We show that visualization and analysis of capillary-driven thinning and pinch-off dynamics of the columnar neck in an asymmetric liquid bridge created by dripping-onto-substrate can be used for characterizing the extensional rheology of complex fluids. Using a particular example of dilute, aqueous PEO solutions, we show the measurement of both the extensional relaxation time and extensional viscosity of weakly elastic, polymeric complex fluids with low shear viscosity η < 20 mPa·s and relatively short relaxation time, λ < 1 ms. Characterization of elastic effects and extensional relaxation times in these dilute solutions is beyond the range measurable in the standard geometries used in commercially available shear and extensional rheometers (including CaBER, capillary breakup extensional rheometer). As the radius of the neck that connects a sessile drop to a nozzle is detected optically, and the extensional response for viscoelastic fluids is characterized by analyzing their elastocapillary self-thinning, we refer to this technique as optically-detected elastocapillary selfthinning dripping-onto-substrate (ODES-DOS) extensional rheometry.A ddition of a dilute amount, even 1−400 ppm (parts per million), of a high molecular weight polymer like poly(ethylene oxide) (PEO, M w > 10 6 g/mol) to a solvent like water is observed to significantly change the fluid response to extensional or stretching flows. 1 Examples include enhanced pressure drop in porous media flows, 1a suppression of rebound in drop impact studies, 2 a discernible birefringence around a stagnation point in cross-slot flows, 3 delayed breakup in dripping, spraying or jetting, 1b,4 and possibly turbulent drag reduction. 5 The influence of polymers is even more remarkable for dilute, aqueous solutions as the measured shear viscosity η(γ) appears to be Newtonian, and elastic modulus, relaxation time, and the first normal stress difference are not measured, or manifested, in steady shear or oscillatory shear tests carried out on the state-of-the-art torsional rheometers. 6 Macromolecular solutions typically exhibit a large and measurable resistance called extensional viscosity, η E , to streamwise velocity gradients characteristic of extensional flows 1b,7 and undergo stress relaxation with a characteristic extensional relaxation time λ E . However, for dilute, aqueous solutions, quantitative measurements of both η E and λ E remain beyond the capability of commercially available devices like CaBER (capillary breakup extensional rheometer). A countable few measurements of extensional relaxation time in dilute aqueous solutions presented in the recent literature 6,7d require bespoke instrumentation not available or easily replicable in most laboratories. The aim of the present study is 3-fold: to describe an extensional rheometry protocol that can be recreated virtually in any laboratory (quite inexpensively for high viscosity fluids), to characterize the extensional viscosity and extensional relaxation time for dilute, aqueous polymer solutions, and to pr...

Stream‐wise velocity‐gradients associated with extensional flows arise in thinning liquid necks spontaneously formed during jetting, printing, coating, spraying, atomization, and microfluidic‐based drop formation. In this contribution, we employ Dripping‐onto‐Substrate (DoS) rheometry protocols to measure the extensional rheology response of intrinsically semi‐dilute polymer solutions by visualizing and analyzing capillary‐driven thinning of a columnar neck formed between a nozzle and a sessile drop. We show that extensional viscosity that quantifies the resistance to stream‐wise velocity gradients is orders of magnitude higher than the shear viscosity. Although shear flows only weakly perturb the chain dimensions, extensional flows can strongly stretch and orient the chains, thus influencing both intra‐ and inter‐chain interactions. We find that the extensional relaxation times for intrinsically semi‐dilute PEO solutions in a good solvent for five different molecular weights increase linearly with concentration, exhibiting a stronger concentration dependence than observed for dilute solutions, or anticipated by blob models, developed for relaxation of weakly perturbed chains in a good solvent. The observed distinction between the concentration‐dependent relaxation dynamics of intrinsically dilute and semi‐dilute solutions arises due the complex influence of stretching, conformational anisotropy, and polymer concentration on excluded volume and hydrodynamic interactions of flexible, highly extensible polymers. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 1692–1704

Liquid transfer and drop formation/deposition processes involve complex free-surface flows including the formation of columnar necks that undergo spontaneous capillary-driven instability, thinning and pinch-off. For simple (Newtonian and inelastic) fluids, a complex interplay of capillary, inertial and viscous stresses determines the nonlinear dynamics underlying finite-time singularity as well as self-similar capillary thinning and pinch-off dynamics. In rheologically complex fluids, extra elastic stresses as well as non-Newtonian shear and extensional viscosities dramatically alter the nonlinear dynamics. Stream-wise velocity gradients that arise within the thinning columnar neck create an extensional flow field, and many complex fluids exhibit a much larger resistance to elongational flows than Newtonian fluids with similar shear viscosity. Characterization of pinch-off dynamics and the response to both shear and extensional flows that influence drop formation/deposition in microfluidic and printing applications requires bespoke instrumentation not available, or easily replicated, in most laboratories. Here we show that dripping-onto-substrate (DoS) rheometry protocols that involve visualization and analysis of capillary-driven thinning and pinch-off dynamics of a columnar neck formed between a nozzle and a sessile drop can be used for measuring shear viscosity, power law index, extensional viscosity, relaxation time and the most relevant processing timescale for printing. We showcase the versatility of DoS rheometry by characterizing and contrasting the pinch-off dynamics of a wide spectrum of simple and complex fluids: water, printing inks, semi-dilute polymer solutions, yield stress fluids, food materials and cosmetics. We show that DoS rheometry enables characterization of low viscosity printing inks and polymer solutions that are beyond the measurable range of commercially-available capillary break-up extensional rheometer (CaBER). We show that for high viscosity fluids, DoS rheometry can be implemented relatively inexpensively using an off-the-shelf digital camera, and for many complex fluids, similar power law scaling exponent describes both neck thinning dynamics and the shear thinning response.

Delayed capillary break-up of viscoelastic filaments presents scientific and technical challenges relevant for drop formation, dispensing, and adhesion in industrial and biological applications. The flow kinematics are primarily dictated by the viscoelastic stresses contributed by the polymers that are stretched and oriented in a strong extensional flow field resulting from the streamwise gradients created by the capillarity-driven squeeze flow. After an initial inertiocapillary (IC) or viscocapillary (VC) regime, where elastic effects seem to play no role, the interplay of capillarity and viscoelasticity can lead to an elastocapillary (EC) response characterized by exponentially-slow thinning of neck radius (extensional relaxation time is determined from the delay constant). Less frequently, a terminal visco-elastocapillary (TVEC) response with linear decay in radius can be observed and used for measuring terminal, steady extensional viscosity. However, both IC/VC–EC and EC–TVEC transitions are inaccessible in devices that create stretched necks by applying a step strain to a liquid bridge (e.g., capillary breakup extensional rheometer). In this study, we use dripping-onto-substrate rheometry to obtain radius evolution data for unentangled polymer solutions. We deduce that the plots of transient extensional viscosity vs. Hencky strain (scaled by the respective values at the EC–TVEC transition) emulate the functional form of the birefringence–macromolecular strain relationship based on Peterlin’s theory. We quantify the duration and strain between the IC/VC–EC and the EC–TVEC transitions using measures we term elastocapillary span and elastocapillary strain increment and find both measures show values directly correlated with the corresponding variation in extensional relaxation time.