Spreading, pinching, and coalescence: the Ohnesorge units

Dynamic duos: the building blocks of dimensional mechanics

Mechanics studies the relationships between space, time, and matter. These relationships can be expressed in terms of the dimensions of length , time , and mass . Each dimension broadens the scope of mechanics. Historically, mechanics emerged from geometry, which considers quantities like lengths or areas, with dimensions of the form . With the Renaissance, quantities combining space and time were considered, like speed, acceleration and later diffusivity, all of the form . Eventually, mechanics reached its full potential by including "mass-carrying" quantities such as mass, force, momentum, energy, action, power, viscosity, etc. These standard mechanical quantities have dimensions of the form where x and y are integers. In this contribution, we show that, thanks to this dimensional structure, these mass-carrying quantities can be readily arranged into a table such that x and y increase along the row and column, respectively. Ratios of quantities in the same rows provide characteristic lengths, while those in the same columns yield characteristic times, encompassing a great variety of physical phenomena from atomic to astronomical scales. Most generally, we show that selecting duos of mechanical quantities that are neither on the same row nor column of the table yields dynamics, where one mechanical quantity is understood as impelling motion, while the other impedes it. The force and the mass are the prototypes of impelling and impeding factors, but many other duos are possible. We present examples from the physical and biological realms, including planetary motion, sedimentation, explosions, fluid flows, turbulence, diffusion, cell mechanics, capillary and gravity waves, and spreading, pinching, and coalescence of drops and bubbles. This review provides a novel synthesis revealing the power of scaling or dimensional analysis, to understand processes governed by the interplay of two mechanical quantities. This elementary decomposition of space, time and motion into pairs of mechanical factors is the foundation of "dimensional mechanics", a method that this review wishes to promote and advance. Pairs are the fundamental building blocks, but they are only a starting point. Beyond this simple world of mechanical duos, we envision a richer universe that beckons with an interplay of three, four, or more quantities, yielding multiple characteristic lengths, times, and kinematics. This review is complemented by online video lectures, which initiate a discussion on the elaborate interplay of two or more mechanical quantities.

Levitation and dynamics of bodies in supersaturated fluids

A body immersed in a supersaturated fluid like carbonated water can accumulate a dynamic field of bubbles upon its surface. If the body is mobile, the attached bubbles can lift it upward against gravity, but a fluid-air interface can clean the surface of these lifting agents and the body may plummet. The process then begins anew, and continues for as long as the concentration of gas in the fluid supports it. In this work, experiments using fixed and free immersed bodies reveal fundamental features of force development and gas escape. A continuum model which incorporates the dynamics of a surface buoyancy field is used to predict the ranges of body mass and size, and fluid properties, for which the system is most dynamic, and those for which body excursions are suppressed. Simulations are then used to probe systems which are dominated by a small number of large bubbles. Body rotations at the surface are critical for driving periodic vertical motions of large bodies, which in turn can produce body wobbling, rolling, and damped surface 'bouncing' dynamics.

Pinching dynamics, extensional rheology, and stringiness of saliva substitutes

Saliva substitutes are human-made formulations extensively used in medicine, food, and pharmaceutical research to emulate human saliva's biochemical, tribological, and rheological properties. Even though extensional flows involving saliva are commonly encountered in situations such as swallowing, coughing, sneezing, licking, drooling, gleeking, and blowing spit bubbles, rheological evaluations of saliva and its substitutes in most studies rely on measured values of shear viscosity. Natural saliva possesses stringiness or spinnbarkeit, governed by extensional rheology response, which cannot be evaluated or anticipated from the knowledge of shear rheology response. In this contribution, we comprehensively examine the rheology of twelve commercially available saliva substitutes using torsional rheometry for rate-dependent shear viscosity and dripping-onto-substrate (DoS) protocols for extensional rheology characterization. Even though most formulations are marketed as having suitable rheology, only three displayed measurable viscoelasticity and strain-hardening. Still, these too, failed to emulate the viscosity reduction with the shear rate observed for saliva or match perceived stringiness. Finally, we explore the challenges in creating saliva-like formulations for dysphagia patients and opportunities for using DoS rheometry for diagnostics and designing biomimetic fluids.

Coalescence of biphasic droplets embedded in free standing smectic A films

We investigate micrometer-sized flat droplets consisting of an isotropic core surrounded by a nematic rim in freely suspended smectic A liquid-crystal films. In contrast to purely isotropic droplets which are characterized by a sharp edge and no long-range interactions, the nematic fringe introduces a continuous film thickness change resulting in long-range mutual attraction of droplets. The coalescence scenario is divided in two phases. The first one consists in the fusion of the nematic regions. The second phase involves the dissolution of a thin nematic film between the two isotropic cores. The latter has many similarities with the rupture of thin liquid films between droplets coalescing in an immiscible viscous liquid.

Rheology and dispensing of real and vegan mayo: the chickpea or egg problem

The rheology, stability, texture, and taste of mayonnaise, a dense oil-in-water (O/W) emulsion, are determined by interfacially active egg lipids and proteins. Often mayonnaise is presented as a challenging example of an egg-based food material that is hard to emulate using plant-based or vegan ingredients. In this contribution, we characterize the flow behavior of animal-based and plant-based mayo emulsions, seeking to decipher the signatures that make the real mayonnaise into such an appetizing complex fluid. We find that commercially available vegan mayos can emulate the apparent yield stress and shear thinning of yolk-based mayonnaise by the combined influence of plant-based proteins (like those extracted from chickpeas) and polysaccharide thickeners. However, we show that the dispensing and dipping behavior of egg-based and vegan mayos display striking differences in neck shape, sharpness, and length. The ratio of apparent extensional to shear yield stress value is found to be larger than the theoretically predicted square root of three for all mayo emulsions. The analysis of neck radius evolution of these extension thinning yield stress fluids reveals that even when the power law exponent governing the intermediate pinching dynamics is similar to the exponent obtained from the shear flow curve, the terminal pinching dynamics show strong local effects, possibly influenced by interstitial fluid properties, finite drop size and deformations, and capillarity.

Coacervate or precipitate? Formation of non-equilibrium microstructures in coacervate emulsions

Non-equilibrium processing of aqueous polyelectrolyte complex (PEC) coacervates is critical to many applications. In particular, many coacervate-forming systems are known to become trapped in out-of-equilibrium states (e.g., precipitation). The mechanism and conditions under which these states form, and whether they age, is not clearly understood. Here, we elucidate the influence of processing on the PEC coarsening mechanism as it varies with flow during mixing for a model system of poly(allylamine hydrochloride) and poly(acrylic acid sodium salt) in water. We demonstrate that flow conditions can be used to toggle the formation of rough, precipitate-like aggregates of micron-scale PEC structures. These structures form at compositions with viscous-dominant equilibrium rheology, and observations of their formation via optical microscopy suggest that they comprise colloidal aggregates of PEC coacervate droplets. We further show that these aggregates exhibit micron-scale coarsening, with a mixing time-dependent characteristic aging time scale. The results show that the formation of precipitate-like structures is not solely determined by composition, but is instead highly sensitive to mass transport and colloidal instability effects. Our observations suggest that the details of mixing flow can provide non-equilibrium structural control of a broad range of PEC coacervate materials orthogonally to structure-property inspired polymeric design. We anticipate that these findings will open the door for future studies on the control of non-equilibrium PEC formation and structure.

Sub-Newtonian coalescence in polymeric fluids

We present a theoretical framework for capturing the coalescence of a pendant drop with a sessile drop in polymeric fluids. The framework is based on the unification of various constitutive laws under a high Weissenberg creeping flow limit. Our results suggest that the phenomenon comes under a new regime, namely, the sub-Newtonian regime followed by the limiting case of arrested coalescence with the arrest angle θ_arrest ∝ Ec-1/2-1, where Ec_-1 is the inverse of Elasto-capillary number. Furthermore, we propose a new time scale T* integrating the continuum variable Ec_-1 and the macromolecular parameter N_e, the entanglement density to describe the liquid neck evolution. Finally, we validate the framework with high-speed imaging experiments performed across different molecular weights of poly(ethylene oxide) (PEO).

Effects of Crude Oil Properties and Dispersant on the Microstructure and Viscosity of Seawater-in-Oil Emulsions

This study examines the effects of crude oil properties and dispersant concentration (Corexit 9500) on the evolution of bulk viscosity, viscoelastic properties, and microstructure of salt water-in-crude oil emulsions. Microscopy, followed by machine-learning-based analysis, provides the size and spatial distribution of the seawater droplets. The crude oils include light Bakken, Alaskan North Slope (ANS), and Louisiana oils, and medium to heavy Platform Henry, Cold Lake, and Platform Gina oils. The light and medium oils entrain water up to 80% by volume, and the heavy oils, up to 25%. The droplet sizes and distance between them decrease with increasing viscosity, with small droplets clustering around larger ones. The Bakken- and ANS-based emulsions are unstable, but all of the emulsions evolve in time. All exhibit a non-Newtonian behavior, with the viscosity decreasing with increasing shear rate. The storage modulus is higher than the loss modulus for light oils, and vice versa for heavy oils. Trends of their nondimensional viscosity are collapsed onto two power laws as a function of the Ohnesorge number involving the properties of the original oil, and the size or distance between droplets. For light oils, the power law exponent decreases with increasing capillary number based on the rheometer shear rate and increases for heavy oils. At high shear rates, the exponents converge to the same value, 0.45, suggesting that the oil viscosity becomes the property that defines the emulsion rheology. The present findings are consistent with previously published data. Premixing the emulsions with dispersant causes separation of most of the water from the light oils, leaving only sparse droplet concentrations. In contrast, owing to slow diffusion rate, only a small fraction of the seawater is extracted from the heavy oil emulsions. Hence, the sparse light oil emulsions become Newtonian, but the heavy ones remain non-Newtonian.