Forward roll coating flows of viscoelastic liquids

Roll coating is distinguished by the use of one or more gaps between rotating cylinders to meter and apply a liquid layer to a substrate. Except at low speed, the two-dimensional film splitting flow that occurs in forward roll coating is unstable; a three-dimensional steady flow sets in, resulting in more or less regular stripes in the machine direction. For Newtonian liquids, the stability of the two-dimensional flow is determined by the competition of capillary and viscous forces: the onset of meniscus nonuniformity is marked by a critical value of the capillary number. Although most of the liquids coated industrially are non-Newtonian polymeric solutions and dispersions, most of the theoretical analyses of film splitting flows relied on the Newtonian model. Non-Newtonian behavior can drastically change the nature of the flow near the free surface; when minute amounts of flexible polymer are present, the onset of the three-dimensional instability occurs at much lower speeds than in the Newtonian case.Forward roll coating flow is analyzed here with two differential constitutive models, the Oldroyd-B and the FENE-P equations. The results show that the elastic stresses change the flow near the film splitting meniscus by reducing and eventually eliminating the recirculation present at low capillary number. When the recirculation disappears, the difference of the tangential and normal stresses (i.e., the hoop stress) at the free surface becomes positive and grows dramatically with fluid elasticity, which explains how viscoelasticity destabilizes the flow in terms of the analysis of Graham [M.D. Graham, Interfacial hoop stress and instability of viscoelastic free surface flows, Phys. Fluids 15 (2003) 1702–1710].     

Helical flow of some non-Newtonian liquids

Rheologica Acta - The equations of Cross and Cassou describing two types of shear-thinning liquids are extended to flow in two dimensions. The resulting equations are then applied to helical flow...     

On pulsatile flow of non-Newtonian liquids

Rheologica Acta - We consider the behaviour of non-Newtonian liquids as they are made to flow through straight pipes of circular cross section under the action of a pressure -gradient which...     

Discernment of non-Newtonian behavior in liquids by acoustic means

An experiment was conducted with the use of a „sonic viscometer” to demonstrate that a change in the constitutive nature of a fluid will alter the overtones that occur from the nonlinearity of the propagation of a sine wave through the fluid. Pure sine waves ranging octave-wise from 500 to 8000Hz were introduced into distilled water, and FFT analyses of the signals received were compared with those resulting from transmission of the same set of sine waves through a 1% solution of polyethylene oxide in distilled water. Differences in the FFT spectra which occur as the result of introducing the polymeric solute indicate that the device could prove viable in indicating small changes in viscous properties. Received: 10 February 1998 Accepted: 1 June 1998     

Rising behavior of single bubble in infinite stagnant non-Newtonian liquids

This work is an experimental study of the rising behavior of single air bubbles in infinite stagnant non-Newtonian liquids. Aqueous solutions of carboxymethyl cellulose (CMC) are selected to study the effect of rheological properties. The high speed photography is employed to record the bubble motion in CMC solutions. The bubble size, rising trajectory, bubble shape and velocities are determined by digital image processing technique. As expected, the rheological properties have great influence on the rising behavior of single bubble. In the less concentrated CMC solutions, the bubble rising process can be divided into three stages according to spatial evolution of bubble shape. The deformation changes the trajectories of rising bubbles and bubble hydrodynamics. As the solution concentration increases, the transitional stage gradually disappears. In the most concentrated CMC solution, the first continuous shape flattening stage is directly followed by a rising process with bubble shape basically constant, the rectilinear path and constant rising velocity. Dimensional analysis is performed to formulate a general dimensionless correlation for the deformation and motion of bubbles in infinite liquids by considering the rheological properties.     

On slip effect in free coating of non-Newtonian fluids

The failure of the current theories to predict the coating thickness of non-Newtonian fluids in free coating operations is shown to be a result of the effective slip at the moving rigid surface being coated. This slip phenomenon is a consequence of stress induced diffusion occurring in flow of structured liquids in non-homogeneous flow fields. Literature data have been analysed to substantiate the slip hypothesis proposed in this work. The experimentally observed coating thickness is shown to lie between an upper bound, which is estimated by a no-slip condition for homogeneous solution and a lower bound, which is estimated by using solvent properties. Some design considerations have been provided, which will serve as useful guidelines for estimating coating thickness in industrial practice.fa exponent in eq. (15) - b n/(4 –n)(n + 1) - Ca Capillary number - D diffusivity - De Deborah number - g acceleration due to gravity - G Goucher number - h thickness profile - h ₀ final coating thickness - K consistency index - L length available for diffusion - L _t tube length - n power-law index - P pressure drop - Q flow rate - R cylinder radius - R _t tube radius - t time available for diffusion - T ₀ dimensionless thickness without slip - T _s dimensionless thickness with slip - U _c theoretically calculated withdrawal velocity to match the film thickness - u _s slip velocity - U withdrawal velocity - U _w theoretically calculated withdrawal velocity based on solvent properties - U ^* effective withdrawal velocity - x distance in the direction of flow - y distance transverse to the flow direction - curvature coefficient - slip coefficient - curvature coefficient - rate of deformation tensor - u _s /U - relaxation time - density - surface tension - shear stress in tube flow - _w wall shear stress in tube flow - stress tensor - _w wall shear stress - T _s /T ₀ NCL-Communication No. 2818     

Developing laminar flows with visco-elastic and non-Newtonian liquids

Summary Developing laminar flows have been studied experimentally in straight pipes of circular cross-section. Velocity profiles have been measured and entry lengths determined for the transition from an initially flat profile to the equilibrium form: flow visualisation using fine tracer particles was the technique used. It has been found that non-Newtonian (pseudo-plastic) fluids have significantly longer development regions than those corresponding to dynamically similar Newtonian conditions. Viscoelastic liquids depart even more from the simple case. The experimental evidence seems to indicate that elastic effects influence the flow field at two differing time scales, not only where the process time is of the same order of magnitude as the natural (relaxation) time of the liquid but also in much slower processes.

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Zusammenfassung Die Entwicklung von laminaren Strömungen wurde experimentell in geraden Rohren mit Kreisquerschnitt untersucht. Die Geschwindigkeitsprofile wurden gemessen und die Eintrittslängen bestimmt, die für den Übergang von dem ursprünglich flachen Profil zur Gleichgewichtsform nötig sind. Die Strömung wurde mit Hilfe von feinen Spurenteilchen sichtbar gemacht. Es zeigte sich dabei, daß nicht-Newtonsche Flüssigkeiten ein deutlich größeres Übergangsgebiet haben als solche, die sich auf dynamisch ähnliche Newtonsche Bedingungen beziehen. Viskoelastische Flüssigkeiten weichen stärker von dem einfachen Fall ab.Das Experiment scheint zu zeigen, daß elastische Effekte das Strömungsfeld in zwei unterschiedlichen Zeitmaßstäben beeinflussen: nicht nur in dem Bereich, in dem die Prozeßzeit von derselben Größenordnung ist wie die Relaxationszeit der Flüssigkeit, sondern auch bei wesentlich langsameren Prozessen.

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Elastohydrodynamics of tensioned web roll coating process

Coating process is an important step in the manufacturing of different products, such as paper, adhesive and magnetic tapes, photographic films, and many other. The tensioned web roll coating is one the several methods used by different industries. It relies on the elastohydrodynamic action between the fluid and the tensioned substrate for transferring and applying the liquid. The main advantage of this method is its ability to apply very thin liquid layers with less sensitivity to mechanical tolerance at relative small cost. Despite its industrial application, theoretical analysis and fundamental understanding of the process are limited. This work analyses this elastohydrodynamic action by solving the differential equations that govern the liquid flow, described by the Navier–Stokes equation, and the web deformation, modelled by the cylindrical shell approximation. The goal is to determine the operating conditions at which the process is two dimensional and defect free. The equations are discretized by the Galerkin/finite‐element method. The resulting non‐linear system of equations is solved by Newton's method coupled with pseudo‐arc‐length continuation in order to obtain solutions around turning points. The theoretical results are used to construct an operating window of the process that is in agreement with limited experimental data. Copyright © 2003 John Wiley & Sons, Ltd.     

Flow enhancement mechanisms of a pulsating flow of non-Newtonian liquids

Summary The pipe flow of non-Newtonian liquids under a fluctuating pressure gradient is considered. Adopting a generalized Maxwell model with full relaxation spectrum and considering only weak-sense stationary pressure-gradient noises, it is shown that there are two mechanisms involved in the flow enhancement: an inelastic and a dynamic mechanism. Both depend on the shear-thinning properties of the liquid in steady and oscillatory flows. For one-frequency pressuregradient noises, the flow enhancement increases with increasing frequency of fluctuation if the modulus of the complex viscosity is a decreasing function of the frequency. Since almost all polymeric liquids are shear-thinning in oscillatory shear flows, this investigation serves as a possible explanation for the data collected byBarnes, Townsend andWalters (1971). This, however, does not necessarily ensure that the constitutive model adopted in this study is free of defect in a general flow field.

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Zusammenfassung Es wird die Rohrströmung einer nicht-newtonschen Flüssigkeit bei fluktuierendem Druckgefälle betrachtet. Für ein verallgemeinertes Maxwell-Modell mit beliebigem Relaxations-Spektrum wird bei Beschränkung auf kleine Schwankungen des Druckgradienten um einen stationären Mittelwert gezeigt, daß zwei Mechanismen zur Steigerung des Durchflusses beitragen, ein unelastischer und ein dynamischer Mechanismus. Beide hängen von den Scherentzähungs-Eigenschaften der Flüssigkeit bei stationären und oszillierenden Beanspruchungen ab. Für eine harmonisch-periodische Druckstörung nimmt die Durchflußsteigerung mit wachsender Schwankungsfrequenz zu, wenn der Betrag der komplexen Viskosität eine mit der Frequenz abnehmende Funktion darstellt. Da nahezu alle Polymerflüssigkeiten bei oszillierenden Scherströmungen Scherentzähung aufweisen, liefert diese Untersuchung eine mögliche Erklärung für die vonBarnes, Townsend undWalters (1971) zusammengestellten Ergebnisse. Dies bedeutet aber nicht notwendigerweise, daß das hier angenommene Modell auch für die Beschreibung allgemeinerer Strömungsfelder angemessen ist.

     

High-speed roll coating with complex rheology fluids

The flow of high solids content suspensions and coating colors through the deformable gap of counter-rotating rolls at high speed was investigated. Measurements of nip pressure profiles in a laboratory film coater were conducted and flow visualization experiments downstream the nip were carried out. A high-speed video system allowed showing the formation, elongation and break up of filaments that yield the misting droplets. The role of rheology on misting was also investigated using shear and extensional data. Results show that misting, mainly generated by film splitting, is reduced when the extensional viscosity of the color is larger.     

Newtonian and non-Newtonian liquids rotating adjacent to a stationary surface

The interaction of a rotating flow and a stationary surface is discussed for a second-order non-Newtonian liquid. Similarity solutions of the governing partial differential equations are obtained for the case of the outer flow in solid-body rotation. The results for the Newtonian case are compared with Bödewadt's series solution of this problem. The non-Newtonian solutions indicate that for certain values of the parameters characterizing the non-linear viscous response and normal stress effects a larger secondary flow is induced in the boundary layer than in the Newtonian case.Also at North Carolina State University Raleigh (N.C.), U.S.A.     

Flow simulation in the nip of a rigid forward roll coater

This paper shows the development of an efficient solution algorithm for the simulation of a forward roll coating flows with free surfaces. The technique is based on the method of successive approximation combined with a method for rapidly finding a good starting point, i.e. a good initial computational domain. Movement of the free surface from the initial to final positions is demonstrated using both kinematic and normal stress schemes. Adaptive domain decomposition at each pseudo time step is performed with no significant cost penalty. The flow field is computed using a finite element solution of the Navier–Stokes equation. The proposed scheme is shown to be flexible enough to accommodate different scenarios over the practical range of many applications, i.e. capillary numbers in the range of 0.01–300, and a wide range of gap settings and rotational speeds. A close match is found between simulation and experimental meniscus profiles as well as nip pressure profiles. Overall the technique is quite robust and is able to simulate a variety of coating flow situations without resorting to over‐simplifications. Copyright © 2005 John Wiley & Sons, Ltd.     

The influence of walls on the motion of a sphere in non-Newtonian liquids

The influence of the contained wall on the drag of a sphere moving through a non-Newtonian fluid is analysed in this work separately for the low Reynolds number and the high Reynolds number regions. In the former, we make use of the two-concentric-sphere model. It is predicted that the wall effect will decrease with the increase of the shear-thinning anomaly and this is in a reasonable agreement with the available experimental data and correlations. The wall effect in the high Reynolds number region is analysed in this work using the cell model (used to study the motion of an assemblage of solid spheres) and the predictions are in satisfactory agreement with the available empirical correlation for non-Newtonian fluids. Presented at the First Conference of European Rheologists, Graz (Austria), April 14–16, 1982.     

On the flow of Newtonian and non-Newtonian liquids through corrugated pipes

Rheologica Acta - Consideration is given to the flow of Newtonian and non-Newtonian liquids through a “corrugated” pipe of circular cross section whose radius sinusoidally along its...     

The flow of Newtonian and non-Newtonian liquids through annular converging regions

A coordinate system is introduced in which one of the three sets of coordinate surfaces is constituted by cones. The axes of the cones coincide, but in general the apices of the cones do not. For this so-called special toroidal coordinate system a set of operations is given involving the nabla operator. A few examples of the use of this special toroidal coordinate system will elucidate its advantages for the analysis of the flow of Newtonian and generalized Newtonian liquids in annular convergent regions.Dedicated to the 60th birthday of Prof. Dr. H. Janeschitz-Kriegl     

On the use of power equations to relate shear-rate to stress in non-Newtonian liquids

Ohne Zusammenfassung

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