Pankaj Doshi

Scaling in pinch-off of generalized Newtonian fluids

Abstract Pinch-off dynamics of slender liquid bridges of generalized Newtonian fluids without and with inertia are studied using asymptotic analysis and numerical computation. The deformation-rate-dependent rheology is described by power law and Carreau models. Because the bridges are slender, their dynamics are governed by a pair of spatially one-dimensional (1D), non-linear evolution equations for the bridge shape and axial velocity. A bridge of a power law fluid under creeping flow conditions exhibits self-similar dynamics in the vicinity of the axial location where the bridge radius is a minimum. The scaling exponents that determine the variation with time remaining to breakup of the bridge radius or radial length scale, axial length scale, and axial velocity are evaluated by a combined analytical and numerical approach. Similarity solutions are obtained by collapsing numerically computed profiles of both the bridge shape and the axial velocity in the vicinity of the axial location where the bridge radius is minimum by rescaling of the transient profiles with radial and axial scalings deduced from theory. This scaling behavior is transitory and inertial effects become significant as pinch-off is approached. Thereafter, a new balance is established between viscous, capillary, and inertial forces that leads to a new self-similar regime which persists until pinch-off. The scaling exponents appropriate to this regime are also determined. Moreover, it is shown theoretically that interface shapes in the vicinity of the singularity are non-slender for values of the power law exponent below 2/3. Similarity solutions are once again obtained in the same manner as that used in the creeping flow limit. Low-viscosity bridges of Carreau fluids are known to exhibit a transition from potential flow (PF) scaling to Newtonian scaling. Here it is demonstrated that high-viscosity bridges of Carreau fluids exhibit a transition from power law scaling to Newtonian scaling. The point of transition between the latter two regimes is predicted in terms of parameters of the Carreau model.

Nonlinear dynamics and breakup of compound jets

Finite-amplitude deformation and breakup of a compound jet, whose core and shell are both incompressible Newtonian fluids, that is surrounded by a passive gas are analyzed computationally by a temporal analysis. The means is a method of lines algorithm in which the Galerkin/finite element method with elliptic mesh generation is used for spatial discretization and an adaptive finite difference method is employed for time integration. The dynamics are initiated by subjecting the inner and the outer interfaces of a quiescent compound jet to axially periodic perturbations that are either in phase (ω=0) or π radians out phase (ω=π), where ω is the phase shift between the disturbances imposed on the two interfaces. The initial growth rates of disturbances obtained from computations are compared and demonstrated to be in excellent agreement with predictions of linear theory [Chauhan et al., J. Fluid Mech. 420, 1 (2000)]. Computations reveal that recirculating flows occur commonly during the deformation and pinch...

Self-similar pinch-off of power law fluids

Pinch-off dynamics of slender liquid threads of power law fluids without inertia are studied by asymptotic analysis. Because the threads are slender, their dynamics are governed by a pair of spatially one-dimensional, nonlinear evolution equations for the thread shape and axial velocity that results from a long-wave asymptotic expansion of the creeping flow equations. By means of an approach that differs from those used previously in analyses of capillary pinching of threads of Newtonian fluids, a similarity transformation is derived that reduces the evolution equations to two coupled similarity equations. As in the Newtonian case, it is shown that for each value of the power law exponent n where 0⩽n⩽1, there is a family of similarity solutions for capillary pinching of threads of power law fluids. For a given family of solutions, the radial and axial scales vary with time τ to pinch-off as τn and τδ, respectively, where δ is the axial scaling exponent. It is shown that for a given family of solutions cha...

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...

Non-self-similar, linear dynamics during pinch-off of a hollow annular jet

Based on an experimental and computational study of the breakup of a drop (jet) of small viscosity in an ambient fluid of large viscosity, Doshi et al. [Science 302, 1185 (2003)] have shown that the breakup of a drop (jet) of zero viscosity in a very viscous ambient fluid gives rise to an unexpected, nonuniversal form of singularity. Doshi et al. conjectured that the nonuniversal dynamics result from the fact that stresses exerted by the inner fluid are negligible. To verify this conjecture and overcome computational difficulties associated with simulating systems in which the disparity between the viscosities of the inner and the outer fluids is large, the breakup of an annular jet whose core is a gas of negligible viscosity is analyzed. Calculations show that as the jet’s minimum radius hmin→0, both core- and shell-side pressures remain bounded while surface tension pressure, which diverges as 1/hmin, is balanced by viscous normal stress exerted by the shell fluid. Simulations show that interfacial poin...

Spontaneous jamming and unjamming in a hopper with multiple exit orifices.

We show that the flow of granular material inside a two-dimensional flat bottomed hopper is altered significantly by having more than one exit orifice. For hoppers with small orifice widths, intermittent flow through one orifice enables the resumption of flow through the adjacent jammed orifice, thus displaying a sequence of jamming and unjamming events. Using discrete element simulations, we show that the total amount of granular material (i.e., avalanche size) emanating from all the orifices combined can be enhanced by about an order of magnitude difference by simply adjusting the interorifice distance. The unjamming is driven primarily by fluctuations alone when the interorifice distance is large, but when the orifices are brought close enough, the fluctuations along with the mean flow cause the flow to unjam.

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.

In-depth experimental analysis of pharmaceutical twin-screw wet granulation in view of detailed process understanding

Twin-screw wet granulation is gaining increasing interest within the pharmaceutical industry for the continuous manufacturing of solid oral dosage forms. However, limited prior fundamental physical understanding has been generated relating to the granule formation mechanisms and kinetics along the internal compartmental length of a twin-screw granulator barrel, and about how process settings, barrel screw configuration and formulation properties such as particle size, density and surface properties influence these mechanisms. One of the main reasons for this limited understanding is that experimental data is generally only collected at the exit of the twin-screw granulator barrel although the granule formation occurs spatially along the internal length of the barrel. The purpose of this study is to analyze the twin-screw wet granulation process using both hydrophilic and hydrophobic formulations, manufactured under different process settings such as liquid-to-solid ratio, mass throughput and screw speed, in such a way that the mechanisms occurring in the individual granulator barrel compartments (i.e., the wetting and different conveying and kneading compartments) and their impact upon granule formation are understood. To achieve this, a unique experimental setup was developed allowing granule characteristic data-collection such as size, shape, liquid and porosity distribution at the different compartments along the length of the granulator barrel. Moreover, granule characteristic information per granule size class was determined. The experimental results indicated that liquid-to-solid ratio is the most important factor dictating the formation of the granules and their corresponding properties, by regulating the degree of aggregation and breakage in the different compartments along the internal length of the twin-screw granulator barrel. Collecting appropriate and detailed experimental data about granule formation along the internal length of the granulator barrel is thus crucial for gaining fundamental physical understanding of the twin-screw wet granulation process.

Interlinked population balance and cybernetic models for the simultaneous saccharification and fermentation of natural polymers.

Simultaneous Saccharification and Fermentation (SSF) is a process where microbes have to first excrete extracellular enzymes to break polymeric substrates such as starch or cellulose into edible nutrients, followed by in situ conversion of those nutrients into more valuable metabolites via fermentation. As such, SSF is very attractive as a one‐pot synthesis method of biological products. However, due to the co‐existence of multiple biochemical steps, modeling SSF faces two major challenges. The first is to capture the successive chain‐end and/or random scission of the polymeric substrates over time, which determines the rate of generation of various fermentable substrates. The second is to incorporate the response of microbes, including their preferential substrate utilization, to such a complex broth. Each of the above‐mentioned challenges has manifested itself in many related areas, and has been competently but separately attacked with two diametrically different tools, i.e., the Population Balance Modeling (PBM) and the Cybernetic Modeling (CM), respectively. To date, they have yet to be applied in unison on SSF resulting in a general inadequacy or haphazard approaches to examine the dynamics and interactions of depolymerization and fermentation. To overcome this unsatisfactory state of affairs, here, the general linkage between PBM and CM is established to model SSF. A notable feature is the flexible linkage, which allows the individual PBM and CM models to be independently modified to the desired levels of detail. A more general treatment of the secretion of extracellular enzyme is also proposed in the CM model. Through a case study on the growth of a recombinant Saccharomyces cerevisiae capable of excreting a chain‐end scission enzyme (glucoamylase) on starch, the interlinked model calibrated using data from the literature (Nakamura et al., Biotechnol. Bioeng. 53:21‐25, 1997), captured features not attainable by existing approaches. In particular, the effect of various enzymatic actions on the temporal evolution of the polymer distribution and how the microbes respond to the diverse polymeric environment can be studied through this framework. Biotechnol. Bioeng. 2015;112: 2084–2105.

Flow of granular matter in a silo with multiple exit orifices: jamming to mixing.

We investigate the mixing characteristics of dry granular material while draining down a silo with multiple exit orifices. The mixing in the silo, which otherwise consists of noninteracting stagnant and flowing regions, is observed to improve significantly when the flow through specific orifices is stopped intermittently. This momentary stoppage of flow through the orifice is either controlled manually or is chosen by the system itself when the orifice width is small enough to cause spontaneous jamming and unjamming. We observe that the overall mixing behavior shows a systematic dependence on the frequency of closing and opening of specific orifices. In particular, the silo configuration employing random jamming and unjamming of any of the orifices shows early evidence of chaotic mixing. When operated in a multipass mode, the system exhibits a practical and efficient way of mixing particles.