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...

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.

Quantitative studies of capillary-driven thinning and pinch-off dynamics of semidilute polyelectrolyte solutions, and their response to extensional flows, typically encountered in drop formation applications, are relatively rare and are the focus of this contribution. Here the pinch-off dynamics and extensional rheology of two model polyelectrolytespoly(sodium 4styrenesulfonate) (NaPSS) and poly(acrylic acid) (PAA)in two different solvents are characterized by using Dripping-onto-Substrate (DoS) rheometry. Unlike shear relaxation time that decreases with increase in concentration in the unentangled, semidilute solutions, the extensional relaxation time of PAA solutions increases with an exponent of 1/2, and the entangled semidilute solutions also exhibit a stronger concentration dependence of 3/2. In contrast, the extensional relaxation time is not measurable for the unentangled, semidilute aqueous NaPSS solutions, though entangled NaPSS solutions show concentration-dependent values. The experiments and analysis described herein elucidate how the interplay of stretching due to electrostatics and hydrodynamics influences extensional rheology response and printability of polyelectrolyte dispersions.

Cellulose gum, also known as sodium carboxymethyl cellulose (NaCMC), is a polysaccharide often used as a thickener or rheology modifier in many industrial complex fluids, including foods. Shear and extensional rheology response influence production and processing of food, as well as the consumer perception and bioprocessing that begin with every bite. Stream-wise velocity gradients associated with extensional flows spontaneously arise during extrusion, calendaring, coating, dispensing, bubble growth or collapse, as well as during consumption including swallowing and suction via straws. The influence of polysaccharides on shear rheology response is fairly well characterized and utilized in food industry. In contrast, elucidating, measuring, and harnessing the extensional rheology response have remained longstanding challenges and motivate this study. The characterization challenges include the lack of robust, reliable, and affordable methods for measuring extensional rheology response. The product design challenges stem from the difficulties in assessing or predicting the influence of macromolecular properties on macroscopic rheological behavior. In this contribution, we address the characterization challenges using dripping-onto-substrate (DoS) rheometry protocols that rely on analysis of capillary-driven thinning and breakup of liquid necks created by releasing a finite volume of fluid onto a substrate. The DoS rheometry protocols emulate the heuristic tests of thickening, stickiness, or cohesiveness based on dripping a sauce from a ladle. We show that adding glycerol or changing salt concentration can be used for tuning the pinch-off dynamics, extensional rheology response, and processability of unentangled solutions of cellulose gum, whereas entangled solutions are relatively insensitive to changes in salt concentration.