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...

Power analysis is a key component for planning prospective studies such as clinical trials. However, some journals in biomedical and psychosocial sciences ask for power analysis for data already collected and analysed before accepting manuscripts for publication. In this report, post hoc power analysis for retrospective studies is examined and the informativeness of understanding the power for detecting significant effects of the results analysed, using the same data on which the power analysis is based, is scrutinised. Monte Carlo simulation is used to investigate the performance of posthoc power analysis.

Freely standing thin liquid films containing supramolecular structures including micelles, nanoparticles, polyelectrolyte-surfactant complexes, and smectic liquid crystals undergo drainage via stratification. The layer-by-layer removal of these supramolecular structures manifests as stepwise thinning over time and a coexistence of domains and nanostructures of discretely different thickness. The layering of supramolecular structures in confined thin films contributes additional non-DLVO, supramolecular oscillatory surface forces to disjoining pressure, thus influencing both drainage kinetics and stability of thin films. Understanding and characterizing the spontaneous creation and evolution of nanoscopic topography of stratifying, freely standing thin liquid films have been long-standing challenges due to the absence of experimental techniques with the requisite spatial (thickness <10 nm) and temporal resolution (<1 ms). Using Interferometry Digital Imaging Optical Microscopy (IDIOM) protocols developed herein, we visualize and characterize size, shape, and evolution kinetics of nanoscopic mesas, terraces, and ridges. The exquisite thickness maps created using IDIOM protocols provide much needed and unprecedented insights into the role of supramolecular oscillatory surface forces in driving growth of such nanostructures as well as in controlling properties and stability of freely standing thin films and, more generally, of colloidal dispersions like foams.

The stability, rheology and applications of foams, emulsions and colloidal sols depend on the hydrodynamics and thermodynamics of thin liquid films that separate bubbles, drops and particles respectively. Thin liquid films containing micelles, colloidal particles, liquid crystals or polyelectrolyte-surfactant mixtures exhibit step-wise thinning or stratification, often attributed to the layer-by-layer removal of the aforementioned supramolecular structures. Stratification proceeds through emergence and growth of thinner circular domains within a thicker film, and the domain expansion dynamics are the focus of this study. Domain and associated thickness variation in foam films made from sodium dodecyl sulfate (SDS) micellar solutions are examined using a Scheludko-type cell with a novel technique we call Interferometry Digital Imaging Optical Microscopy (IDIOM). Below 100 nm, stratification and drainage cause a thickness-dependent variation in reflected light intensity, visualized as progressively darker shades of gray. We show that the domain expansion dynamics exhibit two distinct growth regimes with characteristic scaling laws. Initially, the radius of the isolated domains grows with square root time, and the expansion rate can be characterized by an apparent diffusion constant. In contrast, after a section of the expanding domain coalesces with the Plateau border, the contact line between domain and the surrounding thicker region moves a constant velocity. We show that a similar transition from a constant diffusivity to a constant velocity regime is also realized when a topological instability occurs at the contact line between the growing thinner isolated domain and the surrounding thicker film. Though several studies have focused on the expansion dynamics of isolated domains that exhibit a diffusion-like scaling, the change in expansion kinetics observed after domains contact with the Plateau border has not been reported and analyzed before.

Controlling and predicting the stability and lifetime of freestanding films, including foam and emulsion films, is crucial for many industrial and biological applications. Freestanding films (thickness <100 nm), stabilized by surfactants above the critical micelle concentration, exhibit stratification or stepwise thinning. Stratification proceeds by formation of thinner domains that grow at the expense of surrounding films. In this Article, we address several longstanding challenges related to the experimental characterization and theoretical description of thickness variations, forces, fluxes and flows underlying stratification. We show that nanoridges form and grow at the moving front around expanding domains, and we visualize their shape evolution using Interferometry Digital Imaging Optical Microscopy (IDIOM) protocols with an unprecedented spatiotemporal resolution (thickness <10 nm, time <1 ms). We develop a theoretical model for drainage via stratification under the influence of supramolecular oscillatory surface forces arising from the confinement-induced layering of micelles, and we show that the nanoridge growth and domain expansion dynamics can be modeled quantitatively.