Wetting Lines Research Articles

The effect of end-plate wetting and unpinned contact lines on the filament thinning of strain hardening fluids

The Filament Extension Atomizer™ (FEA) is a unique technology designed for highly viscous or strain-hardening fluids that are otherwise difficult to atomize. The fluid is processed as a thin film between the contact points of two counter-rotating rollers of different materials. As the film is processed beyond the contact point, it is subject to an extensional flow that creates numerous thin filaments. As the filaments are stretched, they thin, and eventually, surface tension causes them to break into tightly dispersed droplets. Certain fluids, particularly those of low to moderate viscosity and high surface tension, can present challenges to atomize in FEA. Due to the tendency of these fluids to coalesce, their wetting on the rollers has been critical in optimizing film formation, though the impact of surface wetting on filament formation and breakup is not well understood. Accordingly, we studied the role of end-plate wetting for a high surface tension, aqueous, strain-hardening polymer solution on filament formation, thinning, and breakup, and fluid transfer to the end-plates, using a modified Capillary Breakup Extensional Rheometer (CABER). We found that filament formation and evolution were dramatically affected by both the wetting and wetting imbalances between the two end-plates, leading to different behavior across different end-plate combinations. The highly imbalanced wetting scenarios (i.e., combining a highly wetting and a non-wetting end-plate) gave rise to the most extreme deviations from classic behavior in conventional CABER experiments, such as long persisting filaments.

Clay Nanotubes Aligned with Shear Forces for Mesenchymal Stem Cell Patterning.

Aligned halloysite nanotubes on solid substrates are fabricated by a shearing method with brush assistance. These clay nanotubes are aligned by shear force in strip-like patterns accomplished with drying ordering at elevated temperatures. The nanotubes' orientation is governed by "coffee-ring" formation mechanisms depending on the dispersion concentration, nanotube charge, and speed of thermos-evaporation. Polarized light irradiated through the patterns demonstrates birefringence and confirms the orientation. Scanning electron microscopy and atomic force microscopy show that the nanotubes are aligned along the direction of the wetting lines above 4 wt%, while they are not oriented at lower concentrations. Halloysite concentration, drying temperature, and type of brush fibers affect the pattern ordering. The aligned halloysite systems on glass, tissue culture plates, and polymer films, provide a promising platform for biocell guiding. Human foreskin fibroblasts proliferated well on the aligned clay patterns and the cell orientation agrees with the nanotube direction. Human bone mesenchymal stem cells (HBMSCs) are also cultured on the organized halloysite coating. The clay patterns support HBMSC proliferation with alignment, and such nanostructured substrates promote osteogenesis differentiation without growth factors. This facile method for preparing aligned halloysite patterns on solid substrates is very promising for surface modification in biotissue engineering.

Modelling polymeric flows in reverse roll coating processes with dynamic wetting lines and air-entrainment: FENE and PTT solutions

Viscoelastic FENE and PTT constitutive models are considered in the simulation of high-speed reverse roll coating flow with polymeric paint solutions, where wetting lines and air-entrainment are incorporated. Both FENE-CR and FENE-P models are utilised to illustrate the influence of shear-thinning in the context of strain-hardening properties. Strain-softening is introduced via PTT solutions in contrast. Steady solutions are derived numerically through a time-stepping hybrid finite element-finite volume sub-cell algorithm with dynamic free-surface location, drawing upon a fractional staged, predictor-corrector, and semi-implicit time-stepping procedure. A systematic computational and rheological study allows for parametric variation in elasticity (Wi-variation), level of strain-hardening (AL), shear-thinning and solvent fraction (β). Various problem aspects are investigated to reveal the influence of viscoelasticity on vortex developments, pressure and lift profiles, shear and strain-rates, and critical stress states. Specific features of viscoelastic flow response are observed by analysing stress and flow structures over a range of Weissenberg numbers. The novel aspects of the work lie in the application of the algorithm to the reverse roll coating process under such viscoelastic fluid models.

Viscoelastic computations for reverse roll coating with dynamic wetting lines and the Phan-Thien-Tanner models

The computational modelling of reverse roll coating with dynamic wetting line has been analysed for various non-Newtonian viscoelastic materials appealing to the Phan-Thien-Tanner (PTT) network class of models suitable for typical polymer solutions, with properties of shear thinning and strain hardening/softening. The numerical technique utilizes a hybrid finite element-sub-cell finite volume algorithm with a dynamic free-surface location, drawing upon a fractional-staged predictor-corrector semi-implicit time-stepping procedure of an incremental pressure-correction form. The numerical solution is investigated following a systematic study which allows for parametric variation in elasticity (We-variation), extensional hardening-softening (e), and solvent fraction (β). Under incompressible flow conditions, linear PTT (LPTT) and exponential PTT (EPTT) models were used to solve the paint strip coatings, under reverse roll-coating configuration. This involves two-dimensional planar reverse roll-coating domains, considering a range of Weissenberg numbers (We) up to critical levels, addressing velocity fields and vortex development, pressure and lift profiles, shear rate, and stress fields. Various differences are observed when comparing solutions for these constitutive models. Concerning the effects of elasticity, increase in We stimulates vortex structures, which are visible at both the downstream meniscus and upstream narrowest nip region, whilst decreasing the peak pressure and lift values at the nip constriction. At low values (e > 0.5, β = 0.1) of extensional viscosity, the LPTT flow fields were much easier to extract, attaining critical We levels up to unity, in contrast to critical We levels of 0.4 for EPTT solutions. This finding is reversed at higher extensional viscosity levels (e < 0.5). This trend reveals qualitative agreement with theoretical studies. Noting flow behaviour under EPTT solution, increasing the peak level of strain hardening/softening is found to stimulate vortex activity around the nip region, with a corresponding increase in peak pressure and lift values.

Droplet migration: Quantitative comparisons with experiment

An important practical feature of simulating droplet migration computationally, using the lubrication approach coupled to a disjoining pressure term, is the need to specify the thickness, H*, of a thin energetically stable wetting layer, or precursor film, over the entire substrate. The necessity that H* be small in order to improve the accuracy of predicted droplet migration speeds, allied to the need for mesh resolution of the same order as H* near wetting lines, increases the computational demands significantly. To date no systematic investigation of these requirements on the quantitative agreement between prediction and experimental observation has been reported. Accordingly, this paper combines highly efficient Multigrid methods for solving the associated lubrication equations with a parallel computing framework, to explore the effect of H* and mesh resolution. The solutions generated are compared with recent experimentally determined migration speeds for droplet flows down an inclined plane.

The physics of moving wetting lines

Scientists tend to think in terms of their most familiar models. It is not accidental that the earliest descriptions of the moving wetting line and its associated dynamic contact angle were in terms of displaced equilibria (chemists), friction (physicists) and viscous bending of the liquid–vapour interface (engineers and mathematicians). Each of these approaches has progressed since its inception, but, while each reflects a different facet of the underlying physical mechanism, and each offers at least a semi-empirical route to its description, none is complete. There is, as yet, no fully agreed treatment that is consistent with all three viewpoints and provides an effective basis for prediction—though at least one new hydrodynamic approach has emerged that goes some way in this direction. This paper seeks to offer a status report: to briefly review each of the current approaches, to illustrate their successes and limitations as revealed by experiment and simulation, and to suggest ways in which the different aspects of wetting dynamics might be investigated in the future.

Wetting Line Behavior on a Locally Surface Treated Poly(tetrafluoroethylene)

Electrochemical treatment of poly(tetrafluoroethylene) (PTFE) surfaces has been effected in localized areas of typical dimension of the order of 200 μm, leading to small regions of increased surface free energy. These have been studied by considering the wetting triple lines of tricresyl phosphate in the vicinity. Good correlation between theoretical predictions and observations of the shapes of the wetting lines was obtained, not only in the outer regions and on the untreated material, but also in the inner, treated zones. A predicted transition from concavity to convexity of the wetting line shape was corroborated by observations. The excess wettability of the treated zones of PTFE decreased following intense light exposure. Excess wettability, as evaluated from experimental data, exceeded predictions, possibly due to nonrespect of Antonow's rule at the local scale.

A finite element method for free surface flows of incompressible fluids in three dimensions. Part II. Dynamic wetting lines

To date, few researchers have solved three-dimensional free surface problems with dynamic wetting lines. This paper extends the free surface finite element method (FEM) described in a companion paper [Cairncross RA, Schunk PR, Baer TA, Sackinger PA, Rao RR. A finite element method for free surface flows of incompressible fluid in three dimensions. Part I. Boundary fitted mesh motion. International Journal for Numerical Methods in Fluids 2000; 33: 375–403] to handle dynamic wetting. A generalization of the technique used in two-dimensional modeling to circumvent double-valued velocities at the wetting line, the so-called kinematic paradox, is presented for a wetting line in three dimensions. This approach requires the fluid velocity normal to the contact line to be zero, the fluid velocity tangent to the contact line to be equal to the tangential component of web velocity, and the fluid velocity into the web to be zero. In addition, slip is allowed in a narrow strip along the substrate surface near the dynamic contact line. For realistic wetting line motion, a contact angle that varies with wetting speed is required because contact lines in three dimensions typically advance or recede at different rates depending upon location and/or have both advancing and receding portions. The theory is applied to capillary rise of static fluid in a corner, the initial motion of a Newtonian droplet down an inclined plane, and extrusion of a Newtonian fluid from a nozzle onto a moving substrate. The extrusion results are compared with experimental visualization. Copyright © 2000 John Wiley & Sons, Ltd.

A finite element method for free surface flows of incompressible fluids in three dimensions. Part II. Dynamic wetting lines

To date, few researchers have solved three-dimensional free surface problems with dynamic wetting lines. This paper extends the free surface finite element method (FEM) described in a companion paper [Cairncross RA, Schunk PR, Baer TA, Sackinger PA, Rao RR. A finite element method for free surface flows of incompressible fluid in three dimensions. Part I. Boundary fitted mesh motion. International Journal for Numerical Methods in Fluids 2000; 33: 375–403] to handle dynamic wetting. A generalization of the technique used in two-dimensional modeling to circumvent double-valued velocities at the wetting line, the so-called kinematic paradox, is presented for a wetting line in three dimensions. This approach requires the fluid velocity normal to the contact line to be zero, the fluid velocity tangent to the contact line to be equal to the tangential component of web velocity, and the fluid velocity into the web to be zero. In addition, slip is allowed in a narrow strip along the substrate surface near the dynamic contact line. For realistic wetting line motion, a contact angle that varies with wetting speed is required because contact lines in three dimensions typically advance or recede at different rates depending upon location and/or have both advancing and receding portions. The theory is applied to capillary rise of static fluid in a corner, the initial motion of a Newtonian droplet down an inclined plane, and extrusion of a Newtonian fluid from a nozzle onto a moving substrate. The extrusion results are compared with experimental visualization. Copyright © 2000 John Wiley & Sons, Ltd.

Visualization of coating flows

An experimental technique for visualizing small-scale film flows is presented. The method utilizes hydrogen bubbles, dye injection, and optical sectioning. Specific aspects of applying this technique to coating processes, distinguished by two free surfaces, liquid-liquid interfaces, static and dynamic wetting lines, and small characteristic dimensions, are discussed in detail. This experimental approach is essential in providing the necessary boundary conditions for modern computer-aided theoretical computations of wetting-related flow fields. The power of the visualization method is demonstrated by examples showing the flow pattern of two liquid films merging on an inclined plane and the flow field of a liquid film being transferred from an inclined plane onto a moving surface.

Wetting phenomena in the two-dimensional ANNNI model in a field

Wetting phenomena at various interface types in the ordered phases of the two-dimensional axial next-nearest neighbour Ising (or ANNNI) model in a field are studied using a transfer matrix approach and Monte Carlo techniques. Different types of wetting at distinct wetting lines or at the bulk phase boundary are identified, which may be tested experimentally in adsorbate systems with a (p×1) ordering, forp equal to two, three or four.

Commensurate-incommensurate phase transitions and wetting in a lattice-gas model with axially competing interactions.

The two-dimensional axial next-nearest-neighbor Ising model in an external magnetic field is studied at low temperatures with the use of transfer-matrix techniques. Commensurate-incommensurate phase boundaries are calculated with improved free-fermion approximations which take into account the presence of both light and heavy walls. Special attention is paid to the case when three different periodicities compete. In the incommensurate phases the structure factor shows a multimodulated structure, which is calculated explicitly. Our approach makes possible the analytic determination of the wetting lines in the 〈2,1〉 phase which end at a new type of multicritical point. Results are tested by Monte Carlo simulations.

The stability of inclined sessile drops

The limits of stability are determined for sessile drops with fixed volume and attached at prescribed wetting lines to inclined solid surfaces. Finite element techniques developed in an earlier paper [Lawal and Brown, J. Colloid Interface Sci., 89, 332 (1982).] are used to calculate the critical points, defined in terms of inclination angle and gravitational Bond number, at which the sessile drop loses stability. For fixed Bond number, axisymmetric sessile shapes on horizontal surfaces lose stability at a drop volume that corresponds to a point of bifurcation to a family of asymmetric shapes. The asymmetric shapes develop toward decreasing volume and are also unstable. Inclining the drop disrupts the axial symmetry and ruptures the bifurcation point into a limit point that marks the maximum volume for existence of stable drop shapes. This mode for loss of equilibrium persists for all inclination angles and is not changed qualitatively by changing the shape of the wetting curve.