High Viscosity Ratios Research Articles

Investigation of the Free‐Surface Flow in Partially Filled Extruders

AbstractIn this work we present the free‐surface flow of high viscous Newtonian liquids in a simplified extruder model, namely the flat‐plate model. Due to high density and viscosity ratios, a free‐surface approach based on the volume of fluid method is used. The material distribution for different degree of fillings and the resulting power consumption is investigated. In addition, the obtained power characteristic is compared against analytical consideration and numerical simulation of a fully filled case. The investigation shows that the power characteristic of a partially filled extruder can be estimated by a fully filled computation. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of surfactant on two-layer channel flow

AbstractThe effect of insoluble surfactant on the interfacial waves in connection with a two-layer channel flow is investigated for low to moderate values of the Reynolds number. Previous studies focusing on Stokes flow (Frenkel & Halpern, Phys. Fluids, vol. 14, 2002, p. L45; Halpern & Frenkel, J. Fluid Mech., vol. 485, 2003, pp. 191–220) are extended by including the inertial effect and the study of low-Reynolds-number flow (Blyth & Pozrikidis, J. Fluid Mech., vol. 521, 2004b, pp. 241–250) is enlarged up to moderate Reynolds number. Linear stability analysis based on the Orr–Sommerfeld boundary value problem identifies a surfactant mode together with an interface mode. The presence of surfactant on the interfacial mode is stabilizing at high viscosity ratio and destabilizing at low viscosity ratio. The threshold of instability is determined as a function of the Marangoni number. A long-wave model is developed to predict the families of nonlinear waves in the neighbourhood of the threshold of instability. Far from the threshold, wave dynamics is explored under the framework of a three-equation model in terms of lower layer flow rate ${q}_{2} (x, t)$, lower liquid-layer thickness $h(x, t)$ and surfactant concentration $\Gamma (x, t)$. Primary instability analysis of a three-equation model captures the result of the Orr–Sommerfeld boundary value problem very well for quite large values of wavenumber. In the nonlinear regime, travelling wave solutions demonstrate deceleration of maximum amplitude and acceleration of speed with the Marangoni number at high viscosity ratio $m\gt 1$ and show completely the opposite behaviour at low viscosity ratio $m\lt 1$. However, both maximum amplitude and speed attain a fixed value with increasing Reynolds number and this leads to saturation of instability.

On the rising motion of a drop in stratified fluids

The rising dynamics of a deformable drop in a linearly stratified fluid is numerically obtained using a finite-volume/front-tracking method. Our results show that the drag coefficient of a spherical drop in a stratified fluid enhances as \documentclass[12pt]{minimal}\begin{document}$C_{d,s}/C_{d,h}-1\sim Fr_d^{-2.86}$\end{document}Cd,s/Cd,h−1∼Frd−2.86 for drop Froude numbers in the range of 4 < Frd < 16. The role of the deformability of the drop on the temporal evolution of the motion is investigated along with stratification and inertial effects. We also present the important role of stratification on the transient rising motion of the drop. It is shown that a drop can levitate in the presence of a vertical density gradient. The drop undergoes a fading oscillatory motion around its neutrally buoyant position except for high viscosity ratio drops where the oscillation occurs around a density level lighter than the neutral buoyancy level. In addition, a detailed characterization of the flow signature of a rising drop in a linearly stratified fluid including the buoyancy induced vortices and the resultant buoyant jet is presented.

Lattice Boltzmann phase-field modeling of thermocapillary flows in a confined microchannel

To understand how thermocapillary forces manipulate the droplet motion in a confined microchannel, a lattice Boltzmann phase-field model is developed to simulate immiscible thermocapillary flows with consideration of fluid–surface interactions. Based on our recent work of Liu et al., 2013 [54], an interfacial force of potential form is proposed to model the interfacial tension force and the Marangoni stress. As only the first-order derivatives are involved, the proposed interfacial force is easily combined with the wetting boundary condition to account for fluid–surface interactions. The hydrodynamic equations are solved using a multiple-relaxation-time algorithm with the interfacial force treated as a forcing term, while an additional convection–diffusion equation is solved by a passive-scalar approach to obtain the temperature field, which is coupled to the interfacial tension by an equation of state. The model is first validated against analytical solutions for the thermocapillary-driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then demonstrated to produce the correct equilibrium contact angle for a binary fluid with different viscosities when a constant interfacial tension is taken into account. Finally, we numerically simulate the thermocapillary flows for a microfluidic droplet adhering on a solid wall and subject to a simple shear flow when a laser is applied to locally heat the fluids, and investigate the influence of contact angle and fluid viscosity ratio on the droplet dynamical behavior. The droplet motion can be completely blocked provided that the contact angle exceeds a threshold value, below which the droplet motion successively undergoes four stages: constant velocity, deceleration, acceleration, and approximately constant velocity. When the droplet motion is completely blocked, three steady vortices are clearly visible, and the droplet is fully filled by two counter-rotating vortices with the smaller one close to the external vortex. The thermocapillary convection is strengthened with decreasing viscosity ratio of the droplet to the carrier fluid. For low viscosity ratios, the droplet motion is completely blocked and exhibits the similar behavior, but the structure of the internal vortices is more complicated at the lowest viscosity ratio. For high viscosity ratios, the droplet motion is partially blocked and undergoes a series of complex transitions, which can be explained as a result of the dynamically varying Marangoni forces.

Dispersive mixing efficiency of an elongational flow mixer on PP/EPDM blends: Morphological analysis and correlation with viscoelastic properties

Polypropylene and ethylene-propylene-diene terpolymer (PP/EPDM) blends were melt compounded in a new mixing device, designed in our laboratory under the trademark of RMX®, which predominantly generates elongational flows. Dispersion of the EPDM minor phase in PP was carried out in both RMX® and in an internal mixer (Haake Rheomix 600) at equivalent specific mixing energies and the resultant morphologies obtained by SEM were analyzed and compared. A better dispersive mixing efficiency of the RMX® mixer, i.e., lower Dn and Dv of the dispersed EPDM phase was observed. The impact of elongational flow was more pronounced for blends having a high viscosity ratio p, indicating an enhanced droplet break-up mechanism, which was attributed to the combination of high shear rates inside the mixing element and important elongational flows in the convergent/divergent zones. The morphology of the blends was correlated with their linear viscoelastic properties by using the Palierne model. Very good agreement was found for the PP/EPDM 80/20 blends but for higher EPDM content, the Palierne model failed to describe the rheological behavior, which was attributed to percolation of the minor phase with increasing the concentration. Higher elasticity at low frequencies was observed for blends processed in the RMX®, which was attributed to a higher generated interfacial area. POLYM. ENG. SCI., 54:1444–1457, 2014. © 2013 Society of Plastics Engineers

Role of the Interphase in the Interfacial Flow Stability in Coextrusion of Compatible Multilayered Polymers

This work aims to highlight the importance of interphase triggered from interdiffusion at neighboring layers on controlling the interfacial flow instability of multilayer coextrusion based on a compatible bilayer system consist of poly(methyl methacrylate) (PMMA) and poly(vinylidene fluoride) (PVDF) melt streams. A fundamental rheological measurement on the bilayer structures provides a good strategy to probe the mutual diffusion process occurred at neighboring layers and to quantify the rheology and thickness of the interphase generated thereof. By implementing steady shear measurements on the multilayer’s, subtle interfacial slippage can be observed at a condition of short welding time and rather high shear rate due to the disentanglement of chains at the interphase. Pre-shear at an early stage on the multilayer was found to greatly promote the homogenizing process by inducing branched structures and hence increasing interfacial area. In coextrusion, some key classical decisive parameters concerning the interfacial instability phenomena such as viscosity ratio, thickness ratio and elasticity ratio, etc. were highlighted. These key factors that are significant in controlling the interfacial stability of coextrusion in an incompatible system seem not that important in a compatible system. In comparison to the severe flow instability observed in the coextrusion of PMMA/PE incompatible bilayer, the coextrusion of PMMA/PVDF compatible bilayer appears to be smooth without apparent interfacial flow instability due to the presence of the interphase. Interdiffusion can reduce (even eliminate) the interfacial flow instability of coextrusion despite of the very high viscosity ratio of PVDF versus PMMA at low temperatures. Indeed, in the coextrusion process, on one hand, the interdiffusion should be studied by taking into account of the effect of polymer chain orientation which was demonstrated to decelerate the diffusion coefficient. On the other hand, the interfacial shear stress was able to promote mixing and homogenizing process at the interface, which favours the development of the interphase and guarantees the stable interfacial flow. The degree of the interphase is related to a lot of parameters like contact time, processing temperature, interfacial shear stress and compatibility of the polymers, etc. Therefore, apart from the classical mechanical parameters, the interphase created from the interdiffusion should be taken into consideration as an important factor on determining the interfacial instability phenomena.

Production of W/O/W (water-in-oil-in-water) multiple emulsions: droplet breakup and release of water

We investigate breakup of W/O/W double emulsion droplets at high viscosity ratios and coalescence of inner water droplets dependent on the dispersed phase content (DPC) of the inner emulsion.The rheological analyses of the inner emulsions confirm the behavior expected from literature – increasing viscosity with increasing DPC and elastic behavior for high DPC. The resulting droplet sizes seem to be influenced only by the viscosity ratio calculated using the viscosity of the inner emulsion. An influence of the elastic properties of the inner emulsions could not be observed. Moreover, breakup of double emulsion droplets seems to follow the same rules as breakup of Newtonian droplets.In the second part of the paper we focus on the release of water from double emulsions by coalescence. A direct correlation between resulting double emulsion droplet sizes and encapsulation efficiency was found for each system. The initial inner dispersed phase content has a big influence on the release rate. This can partly be explained by the influence of the dispersed phase content on collision rate. Moreover, it was found that for high internal phase concentrations inner droplets coalesce with each other. The so formed bigger inner droplets seem to increase the overall release rate.

Progress and investigation on lattice Boltzmann modeling of multiple immiscible fluids or components with variable density and viscosity ratios

Lattice Boltzmann models for simulating multiphase flows are relatively new, and much work remains to be done to demonstrate their ability to solve fundamental test cases before they are considered for engineering problems. From this perspective, a hydrodynamic lattice Boltzmann model for simulating immiscible multiphase flows with high density and high viscosity ratios, up to O(1000) and O(100) respectively, is presented and validated against analytical solutions. The method is based on a two phase flow model with operators extended to handle N immiscible fluids. The current approach is O(N) in computational complexity for the number of different gradient approximations. This is a major improvement, considering the O(N2) complexity found in most works. A sequence of systematic and essential tests have been conducted to establish milestones that need to be met by the proposed approach (as well as by other methods). First, the method is validated qualitatively by demonstrating its ability to address the spinodal decomposition of immiscible fluids. Second, the model is quantitatively verified for the case of multilayered planar interfaces. Third, the multiphase Laplace law is studied for the case of three fluids. Fourth, a quality index is developed for the three-phase Laplace–Young’s law, which concerns the position of the interfaces between the fluids resulting from the different surface tensions. The current model is compatible with the analytical solution, and is shown to be first order accurate in terms of this quality index. Finally, the multilayered Couette’s flow is studied. In this study, numerical results can recover the analytical solutions for all the selected test cases, as long as unit density ratios are considered. For high density and high viscosity ratios, the analytical solution is recovered for all tests, except that of the multilayered Couette’s flow. Numerical results and a discussion are presented for this unsuccessful test case. It is believed that other LB models may have the same problem in addressing the simulation of multiphase flows with variable density ratios.

In‐line turbidity monitoring of the second phase droplets deformation during extrusion

The dispersion and deformation of the second phase during extrusion of polymer mixtures were in real‐time characterized using an in‐line turbidimeter. Three polymer mixtures with constant concentration but very different viscosity ratios (1/4, 1, and 4) were reprocessed up to three times in a twin‐screw extruder. After that they were processed again, having the extruder exit being blocked by an on/off valve, which controls the hold‐on and discharge. The melt turbidity, a variable dependent of the droplets size and shape, was recorded during processing and controlled die‐head pressure discharge. The deformation of the droplets is high and reversible in mixture having viscosity ratio close to 1, indicating no droplet breakup and/or coalescence. In contrast, for high viscosity ratios and high matrix elasticity a hysteresis is formed during deformation/recovery of the droplets. POLYM. ENG. SCI., 53:2422–2428, 2013. © 2013 Society of Plastics Engineers

An Improved Single-Phase Free-Surface Lattice Boltzmann Model with Surface Tension and Wall Adhesion

Free-surface model with surface tension and wall adhesion(wetting) is a very efficient technique to simulate two-phase flows with high density and viscosity ratios, such as etching and casting processes. In this paper, a conservative surface tension and wall adhesion model based on lattice Boltzmann single-phase free-surface method is proposed. The effectiveness of the model is demonstrated by simulating the flows induced by wall adhesion and surface tension, and filling processes in a 2D cavity.

LBM Simulation of a Droplet Dripping Down a Hole

A droplet dripping through a hole, which is located on a horizontal plate, was simulated in the current work. To overcome the numerical instabilities and accommodate the high density and viscosity ratios, Lee’s LBM model was used to simulate the two-phase flow. Also wettability effect was taken into account by imposing the contact angle between solid-liquid and gas phases using Cahn’s wetting theory. The effects of gravitational acceleration, surface tension, equilibrium contact angle, viscosity ratio, density ratio, and also the geometrical parameters, such as the height and width of the hole, have been investigated separately. In addition to numerical results, high numerical stability and ease of using surface tension and contact angle for controlling fascinated the authors to model this problem. High numerical stability in capturing the remaining fine particles on the surface and slender strip of a droplet passing through a small hole is a significant contribution. The results show that gravitational force and adhesion force caused by surface tension, are opposing forces influencing droplet behaviour. Enhancing the contact angle to more than 90 degrees makes the surface hydrophobic and the droplet will drip under gravitational force. Also increasing the surface tension causes increasing adhesion force, which leads to droplet decay. In this case some parts of the droplet will remain on the surface.

Numerical investigation of Newtonian and non-Newtonian multiphase flows using ISPH method

We have presented a multiphase incompressible smoothed particle hydrodynamics method with an improved interface treatment procedure. To demonstrate the effectiveness of the interface treatment which can handle multiphase flow problems with high density and viscosity ratios, we have modeled several challenging two phase flow problems; namely, single vortex flow, square droplet deformation, droplet deformation in shear flow, and finally the Newtonian bubble rising in viscous and viscoelastic liquids. The proposed interface treatment includes the usage of (i) different smoothing functions (in this work, cubic spline kernel function for discretizing equations associated with the calculation of the surface tension force while the quintic spline for the discretization of governing equations and the relevant boundary conditions), and (ii) a new discretization scheme for calculating the pressure gradient. It is shown that with the application of the improved interface treatment, it becomes possible to model multiphase flow problems with the density and viscosity ratios up to 1000 and 100 respectively while using standard projection method. The utilization of cubic spline for the continuum surface force model significantly improves the quality of the calculated interface, thereby eliminating the interphase particle penetrations, and in turn leading to the calculation of more accurate velocity and pressure fields.

The space and time complexity of chaotic mixing of silicate melts: Implications for igneous petrology

We present new experimental results on the study of the space and time modulation of compositional fields during chaotic mixing between mafic and felsic silicate melts. The experimental strategy was planned using numerical simulations performed using the experimental geometry. These mixing experiments were performed using a recently developed experimental apparatus, which is capable of mixing high-viscosity silicate melts at high temperatures and under precisely controlled conditions of fluid-dynamics and strain. The compositional variability produced by the mixing process was investigated both along linear analytical transects and on high-resolution 2D X-ray maps, covering the mixing patterns.Our results indicate that chaotic flow fields represent very powerful dynamics to blend silicate melts, even under laminar fluid dynamic conditions (Reynolds number ca. 10−7) and for dissimilar melts with high viscosity ratios (on the order of 103). The repetition of stretching and folding processes between the two melts induced a strong increase of contact interfaces thus favoring efficient chemical exchanges. As a result the initial mafic composition is no longer detectable in the mixing system after ca. 2h (i.e. the duration of the experiment). A further important result is the observation of highly non-linear patterns in inter-elemental plots produced by the onset of diffusive fractionation processes. This is contrary to common thinking that magma mixing should always produce linear trends between pairs of chemical elements.A new measure, the “concentration variance”, is proposed to quantify chemical element mobility during the mixing process. This measure is statistically robust and can be quantitatively used to measure chemical element mobility independently of the geometry in which the compositional variation (i.e. transects, areas, etc.) is embedded or the local strain history of the mingling.Our results highlight concentration variance as a robust probe of the as yet poorly-understood processes involved in the common petrological process of magma mixing.

Droplet formation and breakup dynamics in microfluidic flow-focusing devices: From dripping to jetting

Droplet formation and breakup dynamics in either dripping or jetting regimes in microfluidic flow-focusing devices were investigated experimentally. More viscous liquids were dispersed into less viscous liquids in square microchannels with 600 and 400 μm wide, respectively. In the dripping regime, for low viscosity ratio of both phases, the variation of the minimum width of the dispersed thread with the remaining time could be scaled as a power–law relationship with exponent related to initial conditions, and the droplet size could be correlated with the flow rate ratio of both phases and the capillary number of the continuous phase; while for high viscosity ratio of both phases, the dispersed thread experiences a linear thinning procedure, and the droplet size can be scaled with the Weber number of the continuous phase. In the jetting regime, the stable jet width was affected by the viscosity ratio and flow rate ratio of both phases. And the relationship between the droplet size and the flow rate ratio of both phases could be scaled as a power–law relation with the exponent dependent on the viscosity ratio of both phases. The analysis of the mode of the maximum instability of the oil jet indicated that the most unstable instability is related to the viscosity ratio of both phases and is almost independent on the flow rate ratio of both phases.

Simulation of the two phase flow of droplet impingement on liquid film by the lattice boltzmann method

A Lattice Boltzmann Method (LBM) with two-distribution functions is employed for simulating the two-phase flow induced by a liquid droplet impinging onto the film of the same liquid on solid surface. The model is suitable for solution of two-phase flow problem at high density and viscosity ratios of liquid to vapor and phase transition between liquid and its vapor. The roles of the vapor flow, the density ratio of liquid to vapor and the surface tension of the droplet in the splashing formation are discussed. It is concluded that the vapour flow induced by the droplet fall and splash in the whole impinging process may affect remarkably the splash behaviour. For the case of large density ratio of liquid to vapor a crown may engender after the droplet collides with the film. However, for the case of small density ratio of liquid to vapor a “bell” like splash may be observed.

Simulation of surface-tension-driven interfacial flow with smoothed particle hydrodynamics method

The method for simulation of surface-tension-driven interfacial flow with smoothed particle hydrodynamics is developed. The calculation of surface tension force is based on the interface reconstruction. The boundary particles for each fluid are detected dynamically. The position of the interface particles are specified in the middle of the boundary particles of each fluid. According to the positions of the interface particles, the interface can be reconstructed. The normal vector and curvature of the interface can be obtained. Then the surface tension force is calculated according to the reconstructed interface. Finally the surface tension force is transferred to the SPH particles near the interface. The accuracy and efficiency of the developed method are investigated. Drop deformation in shear flow, oscillation of square drop, head-on binary collision, and off-center binary collision are simulated. The developed method can be applied to the simulation of surface-tension-driven interfacial flow with high density ratio of up to 797.88 and high viscosity ratio of up to 55.56.

Viscosity ratio: A key factor for control of oil drop size distribution in effervescent atomization of oil-in-water emulsions

The present study focused on the effervescent atomization of oil-in-water emulsions and its influence on the internal emulsion structure. The impact of atomization conditions and nozzle geometry on an oil-in-water emulsion with varied viscosity ratio of disperse phase to emulsion was determined. The viscosity ratio is known as a key factor for the drop breakup in emulsification processes. The results depict that oil drops are broken up according to emulsification mechanisms during atomization. A maximum breakup was found for a viscosity ratio between 0.5 and 1. The expected stress dependency of the drop size change was observed for high viscosity ratios only. Relevance of elongational stress on the drop breakup was proven with significant drop size change at high viscosity ratios. The viscosity ratio thus allows for an efficient control of oil drop size change in effervescent atomization as the spray characteristics are invariant to viscosity changes within certain limits.

Multiphase lattice Boltzmann simulations of buoyancy-induced flow of two immiscible fluids with different viscosities

We study the effects of viscosity differential on buoyancy-induced interpenetration of two immiscible fluids in a tilted channel using a two-phase lattice Boltzmann method implemented on a graphics processing unit. The effects of viscosity differential on the flow structures, average density profiles and front velocities are studied. Relatively stable fingers are observed for high viscosity ratios. The intensity of the interfacial instabilities and the transverse interpenetration of the fluids are seen to increase with decreasing viscosity differential of the fluids.

Natural Convection Investigations in Porous Phase Change Materials

Metal foams with high thermal conductivities are generally considered to have high potential to enhance the heat transfer performance for Phase Change Materials (PCMs). In this parametrical study, the effects of metal foams on heat transfer in PCMs are examined, and the investigation is conducted in the aspects of both heat conduction and natural convection. The findings of this paper are that metal foams significantly improve heat conduction in solid region, whilst suppress natural convection in liquid region. Buoyancy-driven velocities are too weak to produce dominant convection, which is due to high viscosity and low thermal expansion ratio of the PCM, as well as the large flow resistance of metal foams.

Two-phase flow in porous media: power-law scaling of effective permeability

A recent experiment has reported power-law scaling of effective permeability of two-phase flow with respect to capillary number for a two-dimensional model porous medium. In this paper, we consider the simultaneous flow of two phases through a porous medium under steady-state conditions, fixed total flow-rate and saturation, using a two-dimensional network simulator. We obtain power-law exponents for the scaling of effective permeability with respect to capillary number. The simulations are performed both for viscosity matched fluids and for a high viscosity ratio resembling that of air and water. Good power-law behaviour is found for both cases. Different exponents are found, depending on saturation.