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Shiv Nadar University

Chemical Engineering

(SoE) School of Engineering

I&EC Research

<p>Effect of Inlet Contactors of Splitting Distributors for Parallel Microchannels</p>

The present study examines the stability of a thinning straight jet in electrospinning process. The linear stability analysis is carried out to obtain the growth/decay rate of axisymmetric disturbance imposed on the thinning jet. The analysis captures the role of solvent evaporation in the stability behavior of the linear path of the electrospinning jet. In contrast to many prior stability analyses which consider the jet as a cylindrical filament with uniform radius, the present study analyzes the stability of a jet which exhibits thinning under realistic electrospinning conditions. Two different polymeric solutions are considered: the poly-isobutene (PIB) Boger fluid with low electrical conductivity and the highly conductive poly-ethylene oxide (PEO) solution in ethanol/water. At low extensional deformation, the rheology of the unentangled PIB-based Boger fluid is described by the Oldroyd-B model. The PEO solution, on the other hand, experiences a very high elongation rate due to the development of strong axial electric stress. The nonlinear rheology of the entangled PEO solution is appropriately described by the eXtended Pom–Pom (XPP) model, a variant of the classical tube model. The analysis reveals that the instability in low conductivity fluid is driven by the capillary forces, whereas the high conductivity fluid exhibits oscillatory conducting mode of instability driven by the coupled effect of axial electric field and surface charges. For both the reference fluids, the increase in solvent evaporation tends to decrease the disturbance growth rate to the extent that the axisymmetric instability is completely suppressed for a strong enough evaporation. The stabilizing role of solvent evaporation is attributed to the enhancement in fluid viscosity and elasticity due to increased polymer concentration upon evaporation. Thus, by suppressing the onset of axisymmetric instability during the straight jet path, solvent evaporation potentially helps produce smooth fibers without bead formation. © 2020 Elsevier Ltd

World University root node

Polymer

Electrospinning of polymer solutions: An analysis of instability in a thinning jet with solvent evaporation

The stability of fibre spinning flow of a polymeric fluid is analysed in the presence of thermal effects. The spinline is modelled as a one-dimensional slender-body filament of the entangled polymer solution. The previous study (Gupta & Chokshi, J. Fluid Mech., vol. 776, 2015, pp. 268-289) analysed linear and nonlinear stability behaviour of an isothermal extensional flow in the air gap during the fibre spinning process. The present study extends the analysis to take in to account the non-isothermal spinning flow in which the spinline loses heat by convection to the surrounding air as well as by solvent evaporation. The nonlinear rheology of the polymer solution is described using the eXtended Pom-Pom (XPP) model. The non-isothermal effects influence the rheology of the fluid through viscosity, which is taken to be temperature and concentration dependent. The linear stability analysis is carried out to obtain the draw ratio for the onset of instability, known as the draw resonance, and a stability diagram is constructed in the plane. is the critical draw ratio, and is the flow Deborah number. The enhancement in viscosity driven by spinline cooling leads to postponement in the onset of draw resonance, indicating the stabilising role of non-isothermal effects. Weakly nonlinear stability analysis is also performed to reveal the role of nonlinearities in the finite amplitude manifold in the vicinity of the flow transition point. For low to moderate Deborah numbers, the bifurcation is supercritical, and the flow attains an oscillatory state with an equilibrium amplitude post-transition when DR>. The equilibrium amplitude of the resonating state is found to be smaller when non-isothermal effects are incorporated in comparison to the isothermal spinning flow. For very fast flows in the regime of high Deborah numbers, the finite amplitude manifold crosses over to a subcritical state. In this limit, the nonlinearities render the flow unstable even in the linearly stable regime of CD<DRc. © 2018 Cambridge University Press.

Journal of Fluid Mechanics

Stability analysis of non-isothermal fibre spinning of polymeric solutions

The linear stability of a bilayer fiber spinning process is analyzed for axisymmetric disturbances under isothermal conditions. The co-extruded fiber consists of two concentric layers of rheologically stratified polymeric fluids. While the core fluid is an entangled polymer melt described using the eXtended Pom-Pom (XPP) model, the sheath layer is a low molecular weight unentangled polymer modeled as an Upper Convected Maxwell (UCM) fluid. The analysis indicates that, for fast extensional flows, such an arrangement enhances the critical draw ratio of the process over that found from the spinning of XPP fluid alone, thus delaying the onset of draw resonance and stabilizing the system. Further, the range of flow Deborah number for stable spinning is found to be much broader than that for the UCM fluid alone. For low to moderately elastic flows, the stability behavior is governed mainly by the rheology of the more-elastic core layer (XPP fluid), whereas for the highly elastic flows, the stability behavior is dominated by the less-elastic sheath layer (UCM fluid). The sensitivity of the stability diagram with respect to various spinning flow parameters, like the relative fraction of core and sheath layers, the rheological stratification of two fluids, and the spine-line dimensions, has also been examined in order to identify the region of enhanced stability such that the draw resonance is suppressed. © 2017 Elsevier Ltd

Chemical Engineering Science

Stability analysis of bilayer polymer fiber spinning process

The role of die-swell in the stability of fiber spinning flow of entangled polymer melts is analyzed using the linear as well as finite amplitude stability analyses. The nonlinear extensional rheology of polymer is described by using the eXtended Pom-Pom (XPP) model which captures the strain hardening effect present in the realistic flows. The stability of the slender body fiber profile to axisymmetric disturbances is studied under the isothermal conditions. At the top end of the spinning flow near die-exit, the swelling in fiber cross-section area is introduced whose magnitude is governed both by the flow within the die and the outside spinning force. Introducing die-swell in the analysis significantly influences the stability of the spinning flow. The flexibility in the fiber profile at the upstream end of the flow, a feature absent in the previous analyses ignoring die-swell, plays a stabilizing role. However, for a given flow, die-swell implies stronger effective extension than indicated by the apparent draw ratio, defined based on capillary area. This higher effective extension tends to decrease the critical draw ratio for the onset of draw resonance, suggesting destabilizing role of die-swell. The destabilizing role is found to dominate in the overall stability behavior. The stability diagram is constructed by plotting the critical draw ratio for the onset of draw resonance against the flow Deborah number. The sensitivity of the stability behavior on the rheology parameters and the die-geometry has been studied. The finite amplitude disturbances are also considered using the weakly nonlinear stability analysis in order to understand the nature of flow in the proximity of the transition point. The flow exhibits supercritical Hopf bifurcation for low to moderate Deborah numbers, indicating the presence of an oscillatory steady state in the unstable regime. The amplitude of the oscillations in the fiber cross-section area is estimated. The finite amplitude bifurcation crosses over to the subcritical manifold as Deborah number is increased beyond a certain crossover value. The subcritical state for fast flows manifests in the form of unbounded growth of transient disturbances of amplitude greater than a certain threshold value. The die-swell effect tends to lower the Deborah number for the crossover to the subcritically unstable state. © 2016 Elsevier B.V.

Journal of Non-Newtonian Fluid Mechanics

Die-swell effect in draw resonance of polymeric spin-line

The extensional flow of a polymeric fluid during the fibre spinning process is studied for finite-amplitude stability behaviour. The spinning flow is assumed to be inertialess and isothermal. The nonlinear extensional rheology of the polymer is described with the help of the eXtended Pom-Pom (XXP) model, which is known to exhibit a significant strain hardening effect necessary for fibre spinning applications. The linear stability analysis predicts an instability known as draw resonance when the draw ratio, DR, defined as the ratio of the velocities at the two ends of the fibre in the air gap, exceeds a certain critical value, DRc. The critical draw ratio DRc depends on the fluid elasticity represented by the Deborah number, De = λυ0/L, the ratio of the polymer relaxation time to the flow time scale, thus constructing a stability diagram in the DRc-De plane. Here, λ is the characteristic relaxation time of the polymer, υ0 is the extrudate velocity through the die exit and L is the length of the air gap for the spinning flow. In the present study, we carry out a weakly nonlinear stability analysis to examine the dynamics of the disturbance amplitude in the vicinity of the transition point. The analysis reveals the nature of the bifurcation at the transition point and constructs a finite-amplitude manifold providing insight into the draw resonance phenomena. The effect of the fluid elasticity on the nature of the bifurcation and the finite-amplitude branch is examined, and the findings are correlated to the extensional rheological behaviour of the polymer fluid. For flows at small Deborah number, the Landau constant, which captures the role of nonlinearities, is found to be negative, indicating supercritical Hopf bifurcation at the transition point. In the linearly unstable region, the equilibrium amplitude of the disturbance is estimated and shows a limit cycle behaviour. As the fluid elasticity is increased, initially the equilibrium amplitude is found to decrease below its Newtonian value, reaching the lowest value for De when the strain hardening effect is maximum. With further increase in elasticity, the material undergoes strain softening behaviour which leads to an increase in the equilibrium amplitude of the oscillations in the fibre cross-section area, indicating a destabilizing effect of elasticity in this regime. Interestingly, at a certain high Deborah number, the bifurcation crosses over from supercritical to subcritical nature. In the subcritical regime, a threshold amplitude branch is constructed from the amplitude equation. © 2015 Cambridge University Press.

Weakly nonlinear stability analysis of polymer fibre spinning

Nicotinic acid (also known as pyridine-3-carboxylic acid) is widely used in food, pharmaceutical and biochemical industries. The extraction of nicotinic acid by tri-noctylphosphine oxide (TOPO) with kerosene (diluent) is studied. The equilibrium experiments are carried out to investigate the effects of diluent, extractant (TOPO) composition and initial acid concentration on extraction efficiency. The extraction efficiency is found to increase with increasing TOPO composition concentration (0.10 to 0.60 mol.L -1) and found to decrease with increasing initial acid concentration (0.02 to 0.12 mol.L -1). The number of TOPO molecules in the acid:TOPO complex is estimated through proposed mathematical model using graphical methods as well as though an optimization route using the differential evolution algorithm and found to be 1:1 complexes of TOPO and acid with loading ratio of less than 0.5. The extraction equilibrium constants are also determined. Equilibrium extraction constant (K E1) is found to be 3.27 L.mol -1 in the complete range of acid concentrations and extractant (TOPO) concentrations.