remain poorly understood from an empirical and theoretical perspective. The objective of this investigation is to determine the effect of meniscus confinement on the onset of dynamic wetting failure. A novel experimental system is designed to simultaneously view confined and unconfined wetting systems as they approach wetting failure. The experimental apparatus consists of a scraped steel roll that rotates into a bath of glycerol. Confinement is imposed via a gap formed between a coating die and the roll surface. Flow visualization is used to record the critical roll speed at which wetting failure occurs. Comparison of the confined and unconfined data shows a clear increase in the relative critical speed as the meniscus becomes more confined. A hydrodynamic model for wetting failure is developed and analysed with (i) lubrication theory and (ii) a two-dimensional finite-element method (FEM). Both approaches do a remarkable job of matching the observed confinement trend, but only the two-dimensional model yields accurate estimates of the absolute values of the critical speeds due to the highly two-dimensional nature of the stress field in the displacing liquid. The overall success of the hydrodynamic model suggests a wetting failure mechanism primarily related to viscous bending of the meniscus.

Delaying the onset of dynamic wetting failure through meniscus confinement

This work investigates the onset of wetting failure for displacement of Newtonian fluids in parallel channels. A hydrodynamic model is developed for planar geometries where an advancing fluid displaces a receding fluid along a moving substrate. The model is evaluated with three distinct approaches: (i) the low-speed asymptotic theory of Cox [J. Fluid Mech. 168, 169–194 (1986)], (ii) a one-dimensional (1D) lubrication approach, and (iii) a two-dimensional (2D) flow model solved with the Galerkin finite element method (FEM). Approaches (ii) and (iii) predict the onset of wetting failure at a critical capillary number Cacrit, which coincides with a turning point in the steady-state solution family for a given set of system parameters. The 1D model fails to accurately describe interface shapes near the three-phase contact line when air is the receding fluid, producing large errors in estimates of Cacrit for these systems. Analysis of the 2D flow solution reveals that strong pressure gradients are needed to pu...

On the mechanism of wetting failure during fluid displacement along a moving substrate

Characteristic substrate speeds and meniscus shapes associated with the onset of air entrainment are studied during dynamic wetting failure along a planar substrate. Using high-speed video, the behaviour of the dynamic contact line (DCL) is recorded as a tape substrate is drawn through a bath of a glycerol/water solution. Air entrainment is identified by triangular air films that elongate from the DCL above some critical substrate speed. Meniscus confinement within a narrow gap between the substrate and a stationary plate is shown to delay air entrainment to higher speeds for a wide range of liquid viscosities, expanding upon the findings of Vandre, Carvalho & Kumar (J. Fluid Mech., vol. 707, 2012, pp. 496–520). A pressurized liquid reservoir controls the meniscus position within the confinement gap. It is found that liquid pressurization further postpones air entrainment when the meniscus is located near a sharp corner along the stationary plate. Meniscus shapes recorded near the DCL demonstrate that operating conditions influence the size of entrained air films, with smaller films appearing in the more viscous solutions. Regardless of size, air films become unstable to thickness perturbations and ultimately rupture, leading to the entrainment of air bubbles. Recorded critical speeds and air-film sizes compare well to predictions from a hydrodynamic model for dynamic wetting failure, suggesting that strong air stresses near the DCL trigger the onset of air entrainment.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5ADDAB0949E646B997EEECA69061F4FC/S0022112014001104a.pdf/div-class-title-characteristics-of-air-entrainment-during-dynamic-wetting-failure-along-a-planar-substrate-div.pdf

Characteristics of air entrainment during dynamic wetting failure along a planar substrate

Dynamic wetting failure in surfactant solutions

Dynamic wetting failure in curtain coating of Newtonian liquids is studied in this work. A hydrodynamic model accounting for air flow near the dynamic contact line (DCL) is developed to describe two-dimensional (2D) steady wetting and to predict the onset of wetting failure. A hybrid approach is used where air is described by a one-dimensional model and liquid by a 2D model, and the resulting hybrid formulation is solved with the Galerkin finite element method. The results reveal that the delay of wetting failure in curtain coating – often termed hydrodynamic assist – mainly arises from the hydrodynamic pressure generated by the inertia of the impinging curtain. This pressure leads to a strong capillary-stress gradient that pumps air away from the DCL and thus increases the critical substrate speed for wetting failure. Although the parameter values used in the model are different from those in experiments due to computational limitations, the model is able to capture the experimentally observed non-monotonic behaviour of the critical substrate speed as the feed flow rate increases (Blake et al., Phys. Fluids, vol. 11, 1999, p. 1995–2007). The influence of insoluble surfactants is also investigated, and the results show that Marangoni stresses tend to thin the air film and increase air-pressure gradients near the DCL, thereby promoting the onset of wetting failure. In addition, Marangoni stresses reduce the degree of hydrodynamic assist in curtain coating, suggesting a possible mechanism for experimental observations reported by Marston et al. (Exp. Fluids, vol. 46, 2009, pp. 549–558).

Eric Vandre

Papers

Delaying the onset of dynamic wetting failure through meniscus confinement

On the mechanism of wetting failure during fluid displacement along a moving substrate

Characteristics of air entrainment during dynamic wetting failure along a planar substrate

Dynamic wetting failure in surfactant solutions

Dynamic wetting failure and hydrodynamic assist in curtain coating