Onset of transition in the flow of polymer solutions through microtubes

Abstract

Experiments are performed to characterize the onset of laminar–turbulent transition in the flow of high-molecular-weight polymer solutions in rigid microtubes of diameters in the range $390~\unicode[STIX]{x03BC}\text{m}{-}470~\unicode[STIX]{x03BC}\text{m}$ using the micro-PIV technique. By considering flow in tubes of such small diameters, the present study probes higher values of elasticity numbers ($E\equiv \unicode[STIX]{x1D706}\unicode[STIX]{x1D708}/R^{2}$) compared to existing studies, where $\unicode[STIX]{x1D706}$ is the longest relaxation time of the polymer solution, $R$ is the tube radius and $\unicode[STIX]{x1D708}$ is the kinematic viscosity of the polymer solution. For the Newtonian case, our experiments indicate that the natural transition (without the aid of any forcing mechanism) occurs at Reynolds number ($Re$) $2000\pm 100$. As the concentration of polymer is increased, initially there is a delay in the onset of the transition and the transition Reynolds number increases to $2500$. Further increase in concentration of the polymer results in a decrease in the Reynolds number for transition. At sufficiently high concentrations, the added polymer tends to destabilize the flow and the transition is observed to happen at $Re$ as low as $800$. It is also observed that the addition of polymers, regardless of their concentration, reduces the magnitude of the velocity fluctuations after transition. Dye-stream visualization is further used to corroborate the onset of transition in the flow of polymer solutions. The present work thus shows that addition of polymer, at sufficiently high concentrations, destabilizes the flow when compared to that of a Newtonian fluid, thereby providing additional evidence for ‘early transition’ or ‘elasto-inertial turbulence’ in the flow of polymer solutions. The data for the transition Reynolds number $Re_{t}$ from our experiments (for tubes of different diameters, and for two different polymers at varying concentrations) collapse well according to the scaling relation $Re_{t}\propto 1/\sqrt{E(1-\unicode[STIX]{x1D6FD})}$, where $\unicode[STIX]{x1D6FD}$ is the ratio of solvent viscosity to the viscosity of the polymer solution.

Active microrheology to determine viscoelastic parameters of Stokes-Oldroyd B fluids using optical tweezers

“…In the inset, ¢( ) G f and ( ) G f have been plotted against frequency which has been calculated theoretically using the extracted parameter values of the fluid. [33]. The trends of the variation of λ with concentration for our values and those reported earlier clearly appear to be similar.…”

“…We test our technique on a purely viscous fluid-water, for which we obtain very good agreement with well-known literature values, and different viscoelastic solutions of PAM and water where the concentration of the former is varied. At low polymer concentrations, we obtain rather reliable measurements of the time constant λ which match with values in literature [33], while for increased polymer concentrations, the values seem to be unreliable with very small change in the measured μ p with increasing concentration. This we attribute to the limitations of our theory in the case of non-linear viscoelastic fluids and for more complex fluids with additional time constants, which probably is the case when we increase the concentration of PAM in the solution.…”

“…Further, we have proceeded to measure the viscoelastic parameters for samples of Polyacrylamide (PAM) to water solutions at different dilution levels. We observe that our results are in good agreement with that reported recently [33], which have been performed for relatively low polymer concentration solutions. For solutions of higher polymer concentrations, however, the measured polymer contributions to the viscosities are not satisfactory.…”

Linear instability of viscoelastic pipe flow

“…The lack of a hysteretic signature in the experiments of Samanta et al (2013) served as a primary motivation in our search (Garg et al 2018) for a linear instability in viscoelastic pipe flow. The recent experimental work of Chandra et al (2018Chandra et al ( , 2020 further corroborated the findings of Samanta et al (2013), and reported a decrease in the transition Re with increasing concentration in the range 300-800 ppm.…”

Critical-Layer Structures and Mechanisms in Elastoinertial Turbulence

“…While channel flow exhibits a two-dimensional linear instability leading to so-called Tollmien-Schlichting (TS) waves, the critical Reynolds number Re = 5772 is much higher than that observed for transition, so these are not traditionally viewed as playing an important role in Newtonian transition.For flowing polymer solutions under some conditions (low concentration, short polymer relaxation times), transition to turbulence occurs via the usual bypass transition. With further increase in Re, drag reduction sets in, and the flow eventually approaches the so-called maximum drag reduction (MDR) asymptote, an upper bound on the degree of drag reduction that is insensitive to the details of the fluid.Under other conditions, flow transitions directly from laminar flow into the MDR regime, and can do so at a Reynolds number where the flow would remain laminar if Newtonian [2][3][4][5]. Recent experiments and simulations [6][7][8] suggest that turbulence in this regime has structure very different from Newtonian, denoting it as "elastoinertial turbulence" (EIT).…”