Steady Torsional Flows Research Articles

Yield stresses of concentrated suspensions of rigid particles in the volume fraction range of 0.62 to 0.78 via steady torsional flow

Yield stresses of concentrated suspensions of rigid particles in the volume fraction range of 0.62 to 0.78 via steady torsional flow

Parallel-Disk Viscometry of a Viscoplastic Hydrogel: Yield Stress and Other Parameters of Shear Viscosity and Wall Slip.

The rheology, i.e., the flow and deformation properties, of hydrogels is generally a very important consideration for their functionality. However, the accurate characterization of their rheological material functions is handicapped by their ubiquitous viscoplasticity and associated wall slip behavior. Here a parallel-disk viscometer was used to characterize the shear viscosity and wall slip behavior of a crosslinked poly(acrylic acid) (PAA) carbomer hydrogel (specifically Carbopol® at 0.12% by weight in water). It was demonstrated that parallel-disk viscometry, i.e., the steady torsional flow in between two parallel disks, can be used to unambiguously determine the yield stress and other parameters of viscoplastic constitutive equations and wall slip behavior. It was specifically shown that torque versus rotational speed information, obtained from parallel-disk viscometry, was sufficient to determine the yield stress of a viscoplastic hydrogel. Additional gap-dependent data from parallel-disk viscometry could then be used to characterize the other parameters of the shear viscosity and wall slip behavior of the hydrogel. To investigate the accuracy of the parameters of shear viscosity and apparent wall slip that were determined, the data were used to calculate the torque values and the velocity distributions (using the lubrication assumption and parallel plate analogy) under different flow conditions. The calculated torques and velocity distributions of the hydrogel agreed very well with experimental data collected by Medina-Bañuelos et al., 2021, suggesting that the methodologies demonstrated here provide the means necessary to understand in detail the steady flow and deformation behavior of hydrogels. Such a detailed understanding of the viscoplastic nature and wall slip behavior of hydrogels can then be used to design and develop novel hydrogels with a wider range of applications in the medical and other industrial areas, and for finding optimum conditions for their processing and manufacturing.

Dynamics of the sub-ambient gelation and shearing of solutions of P3HT and P3HT blends towards active layer formation in bulk heterojunction organic solar cells.

Organic solar cells (OSCs) containing an active layer consisting of a nanostructured blend of a conjugated polymer like poly(3-hexylthiophene) (P3HT) and an electron acceptor have the potential of competing against silicon-based photovoltaic panels. However, this potential is largely unfulfilled first due to interrelated production and stability issues of organic solar cells and second due to the unscalable nature of the generally employed spin coating process used for the fabrication of organic solar cells. Furthermore, alternatives to spin coating, especially relying on continuous polymer processing methods like extrusion and coating, cannot be readily applied due to the typically low shear viscosity and elasticity of polymer solutions making up the active layer. Recently, He et al. have reported that the gelation of P3HT with [6,6]-phenyl-C61-butyric acid methyl ester (PC60BM) under sub-ambient conditions can provide a new route to the processing of the active layers of bulk heterojunction solar cells. Furthermore, increases in power conversion efficiencies (PCEs) of the P3HT/PC60BM active layer were determined to be possible under certain shearing and thermal histories of the P3HT/PC60BM gels. Here oscillatory and steady torsional flows were used to investigate the gel formation dynamics of P3HT with a recently proposed non-fullerene acceptor o-IDTBR under sub-ambient conditions and compared with the gelation behavior of P3HT/PC60BM blends. The rheological material functions as well as the gel strengths defined on the basis of linear viscoelastic material functions, characterized via small-amplitude oscillatory shearing, were observed to be functions of the P3HT and o-IDTBR concentrations, the solvent used and the shearing conditions. Overall, the P3HT gels which formed upon quenching to sub-zero temperatures were found to be stable during small-amplitude oscillatory shear (linear viscoelastic range) but broke down even at the relatively low shear rates associated with steady torsional flows, suggesting that the shearing conditions used during the processing of gels of P3HT and blends of P3HT with small molecule acceptors can alter the gel structure, possibly leading to changes in the resulting active layer performance.

Shear viscosity and wall slip behavior of a viscoplastic hydrogel

The coupled apparent slip and viscoplastic behavior of a hydrogel consisting of 0.2 wt. % aqueous solution of poly(acrylic acid) was analyzed employing steady torsional and circular tube (capillary) flows. Transparent disks and capillaries fabricated out of borosilicate glass were used to allow velocity measurements. The steady torsional flow of the hydrogel was dominated by wall slip which gave rise to plug flow over the apparent shear rate range of 0.1 to 1 s−1, in agreement with the plug flow observed in the capillary under similar shear stresses. The transition from plug flow provided the yield stress of the hydrogel, which was found to be consistent with velocity data collected over the 0.1–200 s−1 apparent shear rate range of steady torsional and capillary flows. The availability of both pressure drop versus flow rate and wall slip velocity data enabled the validation of correction procedures proposed earlier for the determination of the slip-corrected wall shear rate [Yilmazer and Kalyon, “Dilatancy of concentrated suspensions with Newtonian matrices,” Polym. Compos. 12, 226–232 (1991); D. Kalyon, “Apparent slip and viscoplasticity of concentrated suspensions,” J. Rheol. 49, 621–640 (2005)] and the determination of the shear viscosity parameters. The apparent slip layer thicknesses were found to be consistent with the elastohydrodynamic mechanism proposed by Martin et al. [“Wetting transitions at soft, sliding interfaces,” Phys. Rev. E 65, 031605 (2002)] and Meeker et al. [“Slip and flow in pastes of soft particles: Direct observation and rheology,” J. Rheol. 48, 1295–1320 (2004)] for steady torsional flow but not for capillary flow, emphasizing the role the applied pressure plays in shaping the apparent slip behavior.

Wall slip and extrudate distortion of three polymer melts

A high-density polyethylene (HDPE), a poly(dimethylsiloxane) (PDMS), and an oxetane based alternating block thermoplastic elastomer (TPE) were subjected to steady torsional and capillary flows. HDPE and PDMS exhibited wall slip in steady torsional flow. The shear stress ranges at which wall slip became apparent during steady torsional flow for HDPE and PDMS coincided with the wall shear stress ranges in capillary flow at which distortions of the extrudates emerging from capillary die were first noted. In contrast, TPE did not exhibit wall slip in steady torsional flow (for shear rates up to 200 s−1 and strains up to 25). None of the three polymers exhibited any overshoots of shear stress or first normal stress difference under steady flow conditions, indicating that the often-reported stress overshoots could be artifacts of wall slip. Furthermore, the extrudates of the TPE were relatively smooth and exhibited only minor and nonperiodic surface blemishes. The absence of extrudate distortions under the presumed no-slip condition for TPE emphasizes the intimate link between wall slip and the development of extrudate distortions and strengthens the premise that extrusion flow instabilities can be eliminated under conditions of stable wall slip or stick.

Effects of temperature and surface roughness on time-dependent development of wall slip in steady torsional flow of concentrated suspensions

A flow visualization technique was applied to investigate the time and temperature-dependent development of wall slip and the rheological behavior of a concentrated suspension, containing 63% by volume solid glass spheres and a poly (butadiene-acrylonitrile-acrylic acid) terpolymer matrix, using steady torsional flow. Flow visualization allowed the concomitant determination of the wall slip velocity and the shear viscosity of the concentrated suspension. The deformation rate, shear stress, and the wall slip velocity values during torsional flow were time dependent and asymptotically reached steady-state values. The characteristic time necessary to reach steady state decreased with increasing shear rate and temperature. Increasing temperature also increased the wall slip velocity. The flow visualization technique was further utilized to determine the yield stress of the suspension directly, which was found to decrease with increasing temperature. Increased surface roughness prevented the wall slip of the concentrated suspension under certain conditions; however, it frequently resulted in the fracture of the suspension samples. Sample fracture became more pronounced with the preshearing of the samples.

Normal Stress Behavior of Linear Polyethylene Melts in a Rotational Parallel-Plate Rheometer

Measurement of the total normal thrust generated in steady torsional flow between parallel plates enables one to determine the normal stress quantity [P11−2P22+P33] as a function of shear rate γ̇ for polymer melts. This measurement has been carried out for two linear polyethylene melts of different molecular weight using a modified Maxwell orthogonal rheometer. It is found that the normal stress curves have similar shape but are shifted from one another both horizontally along the γ̇ axis and vertically. A strong correlation exists between [P11−2P22+P33](γ̇) and 2G′(ω), where G′(ω) is the dynamic storage modulus in shear, and the two quantities have identical molecular weight dependencies. The manner of treatment of normal stress data for polymer melts of differing molecular weights is explored, with particular regard to the application of the method of reduced variables. In addition, the predictive ability of the Springs four-constant equation as regards normal stress behavior of polyethylene melts is discussed.