Sumeet Thete

Plethora of transitions during breakup of liquid filaments

Significance Fluid flows, governed by nonlinear equations, permit formation of singularities. Often, singularities are artifacts of neglecting physical effects. However, free-surface flows exhibit observable singularities including filament pinch-off. As filaments thin, slightly (highly) viscous filaments are expected from theory to transition from an inertial (viscous) regime where viscosity (density) is negligible to an inertial–viscous regime where viscous and inertial effects are important. Previous works show this transition either does not occur or occurs for filament radii well below theoretical predictions. We demonstrate that thinning filaments unexpectedly pass through a number of intermediate transient regimes, thereby delaying onset of the final regime. The findings raise the question if similar dynamical transitions arise in problems that are not necessarily hydrodynamic in nature. Thinning and breakup of liquid filaments are central to dripping of leaky faucets, inkjet drop formation, and raindrop fragmentation. As the filament radius decreases, curvature and capillary pressure, both inversely proportional to radius, increase and fluid is expelled with increasing velocity from the neck. As the neck radius vanishes, the governing equations become singular and the filament breaks. In slightly viscous liquids, thinning initially occurs in an inertial regime where inertial and capillary forces balance. By contrast, in highly viscous liquids, initial thinning occurs in a viscous regime where viscous and capillary forces balance. As the filament thins, viscous forces in the former case and inertial forces in the latter become important, and theory shows that the filament approaches breakup in the final inertial–viscous regime where all three forces balance. However, previous simulations and experiments reveal that transition from an initial to the final regime either occurs at a value of filament radius well below that predicted by theory or is not observed. Here, we perform new simulations and experiments, and show that a thinning filament unexpectedly passes through a number of intermediate transient regimes, thereby delaying onset of the inertial–viscous regime. The new findings have practical implications regarding formation of undesirable satellite droplets and also raise the question as to whether similar dynamical transitions arise in other free-surface flows such as coalescence that also exhibit singularities.

Necking in extrusion film casting: The role of macromolecular architecture

Extrusion film casting (EFC) is used on an industrial scale to produce several thousand tons of polymer films and coatings. While significant research has been carried out on necking of films of viscoelastic melts in EFC, the influence of macromolecular chain architecture on the necking behavior is not yet fully understood. In the present research, we have explored experimentally and theoretically the effects of long chain branching and molecular weight distribution on the extent of necking during EFC. Polyethylenes of essentially linear architecture but having narrow and broad molecular weight distributions, and polyethylenes having long chain branching were used for experimental studies. The EFC process was analyzed using the one-dimensional flow model of Silagy et al. [Polym. Eng. Sci. 36(21), 2614–2625 (1996)] in which multimode molecular constitutive equations namely the “extended pom-pom” equation (for long chain branched polymer melts) and the “Rolie–Poly (Rouse linear entangled polymers)” equation...

Nonisothermal analysis of extrusion film casting process using molecular constitutive equations

Extrusion film casting (EFC) is a commercially important process that is used to produce several thousand tons of polymer films and coatings. In a recent work, we demonstrated the influence of polymer chain architecture on the extent of necking in an isothermal film casting operation (Pol et al., J Rheol 57:559–583, 2013). In the present research, we have explored experimentally and theoretically the effects of long-chain branching on the extent of necking during nonisothermal film casting conditions. Polyethylenes of linear and long-chain branched architectures were used for experimental studies. The EFC process was analyzed using the 1-D flow model of Silagy et al. (Polym Eng Sci 36:2614–2625, 1996) in which the energy equation was introduced to model nonisothermal effects, and two multimode constitutive equations, namely the “extended pom-pom” (XPP, for long-chain branched polymer melts) equation and the “Rolie-Poly stretch version” (RP-S, for linear polymer melts) equation, were incorporated to account for the effects of polymer chain architecture. We show that the model does a better job of capturing the qualitative features of the experimental data, thereby elucidating the role of chain architecture and nonisothermal conditions on the extent of necking.

New insights into the use of multi-mode phenomenological constitutive equations to model extrusion film casting process:

This article is concerned with the effect of the individual viscoelastic relaxation modes of a polymer melt on its behavior in polymer melt extrusion film casting process. We compare the predicted versus experimentally obtained film necking or neck-in profile as a function of draw ratio. The predicted necking profile was obtained using well-established one-dimensional isothermal flow kinematics and consisted of using two different phenomenological constitutive equations, upper convected Maxwell and Phan-Thien–Tanner, with a discrete spectrum of relaxation times. The numerical simulations, containing the two different phenomenological constitutive equations, provided an insight into the effect of the slow and the fast relaxing modes on the stresses, strains, and strain/extensional rates that develop in the molten polymer film as it is stretched from the die exit to the chill-roll. The slow relaxing modes follow trends that are directly proportional to strain (similar to Hookean solids), whereas the fast relaxing modes follow trends that are directly proportional to the stretch rate (in accordance with Newton’s law of viscosity). Comparing the numerical predictions with the experiments showed that predictions using the upper convected Maxwell constitutive equation best described the long-chain branched polymers (like low-density polyethylene, which shows extensional strain hardening) in the extrusion film casting process. On the other hand, predictions using the Phan-Thien–Tanner constitutive equation best described the linear polymers (like linear low-density polyethylene, which does not show noticeable extensional strain hardening) in the extrusion film casting process.

Necking in Extrusion Film Casting: Numerical Predictions of the Maxwell Model and Comparison with Experiments

ABSTRACT The role of viscoelasticity in determining the extent of necking of a web of molten polymer extruded in an isothermal steady state extrusion film casting (EFC) process is considered. Following a brief review of experimental and theoretical efforts on this problem, analytical and numerical solutions to a well-established model for extrusion film casting using the Maxwell constitutive equation is presented. The extent of film necking was found to either increase or decrease with draw ratio (DR) depending on the Deborah number (De). The locus of points on the draw ratio-Deborah number diagram at which the draw ratio dependence of the necking width inverts was calculated and compared with the locus that separates the unattainable regime from the experimentally accessible regime. Predicted trends were found to be in qualitative agreement with experimental data for various polyethylene grades.

A new experimental method based on volume measurement for determining axial scaling during breakup of drops and liquid threads

Thread breakup is ubiquitous in drop formation. As liquid threads thin, monitoring the time variation of the thread’s minimum radius hmin and the axial extent of the pinching zone z′ can help decipher the balance of forces governing breakup. The variation of hmin with time from pinch-off, τ ≡ tb − t (t is time; tb is breakup time)—radial scaling—can be determined experimentally from images of drops forming from a nozzle. Thus, all previous experimental studies report radial scaling, viz., hmin ∼ τa (a is the radial scaling exponent). Determination of axial scaling or how z′ varies with τ, z′ ∼ τb (b is the axial scaling exponent), however, is not as straightforward and hence rarely reported. Experimental determination of axial scaling is made difficult because thinning threads can be long and slender, and hence data on time evolution of z′ can be noisy. Moreover, inference of z′ from experiments can be challenging in situations involving suspension drops containing non-Brownian particles where particles can partially protrude out of the interface. We present a new way of determining axial scaling by experimental measurement of the time variation of the volume of the pinching zone and inferring z′ from volume measurements. The accuracy of the new method is tested by new experiments in which the scalings are determined during dripping of Newtonian liquids and are shown to be in excellent accord with scaling predictions and transitions between different regimes predicted from theory and simulation.Thread breakup is ubiquitous in drop formation. As liquid threads thin, monitoring the time variation of the thread’s minimum radius hmin and the axial extent of the pinching zone z′ can help decipher the balance of forces governing breakup. The variation of hmin with time from pinch-off, τ ≡ tb − t (t is time; tb is breakup time)—radial scaling—can be determined experimentally from images of drops forming from a nozzle. Thus, all previous experimental studies report radial scaling, viz., hmin ∼ τa (a is the radial scaling exponent). Determination of axial scaling or how z′ varies with τ, z′ ∼ τb (b is the axial scaling exponent), however, is not as straightforward and hence rarely reported. Experimental determination of axial scaling is made difficult because thinning threads can be long and slender, and hence data on time evolution of z′ can be noisy. Moreover, inference of z′ from experiments can be challenging in situations involving suspension drops containing non-Brownian particles where particles c...

Influence of macromolecular architecture on necking in polymer extrusion film casting process

Extrusion film casting (EFC) is an important polymer processing technique that is used to produce several thousand tons of polymer films/coatings on an industrial scale. In this research, we are interested in understanding quantitatively how macromolecular chain architecture (for example long chain branching (LCB) or molecular weight distribution (MWD or PDI)) influences the necking and thickness distribution of extrusion cast films. We have used different polymer resins of linear and branched molecular architecture to produce extrusion cast films under controlled experimental conditions. The necking profiles of the films were imaged and the velocity profiles during EFC were monitored using particle tracking velocimetry (PTV) technique. Additionally, the temperature profiles were captured using an IR thermography and thickness profiles were calculated. The experimental results are compared with predictions of one-dimensional flow model of Silagy et al1 wherein the polymer resin rheology is modeled using m...