Steady-state extensional viscosity of a linear polymer solution using a differential pressure extensional rheometer on a chip

Abstract

In our earlier theoretical work [Lee and Muller, J. Rheol. 61, 1049–1059 (2017)], we proposed a design for a differential pressure extensional rheometer (DPER) on a chip. Here, we implement the DPER to evaluate the steady-state viscosity of a semidilute poly(ethylene oxide) solution at high and low extension rates. At low extension rates, the extensional viscosity exhibits strain thinning behavior with a power-law exponent of −0.5. At intermediate extension rates, the extensional viscosity exhibits strain thickening. At high extension rates, the extensional viscosity plateau has been estimated, and the corresponding finite extendable nonlinear elastic (FENE) constant is evaluated as 482. A novel method to determine the FENE constant and the extensional relaxation time distribution is presented, which are key parameters for the understanding of the extensional flow of a linear polymer solution.

Effects of flexibility and entanglement of sodium hyaluronate in solutions on the entry flow in micro abrupt contraction-expansion channels

“…13 In the last decades, flow behavior of polymer solutions in microscales has attracted significant attention because it is related to many industrial applications, such as ink-jet printing, fiber spinning, micromixing, lab-on-a-chip techniques, and microrheometry. [14][15][16][17][18][19][20][21][22][23][24][25] A number of studies on aqueous polymer solutions have been conducted through contraction/contraction-expansion flows. 7,12,[14][15][16][17][26][27][28][29][30][31][32][33][34][35][36][37][38][39] When viscoelastic solution flows through a contraction throat, different characteristic flow regimes may appear in the upper stream region of the contraction throat with the increasing flow rate.…”

Concentration Dependence of the Extensional Relaxation Time and Finite Extensibility in Dilute and Semidilute Polymer Solutions Using a Microfluidic Rheometer

“…Graessley classified polymer solutions into five different regimes according to their molecular weights and concentrations . Many studies have focused on the extensional relaxation time in dilute and semidilute polymer solutions using microfluidic and capillary thinning techniques − because the elongational flows are important in many industrial applications, such as in coating, spinning, and biofluidic systems. However, measuring the extensional relaxation time in low-viscosity solutions remains challenging on account of their short relaxation times. − ,,,− Many techniques have been proposed for measuring the extensional relaxation time, such as the capillary breakup extensional rheometry (CaBER), − dripping-onto-substrate (DoS) rheometry, − and using the differential pressure extensional rheometer (DPER) on a chip. , The measurement techniques that are based on capillary-thinning such as CaBER and DoS are available for the measurement of the short extensional relaxation time (λ E ).…”

“…In the DoS rheometry, the neck-thinning behavior associated with an elastocapillary response is well observed compared to the case in CaBER. , The inertial effects associated with moving the top plate can be removed in the DoS rheometry. , A more detailed discussion of the capillary-thinning methods is included in the refs , Both the CaBER and DoS techniques have merit in their simplicity because only one drop of solution is required for the measurement. However, they have weak points, that is, their measurable range of the extension rate (ε̇) in a single-concentration solution is limited, and the time, during which a constant ε̇ value is maintained, is not sufficient for the steady-state to be attained. − Conversely, the microfluidic techniques based on a converging channel ,,,,, such as the DPER , and the extensional viscometer-rheometer-on-a-chip , have advantages, including that the measurable range of ε̇ is wide and ε̇ can be maintained constantly for a long time. The disadvantage of the microfluidic techniques is that experiments with multiple converging channels are required to remove geometric effects, and the proper constitutive equation is required. , In our previous works, , we demonstrated that t obs ≥ t s at low a Wi value and t obs < t s at a high Wi value in a converging channel of the microfluidic rheometer, where t obs is the residence time of the fluid element in a converging channel, t s is the time required to reach steady-state, and Wi is the Weissenberg number .…”

“…However, they have weak points, that is, their measurable range of the extension rate (ε̇) in a single-concentration solution is limited, and the time, during which a constant ε̇ value is maintained, is not sufficient for the steady-state to be attained. − Conversely, the microfluidic techniques based on a converging channel ,,,,, such as the DPER , and the extensional viscometer-rheometer-on-a-chip , have advantages, including that the measurable range of ε̇ is wide and ε̇ can be maintained constantly for a long time. The disadvantage of the microfluidic techniques is that experiments with multiple converging channels are required to remove geometric effects, and the proper constitutive equation is required. , In our previous works, , we demonstrated that t obs ≥ t s at low a Wi value and t obs < t s at a high Wi value in a converging channel of the microfluidic rheometer, where t obs is the residence time of the fluid element in a converging channel, t s is the time required to reach steady-state, and Wi is the Weissenberg number . That is, the extensional flow may reach a steady-state only at low Wi values.…”

“…That is, the extensional flow may reach a steady-state only at low Wi values. Subsequently, we suggested that the geometric effect should be corrected in the measured normal stress in the converging channels . We evaluated the extensional relaxation time distribution and finite extensible nonlinear elastic (FENE) constant for an aqueous 0.5 wt % polyethylene oxide (PEO) solution by the Tikhonov regularization method using the corrected normal stress data with respect to ε̇ …”