Transient Viscosity Research Articles

Crustal Shortening and Rheological Behavior Across the Longmen Shan Fault, Eastern Margin of the Tibetan Plateau

AbstractKnowledge of lithospheric rheology can provide fundamental insights into crustal deformation near the Longmen Shan fault (LMSF). Based on viscoelastic deformation models constrained by interseismic geodetic observations, we obtain an optimal crustal shortening rate of 4.8 ± 0.4 mm/a across the LMSF and an upper mantle viscosity of 5.0 × 1020−21 Pa · s beneath eastern Tibet. More importantly, we find a high‐viscosity zone (>1021 Pa · s) in the lower crust beneath the LMSF, where the steady‐state viscosity is significantly higher than the transient viscosity derived from postseismic deformation. Further investigations with a power‐law rheology suggest that, due to the stress loading of the Wenchuan earthquake and the relaxation afterwards, the effective lower crustal viscosity decreases to ∼1018 Pa · s immediately after the earthquake and finally recovers to interseismic level (∼1021 Pa · s). Our results highlight the stress‐dependent behavior and the viscoelastic effect of rheological structure beneath the LMSF during the earthquake cycle.

Viscoelastic Properties of Fully Biomass-Based Transparent Plastic Comprising Cellulose Acetate and Citrate Ester.

Viscoelastic properties including melt processability were evaluated for a fully biomass-based glassy plastic comprising cellulose acetate (CA) and triethyl citrate (TEC). The TEC exerted an excellent plasticizing effect without dissolving the CA crystals. Pure CA has poor melt processability. In contrast, the TEC-plasticized CA had good melt-processability at 205 °C, which is lower than the degradation temperature of CA. Extrusion was possible even at 1000 s−1 without any flow instabilities, similar to conventional plastics showing good processability at extrusion. Furthermore, there was marked strain-hardening behavior in the transient elongational viscosity, suggesting that various processing operations are possible, such as a long-chain branched polymer. This biomass-based plastic can be used as a substitute for conventional glassy plastics because it is highly transparent and its softening temperature is above 100 °C.

Postseismic Relaxation Following the 2019 Ridgecrest, California, Earthquake Sequence

ABSTRACT The 2019 Ridgecrest, California, earthquake sequence involved predominantly right-lateral strike slip on a northwest–southeast-trending subvertical fault in the 6 July M 7.1 mainshock, preceded by left-lateral strike slip on a northeast–southwest-trending subvertical fault in the 4 July M 6.4 foreshock. To characterize the postseismic deformation, we assemble displacements measured by Global Positioning System (GPS) and Interferometric Synthetic Aperture Radar. The geodetic measurements illuminate vigorous postseismic deformation for at least 21 months following the earthquake sequence. The postseismic transient deformation is particularly well constrained from survey-mode GPS (sGPS) in the epicentral region carried out during the weeks after the mainshock. We interpret these observations with mechanical models including afterslip and viscoelastic relaxation of the lower crust and mantle asthenosphere. During the first 21 months, up to several centimeters of horizontal motions are measured at continuous GPS and sGPS sites, with amplitude that diminishes slowly with distance from the mainshock rupture, suggestive of deeper afterslip or viscoelastic relaxation. We find that although afterslip involving right-lateral strike slip along the mainshock fault traces and their deeper extensions reach a few decimeters, most postseismic deformation is attributable to viscoelastic relaxation of the lower crust and mantle. Within the Basin and Range crust and mantle, we infer a transient lower crust viscosity several times that of the mantle asthenosphere. The transient mantle asthenosphere viscosity is ∼1.3×1017 Pa s, and the adjacent Central Valley transient mantle asthenosphere viscosity is ∼7×1017 Pa s, about five times higher and consistent with an asymmetry in postseismic horizontal motions across the mainshock surface rupture.

Transient and steady shear rheology of particle-laden viscoelastic suspensions

We study the transient and steady shear rheology of rigid particle suspensions in Boger fluids via complete 3D numerical simulations and experiments. We calculate the transient per-particle extra viscosity and primary stress coefficients for suspensions at different particle volume fractions ϕ for a range of Weissenberg numbers (Wi). The per-particle viscosity ( ηp) and the primary normal coefficient ( ψ1p) increase monotonically to steady state in body-fitted (BF) simulations (for dilute suspensions) and immersed boundary (IB) simulations (for nondilute suspensions). We also present experimental measurements including small amplitude oscillatory shear, steady shear, and transient shear measurements at different particle volume fraction suspensions in a Boger fluid. The simulations and experiments suggest that longer strains are needed to achieve steady state at higher ϕ and Wi. We also show the comparison of the BF and the IB simulations with experimental data for the per-particle viscosity and find excellent quantitative agreement between simulations and experiments at Wi=3 but the IB simulations underpredict the steady values at higher Wi=6. Nevertheless, the IB simulations show an increase in the per-particle viscosity with ϕ as witnessed in the experiments. To understand this behavior, we examine the particle-induced fluid stress (PIFS) and the stresslet contributions using a novel method developed for the IB simulations in this work. We find that the PIFS is independent of ϕ but the stresslet values increase with ϕ. Thus, the particle-particle hydrodynamic interactions in nondilute suspensions affect the stresslet and, in turn, the per-particle viscosity at a given Wi.

Incorporating Rheological Nonlinearity into Fractional Calculus Descriptions of Fractal Matter and Multi-Scale Complex Fluids

In this paper, we use ideas from fractional calculus to study the rheological response of soft materials under steady-shearing flow conditions. The linear viscoelastic properties of many multi-scale complex fluids exhibit a power-law behavior that spans over many orders of magnitude in time or frequency, and we can accurately describe this linear viscoelastic rheology using fractional constitutive models. By measuring the non-linear response during large step strain deformations, we also demonstrate that this class of soft materials often follows a time-strain separability principle, which enables us to characterize their nonlinear response through an experimentally determined damping function. To model the nonlinear response of these materials, we incorporate the damping function with the integral formulation of a fractional viscoelastic constitutive model and develop an analytical framework that enables the calculation of material properties such as the rate-dependent shear viscosity measured in steady-state shearing flows. We focus on a general subclass of fractional constitutive equations, known as the Fractional Maxwell Model, and consider several different analytical forms for the damping function. Through analytical and computational evaluations of the shear viscosity, we show that for sufficiently strong damping functions, for example, an exponential decay of fluid memory with strain, the observed shear-thinning behavior follows a power-law response with exponents that are set by the power-law indices of the linear fractional model. For weak damping functions, however, the power-law index of the high shear rate viscosity is set by the terminal behavior of the damping function itself at large strains. In the limit of a very weak damping function, the theoretical formulation predicts an unbounded growth of the shear stress with time and a continuously growing transient viscosity function that does not converge to a meaningful steady-state value. By determining the leading terms in our analytical solution for the viscosity at both low and high shear rates, we construct an approximate analytic expression for the rate-dependent viscosity. An error analysis shows that, for each of the damping functions considered, this closed-form expression is accurate over a wide range of shear rates.

Postseismic Deformation of the 2008 Wenchuan Earthquake Illuminates Lithospheric Rheological Structure and Dynamics of Eastern Tibet

AbstractTectonic research of the Tibetan Plateau has long focused on its deformation style and mechanisms. The 2008 Mw7.9 Wenchuan earthquake ruptured the Longmen Shan fault located at the eastern rim of the plateau and excited a viscoelastic response of the lithosphere. We infer a three‐dimensional (3D) rheological structure of eastern Tibet from modeling nine years of postseismic displacements observed by GPS. Our solution provides tight constraints on the lower‐crustal and upper‐mantle steady‐state viscosities of the Songpan‐Ganzi Terrane as (5.0 ± 0.7) × 1018 and (1.3 ± 0.3) × 1019 Pa s, respectively, consistent with a “jelly sandwich” model of Tibet, but not with some crustal channel flow models featuring much lower viscosities. The inferred lower‐crustal and upper‐mantle transient viscosities are (5.0 ± 1.3) × 1017 and (5.0 ± 1.5) × 1018 Pa s, respectively, suggesting nonlinear deformation mechanisms. The adjacent West Qinling and Sichuan blocks feature an order‐of‐magnitude higher rheological strength, which is consistent with the changes in the crustal material properties and interseismic deformation style across the East Kunlun‐Tazang and Longmen Shan faults. Our results enable us to propose a conceptual 3D tectonic deformation model, in which the eastward extrusion of Tibet is absorbed in the Songpan‐Ganzi crust mainly by E‐W shortening and N‐S extension, accommodated through faulting of conjugate strike‐slip faults in the upper crust and distributed shear in the lower crust.

A constitutive equation for fiber suspensions in viscoelastic media

A viscosity overshoot of fibers filled in a polymer melt under a shear flow is much tougher to predict via the existing constitutive equations of suspension rheology in a viscous media, owing to the effect of fiber orientation on the viscoelastic behavior. The WMT-X (White–Metzner model eXtended by Tseng) viscoelastic fluid model coupled with the typical Dinh–Armstrong fiber suspension model, known as the suspended WMT-X model, is proposed herein. The primary procedure involves verifying the lower viscosity of the completely aligned suspension compared to that of the randomly oriented suspension. In addition, the viscosity overshoot depends on the off-diagonal orientation tensor component in the flow-gradient plane. As a validation, the numerical predictions of transient shear viscosity are in good agreement with the related experimental data.

Exploring GPS Observations of Postseismic Deformation Following the 2012 MW7.8 Haida Gwaii and 2013 MW7.5 Craig, Alaska Earthquakes: Implications for Viscoelastic Earth Structure

AbstractThe Queen Charlotte‐Fairweather Fault (QC‐FF) system off the coast of British Columbia and southeast Alaska is a highly active dextral strike‐slip plate boundary that accommodates ∼50 mm/yr of relative motion between the Pacific and North America plates. Nine MW ≥ 6.7 earthquakes have occurred along the QC‐FF system since 1910, including a MS(G‐R)8.1 event in 1949. Two recent earthquakes, the October 28, 2012 Haida Gwaii (MW7.8) and January 5, 2013 Craig, Alaska (MW7.5) events, produced postseismic transient deformation that was recorded in the motions of 25 nearby continuous Global Positioning System (cGPS) stations. Here, we use 5+ yr of cGPS measurements to characterize the underlying mechanisms of postseismic deformation and to constrain the viscosity structure of the upper mantle surrounding the QC‐FF. We construct forward models of viscoelastic deformation driven by coseismic stress changes from these two earthquakes and explore a large set of laterally heterogeneous viscosity structures that incorporate a relatively weak back‐arc domain; we then evaluate each model based on its fit to the postseismic signals in our cGPS data. In determining best‐fit model structures, we additionally incorporate the effects of afterslip following the 2012 event. Our results indicate the occurrence of a combination of temporally decaying afterslip and vigorous viscoelastic relaxation of the mantle asthenosphere. In addition, our best‐fit viscosity structure (transient viscosity of 1.4–2.0 × 1018 Pa s; steady‐state viscosity of 1019 Pa s) is consistent with the range of upper mantle viscosities determined in previous studies of glacial isostatic rebound and postseismic deformation.

Relaxation of Tibetan Lower Crust and Afterslip Driven by the 2001 Mw7.8 Kokoxili, China, Earthquake Constrained by a Decade of Geodetic Measurements

AbstractWe model the time‐dependent postseismic displacements following the 2001 Mw7.8 Kokoxili earthquake, including both GPS (2001–2002 for near‐field and 2001–2010 for far‐field) and descending‐track InSAR line‐of‐sight time series (2003–2010) to study three postseismic deformation processes. The predicted deformation patterns and magnitude from poroelastic rebound are inconsistent with the geodetic observations. Far‐field postseismic deformation (>200 km from rupture) is primarily induced by upper mantle viscoelastic relaxation beneath Tibet and the Qaidam Basin and places a lower bound on transient and steady‐state viscosities on the order of 1019–1020 Pas. Shallow stress‐driven afterslip (<20 km) on the Kunlun Pass fault localizes deformation in the near‐fault area and helps explain the GPS‐measured displacement gradient across the fault. Deep stress‐driven afterslip in the downdip region of the coseismic rupture (>20 km) has an amplitude of ∼1 m during the first 3 years. Our results indicate that the consideration of deep afterslip increases our estimates of transient viscosity of the lower crust beneath Tibet and the Qaidam basin for this earthquake by as much as a factor of three. Our combined model incorporating viscoelastic relaxation and afterslip suggests that the effective transient and steady‐state viscosities in the Tibetan lower crust are 5 × 1018 Pas and 4 × 1019 Pas, respectively (transient viscosity = 2 × 1018 Pas without afterslip considered), while the effective transient and steady‐state viscosities below the Qaidam Basin area are 1 × 1019 Pas and 6 × 1019 Pas (transient viscosity = 4 × 1018 Pas without afterslip considered).

Elongational viscosity scaling of polymer melts with different chemical constituents

Morelly et al. (Macromolecules 52:915-922, 2019) reported transient and steady-state elongational viscosity data of monodisperse linear polymer melts obtained by filament-stretching rheometry with locally controlled strain and strain rate and found different power law scaling of the elongational viscosities of polystyrene, poly(tert-butylstyrene) and poly(methyl-methacrylate). Very good agreement is achieved between data and predictions of the extended interchain pressure (EIP) model (Narimissa et al. J. Rheol. 64, 95-110 (2020)), based solely on linear viscoelastic characterization and the Rouse time τR of the melts. The analysis reveals that both the normalized elongational viscosity and the normalized elongational stress are dependent on the number of entanglements (Z) and the ratio of entanglement molar mass Mem to critical molar mass Mcm of the melts in the linear viscoelastic regime through {eta}_E^0/left({G}_N{tau}_Rright)propto {left({M}_{mathrm{em}}/{M}_{mathrm{cm}}right)}^{2.4}{Z}^{1.4} and {sigma}_E^0/{G}_Npropto {left({M}_{mathrm{em}}/{M}_{mathrm{cm}}right)}^{2.4}{Z}^{1.4} Wi , while in the limit of fast elongational flow with high Weissenberg number Wi={tau}_Rdot{varepsilon} , both viscosity and stress become independent of Z and Mem/Mcm, and approach a scaling which depends only on Wi, i.e. ηE/(GNτR) ∝ Wi−1/2 and σE/GN ∝ Wi1/2. When expressed by an effective power law, the broad transition from the linear viscoelastic to the high Wi regime leads to chemistry-dependent scaling at intermediate Wi depending on the number of entanglements and the ratio between entanglement molar mass and critical molar mass.

Modeling of nonlinear extensional and shear rheology of low‐viscosity polymer melts

AbstractThe hierarchical multi‐mode molecular stress function (HMMSF) model developed by Narimissa and Wagner [Rheol. Acta 54, 779–791 (2015), and J. Rheol. 60, 625–636 (2016)] for linear and long‐chain branched (LCB) polymer melts were used to analyze the set of transient elongational and shear viscosity data of two LCB low‐density polyethylenes (1840H and 2426 k), and a linear poly‐(ethylene‐co‐α‐butene), PEB A‐780090 as reported by [Li et al. J. Rheol. 64, 177 (2020)], who had developed a new horizontal extensional rheometer to extend the lower limits of elongational viscosity measurements of polymer melts. Comparison between model predictions and elongational stress growth data reveals excellent agreement within the experimental window, and good consistency with shear stress growth data, based exclusively on the linear‐viscoelastic relaxation spectrum and only two nonlinear model parameters, the dilution modulus GD for extensional flows, and in addition a constraint release parameter for shear flow.

Thin crème brûlée rheological structure for the Eastern California Shear Zone

AbstractSince the occurrence of the 1992 CE Mw 7.3 Landers and 1999 Mw 7.1 Hector Mine earthquakes in the Mojave Desert (California, USA), postseismic deformation following both earthquakes has been intensively studied, and models with a strong crust overlying a low-viscosity mantle asthenosphere have been favored. However, we recently found that the near-field postseismic transients after the two earthquakes have lasted longer than previously thought, which requires a revision of the postseismic modeling. Our new modeling results based on the revised postseismic transients show that: (1) the effective viscosity of the lower crust beneath the Mojave region at the decadal time scale is ∼2 × 1020 Pa·s (transient viscosity ∼2 × 1019 Pa·s), i.e., only ∼5 times that of the underlying mantle asthenosphere, and (2) the transient viscosity of the upper mantle exhibits a time-dependent increase, providing fresh geodetic evidence for frequency-dependent rheology (e.g., Andrade or extended Burgers rheology). The inferred transient rheology for the first year agrees well with that obtained for the July 2019 Mw 6.4 and Mw 7.1 Ridgecrest earthquakes ∼180 km north of the two Mojave events. Our modeling results support a thin crème brûlée model for the Eastern California Shear Zone (part of the Pacific-North America plate boundary) in which both the lower crust and the upper mantle exhibit ductility at decadal time scales.

Heterogeneous Power‐Law Flow With Transient Creep in Southern California Following the 2010 El Mayor‐Cucapah Earthquake

AbstractThe rheology of the crust and mantle and the interaction of viscoelastic flow with seismic/aseismic slip on faults control the state of stress in the lithosphere over multiple seismic cycles. The rheological behavior of rocks is well constrained in a laboratory setting, but the in situ properties of the lithosphere and its lateral variations remain poorly known. Here, we access the lower‐crustal rheology in Southern California by exploiting 8 years of geodetic postseismic deformation following the 2010 El Mayor‐Cucapah earthquake. The data illuminate viscoelastic flow in the lower crust with lateral variations of effective viscosity correlated with the geological province. We show that a Burgers assembly with dashpots following a nonlinear constitutive law can approximate the temporal evolution of stress and strain rate, indicating the activation of nonlinear transient creep before steady‐state dislocation creep. The transient and background viscosities in the lower crust of the Salton Trough are on the order of ~1018 and ~1019 Pa s, respectively, about an order of magnitude lower than those in the surrounding regions. We highlight the importance of transient creep, nonlinear flow laws, and lateral variations of rheological properties to capture the entire history of postseismic relaxation following the El Mayor‐Cucapah earthquake.

Modification of Poly(Lactic Acid) Rheological Properties Using Ethylene–Vinyl Acetate Copolymer

The effect of ethylene–vinyl acetate copolymer (EVA) addition on the rheological properties of poly(lactic acid) (PLA) was studied. EVA exhibited strain-hardening behavior in the transient elongational viscosity due to its long-chain branch structure, whereas PLA did not show any strain-hardening. The blends showed sea-island structure, in which the size of EVA droplets decreased with the vinyl acetate content in EVA. It should be noted that the blends showed strain-hardening behavior even though EVA is not in the continuous phase. During elongational flow, EVA droplets deform to the fibrous shape owing to hydrodynamic force applied by the matrix PLA, and eventually their deformation is greatly reduced as a result of the strain-hardening. Consequently, the blend system behaved like a rigid-fiber dispersion, which are known to show enhanced elongational viscosity. Finally, the processability of a tubular-blown film was improved by the EVA addition because of the strain-hardening.

Linear wormlike micelles behave similarly to entangled linear polymers in fast shear flows

We report shear startup data on solutions of entangled linear wormlike micelles, only differing in the concentration of a binding aromatic salt. Wormlike micelles behave similarly to ordinary polymers in fast shear flows, exhibiting pronounced overshoots as well as tiny undershoots in transient shear viscosity, before approaching the steady state. The analogy is here emphasized by successfully comparing data with predictions of a constitutive equation recently adopted for ordinary entangled polymers. In the fast shear flow, entangled linear wormlike micelles appear to align, stretch, and tumble just like polymeric chains.

Understanding the viscosity decline of poly(amic acid) solution from the correlation point of view

The effects of storage time and temperature on the properties of poly(amic acid) (PAA) solution were re-examined by dynamic and static light scattering. One fast and one slow relaxation modes were observed in fresh prepared semidilute solution. The fast mode corresponds to cooperative diffusion of chain segments inside each “blob” while the slow mode comes from the long-range correlated concentration fluctuation of transient network. Chains relaxation during storage at room temperature (20 °C) leads to the disentanglement of transient network and viscosity drop, thereby only one fast relaxation mode was observed which was related to the mutual diffusion of separated polymer chains. Cooling (to 2 °C) rejuvenates the solution to a certain extent, by which the slow relaxation mode can be regenerated and viscosity re-rises. These results indicate that PAA solutions experience a slow thermodynamic and kinetic transition during storage. Hydrolysis may not be the only reason responsible for the viscosity decrease of the PAA solution, the arrangement of chain conformation during storage should be accounted for.

High pressure rheological studies of methane hydrate slurries formed from water-hexane, water-heptane, and water-decane multiphase systems

High pressure rheological properties of methane hydrate slurries entail the high-pressure rheometer that can deliver a suitable mixing to form in situ methane hydrate from the multiphase system. However, the hydrate formation was extremely challenging in conventional cup and bob geometry due to its plane surface. In this work, modified Couette geometry has been used in a high pressure rheometer to study in situ formation and dissociation of methane hydrate slurries formed from multiphase water-hexane (C6H14), water-heptane (C7H16) and water-decane (C10H22), with varying water-to-liquid hydrocarbon ratios (50:50, 30:70 v/v). Rheological properties such as viscosity, flow curve measurements, viscoelastic properties have been measured during hydrate formation and dissociation. Transient viscosity measurements are carried out at 10 MPa and 275.15 K at a shear rate of 1000 s−1. It was observed that the viscosity increases significantly during hydrate induction. Viscosity profile has shown bobbing behavior during the course of hydrate formation indicating in situ morphological changes (agglomeration and breakage of hydrate crystals) during hydrate formation. Flow curves indicate strong shear thinning behavior. Viscosity profile of methane hydrate slurries were also observed for each case during the hydrate dissociation using thermal stimulation. The peak in the viscosity has been identified near hydrate equilibrium condition during dissociation. Dynamic viscoelastic properties indicate solid behavior of methane hydrate slurries. The present study provides significant contribution on the rheology of methane hydrate slurries formed from multiphase systems in the context of flow assurance applications.

Nonlinear rheology and dynamics of supramolecular polymer networks formed by associative telechelic chains under shear and extensional flows

Nonequilibrium computer simulations have been applied to study the shear and extensional flow behavior of supramolecular polymer networks (SPNs) formed by unentangled and weakly entangled associative telechelic chains and their nonassociative polymer melt counterparts. The reversible bonding of the associative end monomers or stickers leads to the formation of percolated transient networks and consequently stronger mechanical properties of the SPNs than their melt counterparts. In startup shear, the transient shear viscosities η ( t ) and first normal stress coefficients Ψ 1 ( t ) of both the SPN and melt systems show overshoot behavior, but only the SPNs demonstrate transient strain hardening at high shear rates. In startup planar extensional flows, all systems demonstrate the characteristic extensional strain hardening behavior. The transient extensional viscosities η E ( t ) of the SPNs undergo a small overshoot before entering the steady state, which was not observed in the nonassociative polymer melts. For both types of polymer systems with unentangled and weakly entangled chain lengths, the steady-state shear viscosities show typical shear-thinning behavior, while the steady-state extensional viscosities demonstrate extension hardening, which are consistent with published simulation and experimental works. The observed flow behavior can be well understood from the flow-induced non-Gaussian chain stretching and segment orientation in all polymer systems studied, as well as the additional relaxation mechanisms in the SPNs, including the flow-induced reduction in the density of elastically active strands, the increment in the probability for the stickers to exchange their associated partners, and the reduction in the average sticky bond lifetimes at high strain rates.

Critical condition of electrohydrodynamic jetting from a polymer-solution droplet on a conductive wire

An experimental study was conducted to determine the threshold electrostatic field to initiate electrohydrodynamic jetting from a polymer solution droplet wetting on a conductive wire. The study is crucial to understand the roles of the material and process parameters in wire-based needleless electrospinning for controllable mass production of continuous nanofibers. Two types of polymer solutions, i.e., polyacrylonitrile/N,N-dimethylformamide (PAN/DMF) and aqueous polyethyloxide solution (PEO/H2O), with the mass concentrations of 4%, 8%, 12%, and 16% for PAN and 1%, 2%, 4%, 6%, and 8% for PEO, respectively, were considered in the experiments. Taut thin copper wires with diameters of 0.254, 0.508, 1.016, and 1.524 mm (i.e., 0.01, 0.02, 0.04, and 0.06 in.) were utilized, respectively, as the positive electrodes. The effects of the polymer concentration and wire diameter on the threshold electrical voltage for jetting initiation and nanofiber diameter were examined. Given the droplet volume and spacing between the copper wire and fiber collector, experimental observations show that the threshold electrical voltage increases with increasing either polymer mass concentration or wire diameter. In addition, the effects of polymer mass concentration on the transient shear viscosity and surface tension of the PAN/DMF solutions were examined. It shows the positive correlation between the transient shear viscosity and polymer mass concentration, shear thinning of the polymer solution at a high shear rate, and nearly constant surface tension of the polymer solution in the range of the present PAN mass concentration. Furthermore, a simple electrostatic model is formulated to phenomenologically elucidate the experimental observations. The present study provides useful scaling laws for controllable scale-up nanofiber fabrication by means of a wire-based needleless electrospinning technique.

Correction to: Experimental and numerical study on transient elongational viscosity for PP/LDPE blends

Correction to: Experimental and numerical study on transient elongational viscosity for PP/LDPE blends