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The upstream effect of inlet contactors (T, Y, Cross-T, and Cross-Y) with splitting distributors for parallel microchannels on gas–liquid flow uniformity were studied. Splitting distributors were designed to have a width reduction by a factor of √2 between successive blocks to ensure a flow uniformity in terms of relative lengths of bubbles/slugs (L Bubble/Slug/W Channel). Hydrodynamic parameters such as formation dynamics, splitting dynamics, relative lengths, and dimensionless volumes of bubbles/slugs were investigated for different inlet contactors. For Cross-T and Cross-Y inlet contactors, symmetrical splitting of bubbles/slugs and flow uniformity were observed for a wider range of continuous phase flow rates (Q Water+SDS) at a fixed dispersed phase flow rate (Q Air) than for T and Y inlet contactors channels. Nonsplitting of bubbles/slugs was observed for Ca Critical > 0.0035 and 0.0038 for T and Y inlet contactors, respectively. However, the dimensionless volumes of bubbles/slugs in all blocks of Cross-T and Cross-Y channels were found to be constant for Q Water+SDS > 5.32 mL/min. The slug flow regime was observed in all inlet contactors, whereas a bubbly flow regime was observed only in the Cross-Y contactor channel. On the basis of the experimental results, a unique correlation was proposed to predict the relative lengths of bubbles/slugs in parallel microchannels with a mean relative deviation of 14.65%.

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, DR c . The critical draw ratio DR c depends on the fluid elasticity represented by the Deborah number, De = λv 0 /L, the ratio of the polymer relaxation time to the flow time scale, thus constructing a stability diagram in the DR c -De plane. Here, λ is the characteristic relaxation time of the polymer, v 0 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.

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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 $DR_{c}{-}De$ plane. $DR_{c}$ is the critical draw ratio, and $De$ 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 $DR>DR_{c}$. 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 $DR<DR_{c}$.