The effect of shear‐thickening on the stability of slot‐die coating

Slot‐die coating is an economical roll‐to‐roll processing technique with potential to revolutionize the fabrication of nano‐patterned thin films at high throughput. In this study, the impact of shear‐thickening of the coating fluid on the stability of slot‐die coating was investigated. For the coating fluid, a model system fumed silica nanoparticles dispersed in polypropylene glycol was chosen. These dispersions exhibit shear and extensional thickening characterized through steady shear and capillary break‐up measurements. The critical web velocity for the onset of coating defect for different flow rates was measured, while the type of coating defect was visualized using a high speed camera. For the shear thickening particle dispersions, the coating failed through the onset of a ribbing instability. The critical web velocity for the onset of coating defect was found to decrease with increasing particle concentration and increasing fluid viscosity. The minimum wet thickness was studied as a function of capillary number for the particle dispersions and compared with a series of Newtonian fluids with similar viscosities. In all cases, shear‐thickening behavior was found to stabilize coating by reducing the minimum wet coating thickness when compared against a Newtonian fluid with similar viscosity at the same capillary number. Conversely, the shear‐thinning fluids tested destabilized the coating by increasing the minimum wet thickness when compared against a Newtonian at the same capillary number. The impact of shear‐thickening on slot‐die coating was further studied by quantifying the evolution of the ribbing instability with increasing web speed and by conducting tests over a wide range of coating gaps. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4536–4547, 2016     

Capillary viscometry: A complete analysis including pressure and viscous heating effects

Capillary viscometers have been used extensively, because of their simplicity and reliability, to measure the viscosity of fluids over a wide range of shear rates. However, in capillary flow, the shear rate is not uniform throughout the capillary, a pressure gradient is established in the direction of flow, and the temperature of the fluid is nonuniform due to viscous dissipation. In the present work, a general, simple and practical method is proposed for correcting for the effects of pressure variation and viscous dissipation in determining the viscosity of polymer melts at high pressures. The method essentially involves the estimation of temperature, pressure, shear rate, and shear stress under a variety of experimental conditions at a predetermined point in the capillary. As such, it may be considered as a generalized extension of the classical Rabinowitsch-Mooney method for estimating true viscosity in capillary flow.     

STEADY SHEAR FLOW PROPERTIES OF HIGH SOLIDS SOFTWOOD KRAFT BLACK LIQUORS: EFFECTS OF TEMPERATURE, SOLIDS CONCENTRATIONS, LIGNIN MOLECULAR WEIGHT AND SHEAR RATE

The steady shear flow properties of several softwood kraft black liquors (slash pine) from a two level, four variable factorially designed pulping experiment were determined for solids concentrations from 50% to 85%, temperatures from 40°C to 140°C and shear rates up to 10,000 s-1 by using Instron capillary and Haake coaxial cylinder rheometers. It was shown that the slip velocity at the wall of the capillary is insignificant and that a two capillary method can be used to determine the viscosity of the samples. At high solids, black liquor can exhibit non-Newtonian behavior dependent upon temperature, solids concentrations, solids composition and shear rate. In general, the liquors behave as pseudoplastic fluids. The exact level of viscosity at any given condition is dependent upon the solids composition which will vary from liquor-to-liquor. The flow behavior of the liquors was described using power-law, Cross and Carreau-Yasuda models. Superposition principles developed for polymer melts and concentrated polymer solutions were applied to obtain reduced correlations for viscosity behavior of the liquors. By using a suitable reference temperature, related to the glass transition temperature of black liquors, a generalized WLF type shift factor was obtained for the liquors used in this study and can be used to obtain a reduced plot of viscosity behavior of other black liquors.     

A stochastic analysis of the flow of two immiscible fluids in porous media: The case when the viscosities of the fluids are equal

A new stochastic theory is developed to explain the flow of two immiscible fluids in porous medium when the viscosity difference between two fluids is zero. In an individual micropore the radius of curvature of the interface separating the fluids is assumed constant and flow is modeled by the random jumping of microscopic interfaces. A one dimensional model composed of an array of parallel capillary tubes of constant radius is analyzed in detail. For the case in which two fluids have equal viscosity an analytical solution is obtained. The fluid displacement process is Fickian and dispersion is described in terms of a diffusion or spreading constant.     

Rheology-morphology relationships in nylon 6/liquid-crystalline polymer blends

Extrusion measurements have been carried out on blends of nylon 6 and a liquid-crystalline copolyesteramide (LCP). The flow curves at low temperature show a behavior similar to that of pure LCP with a rapid rise of the viscosity at low shear rates. At high shear rates the viscosity is lower than that for each of the two components. This minimum has been attributed to the lack of interactions between the two phases and to the formation of fibrils of the LCP phase. The SEM analysis shows, indeed, that fibrils of the LCP phase are produced in the convergent flow at the inlet of the capillary at high shear rates. These fibrils are lost during the flow in the long capillary.     

Dynamic modeling of drainage through three-dimensional porous materials

The interplay of viscous, gravity and capillary forces determines the flow behavior of two or more phases through porous materials. In this study, a rule-based dynamic network model is developed to simulate two-phase flow in three-dimensional porous media. A cubic network analog of porous medium is used with cubic bodies and square cross-section throats. The rules for phase movement and redistribution are devised to honor the imbibition and drainage physics at pore scale. These rules are based on the pressure field within the porous medium that is solved for by applying mass conservation at each node. The pressure field governs the movement and flow rates of the fluids within the porous medium. Film flow has been incorporated in a novel way. A pseudo-percolation model is proposed for low but non-zero capillary number (ratio of viscous to capillary forces). The model is used to study primary drainage with constant inlet flow rate and constant inlet pressure boundary conditions. Non-wetting phase front dynamics, apparent wetting residuals (S_wr), and relative permeability are computed as a function of capillary number (N_ca), viscosity ratio (M), and pore-throat size distribution. The simulation results are compared with experimental results from the literature. Depending upon the flow rate and viscosity ratio, the displacement front shows three distinct flow patterns—stable, viscous fingering and capillary fingering. Capillary desaturation curves (S_wr vs. N_ca) depend on the viscosity ratio. It is shown that at high flow rates (or high N_ca), relative permeability assumes a linear dependence upon saturation. Pseudo-static capillary pressure curve is also estimated (by using an invasion percolation model) and is compared with the dynamic capillary pressure obtained from the model.     

Adhesive Dispensing Process Analysis: Steady-State Dispensing of One-Component Adhesives

The process of dispensing one-component heat-cure adhesives was investigated in order to understand current application processes and to guide new process development. Typical one-component adhesives exhibit non-Newtonian rheological behavior, and hence Newtonian fluid mechanics does not adequately describe the dispensing process. In the present study, the adhesives were modeled as Bingham fluids possessing a yield stress and a steady state viscosity. The model of the dispensing apparatus includes four major flow sections connected in a serial configuration. The fluid mechanics equations derived for Bingham fluids in the individual flow sections were solved by numerical methods in order to understand the interrelationships between the material variables (e.g. yield stress, viscosity, temperature dependencies) and process variables (e.g. pressure, flow geometry, temperature, output). The concept of the model is generic and the details of the model can be modified for any forced-flow adhesive application process.

The adhesive flow properties significantly influence the process output. Dispensing temperature, among the process variables, has the strongest effect on process output. A ± 1.0·C perturbation in the dispensing temperature can cause as much as a 14% variation in the bead size for the range of adhesives studied. Differences in flow characteristics result in differences in processability and non-linear temperature/pressure sensitivity. The non-linear sensitivity can be eliminated by operating the dispensing process isothermally. Finally, the process limits for one-component adhesives, which are susceptible to chemical instability induced by viscous heating during processing, are defined and discussed in terms of a modified Brinkman number that takes into account viscous dissipation, heat conduction and convection, and chemical stability of the material during processing.     

Snap‐off of a liquid drop immersed in another liquid flowing through a constricted capillary

Emulsions are encountered at different stages of oil production processes, often impacting many aspects of oilfield operations. Emulsions may form as oil and water come in contact inside the reservoir rock, valves, pumps, and other equipments. Snap‐off is a possible mechanism to explain emulsion formation in two‐phase flow in porous media. Quartz capillary tubes with a constriction (pore neck) served to analyze snap‐off of long (“infinite”) oil droplets as a function of capillary number and oil‐water viscosity ratio. The flow of large oil drops through the constriction and the drop break‐up process were visualized using an optical microscope. Snap‐off occurrence was mapped as a function of flow parameters. High oil viscosity suppresses the breakup process, whereas snap‐up was always observed at low dispersed‐phase viscosity. At moderate viscosity oil/water ratio, snap‐off was observed only at low capillary number. Mechanistic explanations based on competing forces in the liquid phases were proposed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Energy Dissipation Rates of Newtonian and Non‐Newtonian Fluids in a Stirred Vessel

Energy dissipation rates of water and glycerol as Newtonian fluids and carboxyl methyl carbonate solution as non‐Newtonian fluid in a stirred vessel are investigated by 2D particle image velocimetry and compared. Mean velocity profiles reflect the Reynolds (Re) number similarity of two flow fields with different rheological properties, but the root mean square velocity profiles differ in rheology at the same Re‐number. Energy dissipation rates are estimated by direct calculation of fluctuating velocity gradients. The varying energy dissipation rates of Newtonian and non‐Newtonian fluids result from the difference in fluid rheology and apparent viscosity distribution which decides largely the flow pattern, circulation intensity, and rate of turbulence generation.     

Rheological effects of the incorporation of chlorinated polyethylene compatibilizers in a HDPE/PVC blend

Small‐amplitude oscillatory measurements, creep and recoil experiments, capillary extrusion flow and shrinkage measurements have been performed to elucidate the effect of block and random chlorinated polyethylene (CPE) on the rheological properties of a ternary high density polyethylene (HDPE)/ poly(vinyl chloride) (PVC)/CPE system. It is observed that the storage modulus, the complex viscosity and the steady stale viscosity at low shear rates decrease when a small amount of CPE is incorporated to 50/50 (wt.) HDPE/PVC binary blend. However, at high shear rates, in experiments performed in extrusion flow, the trend is reversed, and the incorporation of CPE to the binary blend increases viscosity. The high melt elasticity of HOPE is severely reduced when this polymer is mixed with PVC, but when CPE is included as a third component, elastic recovery is considerably increased. All these rheological results, which are independent of type (block or random) of CPE used, are explained considering the morphological changes produced by CPE and during extrusion flow.     

Two-phase flow in porous media

Two-phase flow in porous media depends on many factors, such as displacement vs steady two-phase flow, saturation, wettability conditions, wetting fluid vs non-wetting fluid is displacing, the capillary number, interfacial tension, viscosity ratio, pressure gradient, uniformly wetted vs mixed-wet pore surface, uniform vs distributed pore throats, small vs large pores, well-connected pores vs pores connected by small throats, etc. These parameters determine how the two fluids are distributed in the pores, e.g. whether they flow in seperate channels or side-by-side in the same channels, either with both fluids being continous or only one fluid being continous and the other discontinuous. In displacement, the capillary number and the viscosity ratio determine whether the displacement front is sharp, or if there is either capillary or viscous fingering.     

Effect of Viscosity on the Hydrodynamics of Liquid Processes in Microchannels

The hydrodynamics of single‐phase liquid flow with relatively high fluid viscosities in a microchannel was investigated experimentally. The results showed that the conventional theory could predict the single‐phase flow with high fluid viscosities in microchannels. Furthermore, the effect of viscosity on the slug flow of two immiscible liquid phases in a microchannel was studied with high‐speed imaging techniques. It was found that a higher dispersed‐phase viscosity quickened the flow pattern transition from slug flow to parallel flow and resulted in smaller slugs. A modified capillary number representing the mutual effects of the viscosities of the continuous phase and the dispersed phase was proposed for predicting the slug sizes in microchannels.     

Droplet formation of H2SO4/alkane system in a T‐junction microchannel: Gravity effect

A special system of concentrated sulfuric acid (H₂SO₄) and n‐hexane was used to study the droplet formation in a glass T‐junction microchannel with H₂SO₄ as the continuous phase. The effects of capillary number, flow ratio, and viscosity ratio on the droplet formation were investigated. The effect of gravity was explored by changing the flow direction in the microchannel. Results showed that the formation of transition flow pattern from squeezing to dripping is much easier for this special system compared with common aqueous/organic systems. This phenomenon is due to the considerably higher viscosity of H₂SO₄ than that of common aqueous phase and the higher density difference of the system compared with those of common systems. In addition to capillary number and flow ratio, gravity evidently affects the formation of droplets and flow patterns. The droplet size is smaller than that during the horizontal flow when the flow direction is consistent with gravity. By contrast, flow direction contrary to that of gravity results in larger droplet size than that at horizontal flow. This phenomenon provides guidance on the operation of these special systems in microchannels. Finally, mathematical models of droplet size at different flow patterns have been established, and these models can predict droplet size very well. This study could be helpful to extend the application of microreactors to new working systems. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4564–4573, 2016     

Three‐Dimensional Simulation of Bubble Formation Through a Microchannel T‐Junction

Three‐dimensional simulations of bubble formation in Newtonian and non‐Newtonian fluids through a microchannel T‐junction are conducted by the volume‐of‐fluid method. For Newtonian fluids, the critical capillary number Ca for the transition of the bubble breakup mechanism is dependent on the velocity ratio between the two phases and the microchannel dimension. For the power law fluid, the bubble diameter decreases and the generation frequency increases with higher viscosity parameter K and power law index n. For a Bingham fluid, the viscous force plays a more important role in microbubble formation. Due to the yield stress τ_y, a high‐viscous region is developed in the central area of the channel and bubbles deform to a flat ellipsoid shape in this region. The bubble diameter and generation frequency are almost independent of K.     

T型微流控芯片中微液滴破裂的数值模拟

利用VOF模型对T型结构微流控芯片中微液滴的三维破裂过程进行了数值模拟,获得了液滴发生破裂和不会破裂两种流型。一定轴向长度的微液滴对应着一个临界毛细数,当主流流体的毛细数大于此临界毛细数时,微液滴发生破裂并分别流向T型结构两侧;否则不会发生破裂,微液滴流向任意一侧。通过多个工况的计算,拟合了临界毛细数与微液滴相对轴向长度的关系,探讨了黏度比对微液滴破裂的影响。发现黏度比越小,微液滴越易发生破裂。     

Simulations of microfluidic droplet formation using the two-phase level set method

Microdroplet formation is an emerging area of research due to its wide-ranging applications within microfluidic based lab-on-a-chip devices. Our goal is to understand the dynamics of droplet formation in a microfluidic T-junction in order to optimize the operation of the microfluidic device. Understanding of this process forms the basis of many potential applications: synthesis of new materials, formulation of products in pharmaceutical, cosmetics and food industries. The two-phase level set method, which is ideally suited for tracking the interfaces between two immiscible fluids, has been used to perform numerical simulations of droplet formation in a T-junction. Numerical predictions compare well with experimental observations. The influence of parameters such as flow rate ratio, capillary number, viscosity ratio and the interfacial tension between the two immiscible fluids is known to affect the physical processes of droplet generation. In this study the effects of surface wettability, which can be controlled by altering the contact angle, are investigated systematically. As competitive wetting between liquids in a two-phase flow can give rise to erratic flow patterns, it is often desirable to minimize this phenomenon as it can lead to a disruption of the regular production of uniform droplets. The numerical simulations predicted that wettability effects on droplet length are more prominent when the viscosity ratio λ (the quotient of the viscosity of the dispersed phase with the viscosity of the continuous phase) is O(1), compared to the situation when λ is O(0.1). The droplet size becomes independent of contact angle in the superhydrophobic regime for all capillary numbers. At a given value of interfacial tension, the droplet length is greater when λ is O(1) compared to the case when λ is O(0.1). The increase in droplet length with interfacial tension, σ, is a function of with the coefficients of the regression curves depending on the viscosity ratio.     

Orifice Flowmeter for Measuring Extensional Rheological Properties

Extensional rheological properties play an important role in processes in which the fluid is subjected to highly decelerated or accelerated flows. This paper describes an orifice flowmeter used to measure extensional properties of rheologically complex fluids at high strain rates. The operating principle of the flowmeter is based on the pressure drop due to the flow through a small size orifice. The flowmeter was first calibrated, by plotting the pressure drop‐flow rate curve of the orifice, in terms of a dimensionless Euler number versus Reynolds number. Newtonian fluids consisting of aqueous solutions of corn syrup were used as calibration fluids. The calibration curve was then used to determine the apparent extensional viscosity of three different paper coating colors. The apparent extensional viscosity is compared to the shear viscosity in terms of the Trouton ratio. The Trouton ratio for one coating color is shown to exceed considerably the theoretical value of 3 expected for Newtonian fluids.     

Rheology of Glaze Suspensions

Rheological properties of suspensions and ceramic glaze slurries under steady flow conditions have been considered. Colloidal forces play an important role in the rheology of such ceramic slurries. Since the potential function characterizes the rheology of colloidal systems, a new dimensionless group, viz. potential number, is introduced within a dimensional analysis representing the relative significance of the potential to the Brownian energy. In order to relate the relative viscosity to other dimensionless groups, a new model is proposed by the inclusion of an extra term in addition to that of the hard‐sphere theory owing to the fact that the presence of colloidal forces always increases the fluid viscosity with respect to that predicted by the hard‐sphere. Steady viscosity measurements have been carried out on ceramic glaze suspensions at different volume fractions, particle diameters, and shear rates. Experimental results have been used to modify the model relating the relative viscosity to the Péclet number, potential number, volume fraction, and maximum packing fraction.     

Steady Flow of Power Law Fluids across a Circular Cylinder

The momentum equations describing the steady cross‐flow of power law fluids past an unconfined circular cylinder have been solved numerically using a semi‐implicit finite volume method. The numerical results highlighting the roles of Reynolds number and power law index on the global and detailed flow characteristics have been presented over wide ranges of conditions as 5 ≤ Re ≤ 40 and 0.6 ≤ n ≤ 2. The shear‐thinning behaviour (n < 1) of the fluid decreases the size of recirculation zone and also delays the separation; on the other hand, the shear‐thickening fluids (n > 1) show the opposite behaviour. Furthermore, while the wake size shows non‐monotonous variation with the power law index, but it does not seem to influence the values of drag coefficient. The stagnation pressure coefficient and drag coefficient also show a complex dependence on the power law index and Reynolds number. In addition, the pressure coefficient, vorticity and viscosity distributions on the surface of the cylinder have also been presented to gain further physical insights into the detailed flow kinematics.     

Modelling of the continuous foaming operation by dimensional analysis

In this study, a dimensional analysis of the continuous foaming operation by whipping was performed. Newtonian model fluids were formulated with controlled rheology and interfacial properties. The viscosity has been modified by changing the dilution of glucose syrup and surface tension has been modified by using two different surfactant species (whey protein and sucrose ester). Foams have been produced on an instrumented industrial rotor–stator mixer by varying the rotation speed, flow rates and pressure. An image analysis method which makes possible to characterize accurately the bubble sizes was performed on each samples. A dimensional analysis allowed to describe in a general way the foaming operation with dimensionless ratios and also enabled to weigh the magnitude of each operating parameter. A model which predicts bubble size, depending on process parameters and those related to the products has been established. This model offers a new definition of capillary number. The major influence of this number provides information on the mechanisms involved in the process. However, the approach also shows that other phenomena affect the bubble size.