The influence of viscoelasticity on the emptying of liquids from model gravure cells is studied via numerical simulations. The simulations use a finite-element/front-tracking method, and viscoelastic effects are described with the FENE-P model. Two different model configurations featuring moving contact lines are considered. In the first, there is a free surface and an outlet boundary, and the liquid is driven out of a cavity by a combination of horizontal substrate motion and an imposed pressure gradient. In the second, there are two free surfaces, and the liquid is driven out of the cavity through both horizontal and vertical substrate motion. For the first configuration, it is found that viscoelasticity aids cavity emptying through gradients in the first normal stress difference that are generated by the relative motion of the substrate and cavity. For the second configuration, vertical substrate motion promotes cavity emptying, with the effect enhanced when viscoelasticity is present. (C) 2015 Elsevier B.V. All rights reserved.

Melt blowing is a common process for the production of polymer fibers, but its effectiveness can be greatly influenced by the occurrence of fiber whipping. This paper reports the results of a systematic parametric study aimed at elucidating the factors that determine the onset of whipping in the melt blowing process. A quasi-one-dimensional model developed by Yarin and co-workers [J. Appl. Phys. 108 (2010) 034913] is analyzed in detail and extended to consider the influence of different constitutive models. It is found that whipping requires sufficiently large levels of inertia in the fiber and air, as well as a strong inlet perturbation. Strong longitudinal stresses along the jet axis are required too, although elasticity is not necessary. Also essential are a drag force that varies along the fiber length, and an air velocity that decreases in magnitude away from the fiber centerline. Comparison of results from several different constitutive models suggests that melt inertia rather than melt rheology is the more dominant factor in controlling fiber shapes. The results of the present work are expected to be helpful for the development of more quantitatively accurate models of the melt blowing process.

Shear-banding phenomenon in the entangled polymer systems was investigated in a planar Couette cell with the diffusive Rolie-Poly (ROuse LInear Entangled POLYmers) model, a single-mode constitutive model derived from a tube-based molecular theory. The steady-state shear stress σ s was constant in the shear gradient direction while the local shear rate changed abruptly, i.e., split into the bands. We focused on the molecular conformation (also calculated from the Rolie-Poly model) around the band boundary. A band was found also for the conformation, but its boundary was much broader than that for the shear rate. Correspondingly, the first normal stress difference (N 1) gradually changed in this diffuse boundary of the conformational bands (this change of N 1 was compensated by a change of the local pressure). For both shear rate and conformation, the boundary widths were quite insensitive to the macroscopic shear rate but changed with various parameters such as the diffusion constant and the relaxation times (the reptation and the Rouse times). The broadness of the conformational banding, associated by the gradual change of N 1, was attributed to competition between the molecular diffusion (in the shear gradient direction) and the conformational relaxation under a constraint of constant σ s.

We demonstrate that polyelectrolyte (PE) multilayer thin films deposited on patterned posts with incredibly large numbers of bilayers, which would not be possible with the conventional Layer-by-Layer (LbL) deposition methods, can be obtained in a short process time using alternating polyelectrolyte droplets generated in a microfluidic channel, representing a significant advantage over the conventional processes based on polyelectrolyte deposition followed by the separation of such substrates (typically colloidal particles) with centrifugation and sonication. Positively- and negatively-charged polyelectrolyte droplets were alternatively generated in a microfluidic channel by controlling the capillary number (Ca) as well as the fraction of dispersed phase over the continuous phase. Patterned posts, serving as the substrates for the PE deposition, were created with photo-curable polymers using the optofluidic maskless lithography. The impact of these PE droplets onto the patterned posts allowed the alternative adsorption of PEs, similar to the conventional LbL deposition methods. It was shown that the intensity of fluorescence dye tagged onto (+)-charged PEs adsorbed on the post(s), taken with confocal laser scanning microscopy, increases with deposition time and varies around the post(s). The effect of post shape and interval between the two posts for the droplet-based LbL deposition was also experimentally investigated and analyzed, in connection with the numerical simulations, to elucidate the underlying principles of relevant two-phase flows.

We performed numerical and experimental studies on the viscous folding in diverging microchannel flows which were recently reported by Cubaud and Mason (Phys Rev Lett 96:114501, 2006a). We categorized the flow patterns as “stable”, “folding,” and “chaotic” depending on channel shape, flow ratio, and viscosity ratio between two fluids. We focused on the effect of kinematic history on viscous folding, in particular, by changing the shape of diverging channels: 90°, 45°, and hyperbolic channel. In experiments, the proposed power–law relation (\( f\sim \dot{\gamma }^{1},\) where f is the folding frequency, and \( \dot{\gamma }\) is the characteristic shear rate) by Cubaud and Mason (Phys Rev Lett 96:114501, 2006a) was found to be valid even for hyperbolic channel. The hyperbolic channel generated moderate flows with smaller folding frequency, amplitude, and a delay of onset of the folding compared with other two cases, which is considered to be affected by compressive stress when compared to the simulation results. In each channel, the folding frequency increases and the amplitude decreases as the thread width decreases since higher compressive stress is applied along the thin thread. The secondary folding was also reproduced in the simulation, which was attributed to locally heterogeneous development of compressive stresses along the thread. This study proves that the viscous folding can be controlled by the design of flow kinematics and of the compressive stresses at the diverging region.

Recently, we reported how viscoelasticity affects drop dynamics in a microchannel flow using the finite element-front tracking method (FE-FTM). In this work, we investigate drop dynamics for a wider range of parameters: viscosity ratio between droplet and medium (), capillary number (Ca), droplet size, and fluid elasticity. The Oldroyd-B model is adopted as the constitutive equation for the viscoelastic fluid. We observe that the drop deformation in a microfluidic channel is dependent on Ca ,w hich is more pronounced for smaller values. The present work shows that viscoelasticity plays an important role in drop dynamics with increasing values for Newtonian droplet in viscoelastic medium, which can be attributed to high normal stress developed in narrow film thickness between droplet and channel for higher values. We also study circulation problem inside droplets, which is important in practice, such as in droplet reactor application. The present work shows that circulation intensity is enhanced with decreasing values. We find that the relevance of viscoelastic effects on internal circulation is dependent on values, and the circulation intensity is distinctively decreased with increasing elasticity for high values for Newtonian droplet in viscoelastic medium. We expect that the present work be helpful not only in controlling droplets but also to improve our physical insight on drop dynamics in microchannel flows.

Recently, we reported how viscoelasticity affects drop dynamics in a microchannel flow using the finite element-front tracking method (FE-FTM). In this work, we investigate drop dynamics for a wider range of parameters: viscosity ratio between droplet and medium (χ), capillary number (Ca), droplet size, and fluid elasticity. The Oldroyd-B model is adopted as the constitutive equation for the viscoelastic fluid. We observe that the drop deformation in a microfluidic channel is dependent on Ca, which is more pronounced for smaller χ values. The present work shows that viscoelasticity plays an important role in drop dynamics with increasing χ values for Newtonian droplet in viscoelastic medium, which can be attributed to high normal stress developed in narrow film thickness between droplet and channel for higher χ values. We also study circulation problem inside droplets, which is important in practice, such as in droplet reactor application. The present work shows that circulation intensity is enhanced with decreasing χ values. We find that the relevance of viscoelastic effects on internal circulation is dependent on χ values, and the circulation intensity is distinctively decreased with increasing elasticity for high χ values for Newtonian droplet in viscoelastic medium. We expect that the present work be helpful not only in controlling droplets but also to improve our physical insight on drop dynamics in microchannel flows.

The droplet dynamics passing through a cylinder obstruction was investigated with direct numerical simulations with FE-FTM (Finite Element-Front Tracking Method). The effect of droplet size and capillary number (Ca) was studied for both Newtonian and viscoelastic fluids. In the case of Newtonian droplet immersed in Newtonian medium, the droplet breakup induced by the geometric hindrance depends on the droplet size. As Ca increases, the short droplets (1.3 times longer than the channel width) break up while passing through the obstruction. However, the breakup does not occur for longer droplets (1.8 times longer than the channel width). When the viscoelastic fluid characterized by the Oldroyd-B model is considered, the Newtonian droplet immersed in viscoelastic medium breaks up into two smaller droplets while passing through the cylinder obstruction with increasing Dem (Deborah number of the medium). We also show that the normal stress difference plays a key role on the droplet breakup and the droplet extension. The normal stress difference is enhanced in the negative wake region due to the droplet flow, which also promotes droplet extension in that region. This numerical study provides information not only on underlying physics of the droplet flows passing through a cylinder obstruction but also on the useful guidelines for microfluidic applications.

The prediction of pressure drop for a droplet flow in a confined microchannel is presented using FE-FTM (Finite Element - Front Tracking Method). A single droplet is passing through 5:1:5 contraction - straight narrow channel - expansion flow domain. The pressure drop is investigated especially when the droplet flows in the straight narrow channel. We explore the effects of droplet size, capillary number (Ca), viscosity ratio (chi) between droplet and medium, and fluid elasticity represented by the Oldroyd-B constitutive model on the excess pressure drop (Delta p(+)) against single phase flow. The tightly fitted droplets in the narrow channel are mainly considered in the range of 0.001 <= Ca <= 1 and 0.01 <= chi <= 100. In Newtonian droplet/Newtonian medium, two characteristic features are observed. First, an approximate relation Delta p(+)similar to chi is observed for chi >= 1. The excess pressure drop necessary for droplet flow is roughly proportional to chi. Second, Delta p(+) seems inversely proportional to Ca, which is represented as Delta p(+)similar to Ca-m with negative in irrespective of chi. In addition, we observe that the film thickness (delta(f)) between droplet interface and channel wall decreases with decreasing Ca, showing delta(f)similar to Ca-n with positive n independent of chi. Consequently, the excess pressure drop (Delta p(+)) is strongly dependent on the film thickness (delta(f)). The droplets larger than the channel width show enhancement of Delta p(+), whereas the smaller droplets show no significant change in Delta p(+). Also, the droplet deformation in the narrow channel is affected by the flow history of the contraction flow at the entrance region, but rather surprisingly Delta p(+) is not affected by this flow history. Instead, Delta p(+) is more dependent on delta(f) irrespective of the droplet shape. As for the effect of fluid elasticity, an increase in delta(f) induced by the normal stress difference in viscoelastic medium results in a drastic reduction of Delta p(+).

We implemented a finite element-front tracking method (FE-FTM) to understand the drop dynamics in microfluidic applications. We investigated the effect of viscoelasticity of both drop and medium. The Oldroyd-B model was used for viscoelastic fluid, and DEVSS-G/SUPG/Matrix logarithm were applied to improve numerical stability. We applied the algorithm to a drop deformation problem in 5:1:5 planar contraction - narrow channel - expansion flow. One of our goals is to propose the strategy to control the drop shape by exploring the effect of viscoelasticity of drop and medium. Here, we studied three different viscosity ratios between drop and medium by setting the ratio as 100 (more viscous drop), 1 and 0.01 (more viscous medium). In Newtonian fluids, the effects of drop size and capillary number (Ca) were investigated to get physical insights on drop deformation. As for fluid elasticity, the effect of Deborah number (De) was especially enhanced in more viscous drop case, while the effect was insignificant in other cases. The present study would be helpful to investigate viscoelastic effects on drop dynamics in microfluidics.

We implemented a finite element-front tracking method (FE-FTM) to understand the drop dynamics in microfluidic applications. We investigated the effect of viscoelasticity of both drop and medium. The Oldroyd-B model was used for viscoelastic fluid, and DEVSS-G/SUPG/matrix logarithm algorithms were applied to improve numerical stability. We first verified the reliability of the algorithm by comparing with previous results under simple shear flow. The results were in good agreement with previous reports in a wide range of parameters such as capillary number (Ca) and Deborah number (De). Then we applied the algorithm to a 5:1:5 planar contraction – narrow channel – expansion flow which is typical microfluidic flows. One of the goal of this study is to explore the effect of viscoelasticity of drop and medium on drop deformation, and to propose the strategy to control the drop shape. When a Newtonian drop was suspended in a viscoelastic medium, in the narrow channel region, we observed an ‘ellipsoid-like drop’ in contrast to a ‘bullet-like drop’ which is the typical shape for the case of a Newtonian drop in Newtonian medium. When a viscoelastic drop is suspended in Newtonian medium, the extent of ‘drop swell’ to the cross-stream direction was enhanced at the exit of the narrow channel. We explained these phenomena in terms of the normal stress difference developed in the viscoelastic fluid. The present study shows that the viscoelasticity plays a significant role on drop dynamics and drop shape in particular. We expect this study will be helpful to understand the drop dynamics in microchannel flow, and provide useful information in manipulating drops in complicated geometries such as microfluidic channels.

The two-dimensional deformation of immiscible drop in simple shear flow was investigated using the front tracking method.Interface particles were traced by Runge-Kutta 2 nd order method and the boundary immersed method was used for calculation of surface tension force at the global mesh.Isothermal, incompressible and creeping flow was assumed.The main purpose of this research is to analyze the effect of viscosity ratio and elasticity on the drop deformation.Oldroyd-B model was used as a constitutive equation with stabilizing schemes such as DEVSS-G/SUPG and matrix logarithm.As for the Newtonian drop deformation in the Newtonian matrix, there was no breakup until Ca=1 when the viscosity ratio was one.And the damped oscillation was observed when the viscosity ratio was not unity.The effect of elasticity on the drop deformation was also investigated.As De increased, the drop was more deformed and orientation angle declined to the shear direction.

In this work, we present high-resolution solutions for viscoelastic 4:1 planar contraction flow problems using a transient finite element method based on the fractional step method (FSM) and stabilization techniques (DEVSS-G/DG) with linear equal-order interpolation function. The Oldroyd-B model was used as the constitutive equation. A parallel multi-frontal algorithm was implemented to enhance computational speed and all solutions were obtained on a parallel machine. The vortex intensity and the re-attachment length of corner vortex show good mesh-convergent behavior and are compared with previous results from the literature. In particular, the present results are in good agreement with the predictions of the high-resolution finite volume method of Alves et al. [15]. This may be the first case that quantitative agreement is obtained between studies using different numerical methods for the benchmark problem of 4:1 planar contraction flow. As there has been little quantitative agreement in the previous investigations and only few simulation results with highly refined meshes exit, this study may well be regarded as accurate and meaningful in the sense that reasonable convergence is achieved for prediction of 4:1 planar contraction flow using transient finite element methods.

The effect of flow conditions on the “negative wake” generation (longitudinal velocity overshoot behind a cylinder in the viscoelastic fluid flow along the centerline) has been investigated. FENE-CR model that predicts constant shear viscosity and controlled extensional viscosity was considered as a constitutive equation. The discrete elastic viscous split stress-G/streamline upwind Petrov–Galerkin (DEVSS-G/SUPG) formulation was employed and the high-resolution solutions were obtained with an efficient iterative solver based on the incomplete LU(0)-type preconditioner and BiCGSTAB. We found that the “negative wake” generation was more obvious in uniform flow conditions than in Poiseuille flow, which suggests that the experimentally unrevealed “negative wake” generation of Boger fluids could be partially attributed to the geometrical effect of Poiseuille flow. The “negative wake” generation was more discernable at low extensibility and high value of viscosity ratio, which agrees well with the previous studies. In addition, we could observe an undershoot phenomenon in Poisseuille flow condition, which has never been reported.

Vortex enhancement mechanism in 4:1 planar contraction flow of a viscoelastic fluid has been investigated, where the Oldroyd-B model was considered as a constitutive equation. Finite element method was used based on the fractional step method for time marching and DEVSS/DG as a stabilizing scheme. The prediction of vortex dynamics agreed well with the experimental results. At first, a lip vortex was generated at the reentrant corner at low Weissenberg number (We). As We increases, the size of the salient corner vortex becomes reduced, while the lip vortex becomes more pronounced and finally takes over the corner vortex. The trajectory of a lip vortex at high We was found to follow the steady state positions of the lip vortex at lower We, which means that the fluid has a memory and there exists a simple relationship between We and time. Accordingly, a simple universal behavior was found to dominate the vortex enhancement mechanism in the 4:1 planar contraction flow of the Oldroyd-B fluid.

The effect of molecular parameters on the steady vortex behaviors in the inertial viscoelastic flow past a cylinder has been investigated. FENE-CR model was considered as a constitutive equation. A recently developed iterative solution method (Kim et al., (in press)) was found to be successfully applicable to the computation of inertial viscoelastic flows. The high-resolution computations were carried out to understand the detailed flow behaviors based on the efficient iterative solution method armed with ILU(0) type pre-conditioner and BiCGSTAB method. The discrete elastic viscous split stress-G/streamline upwind Petrov Galerkin (DEVSS-G/SUPG) formulation was adopted as a stabilization method. The vortex size decreased as elasticity increases. However, the vortex enhancement was also observed in the case of large extensibility, which means that the vortex behavior is strongly dependent upon the material parameters. The longitudinal gradient of normal stress was found to retard the formation of vortex, whereas the extensional viscosity played a role in the vortex enhancement. The present results are expected to be helpful for understanding the inertial vortex dynamics of viscoelastic fluids in the flow past a confined cylinder.