The research, carried out by Jeyapradhap Thirisangu and Karthick Subramani of the Indian Institute of Information Technology, Design and Manufacturing, Kancheepuram in Chennai, builds on a growing body of work showing that droplets beyond the Rayleigh limit behave in strikingly non-intuitive ways under acoustic fields. Within the Rayleigh limit, where the droplet diameter is much smaller than the acoustic wavelength, the minimum acoustic energy density needed to suspend a droplet against gravity is essentially independent of size. Beyond that limit, the two authors demonstrate theoretically that this critical energy density becomes highly size-dependent and, remarkably, non-monotonic: it rises to a peak, falls, and then alternates in a pattern of ever-larger peaks and troughs as droplet size increases.

The origin of this strange behavior lies in the internal structure of the standing wave as seen by a large droplet. When a droplet spans multiple pressure nodes and antinodes, different regions of its volume sit in zones of opposing acoustic force. The portion located a quarter-wavelength below a pressure node experiences an upward force, while the portion a quarter-wavelength above the node experiences a downward force. These opposing contributions partially cancel each other, reducing the net acoustic force available to fight gravity. As the droplet grows, the volume contributing to the positive, gravity-defying force shrinks relative to the whole, so the energy needed for suspension climbs. Past a certain size, however, the balance shifts again: more of the droplet volume begins to contribute to the positive net force, and the critical energy density falls. The result is an alternating pattern in which, counterintuitively, some larger droplets require less acoustic energy to levitate than smaller ones in the very same wavefield.

Thirisangu and Subramani exploit this non-monotonic physics to build what they call acoustic sorting beyond the Rayleigh limit. In their simulations, performed with COMSOL Multiphysics 6.0 on a two-dimensional channel 12 millimeters wide and 6 millimeters tall, water droplets are suspended in mineral oil and subjected to a plane standing acoustic wave applied along the height of the channel. The computational domain, discretized with more than 800,000 grid elements and a maximum grid size of 15 microns, solves the incompressible mass continuity and momentum equations together with an advection-diffusion equation for the phase field that tracks the droplet interface, with the acoustic force incorporated as a body force and gravity and interfacial tension included in the framework.

The sorting demonstrations come in three flavors. In the first case, at a frequency of a few kilohertz corresponding to a wavelength of several millimeters, the authors apply an acoustic energy density at which the larger droplet, of a size that sits in the suspending regime, remains levitated, while the smaller droplet, whose critical energy density is higher, settles under gravity. In the second case, simply by changing the frequency and adjusting the energy density, the situation reverses: the bigger droplet settles while the smaller one suspends. The third case is the most intriguing of all. At the same applied conditions under which both the smallest and largest droplets settle, a droplet of intermediate size can be suspended, because its critical energy density happens to fall below the applied value while the critical values of its smaller and larger neighbors do not.

This intermediate-size selectivity is impossible within the Rayleigh limit. There, because the suspension threshold is size-independent, a given acoustic energy density either levitates droplets of all sizes or lets them all settle. Beyond the Rayleigh limit, the non-monotonic curve of critical energy density versus size creates windows in which droplets of a chosen size band can be held aloft while everything else falls. The authors show that the settling and suspending regimes are separated by a simple criterion: if the applied acoustic energy density is below the critical value for a given droplet size, the droplet settles; if it equals or exceeds it, the droplet suspends. A non-dimensional version of this curve allows the same analysis to be transferred to any wavelength, so the sorting conditions can be computed for whatever frequency the experimenter chooses.

The authors go further and lay out a three-step recipe for extracting arbitrary intermediate-sized droplets from a broad size range. First, the wavelength is chosen so that the ratio of droplet size to wavelength places the target size at the first local minimum of the critical energy density curve; applying the corresponding energy density then settles all droplets larger than the target while leaving the target and everything smaller suspended. Second, the frequency is retuned so that the target size sits at the first local maximum of the curve, and an energy density slightly below the target’s critical value is applied; now the smaller droplets remain suspended while droplets of the target size begin to settle. Third, while the target droplets are settling, the energy density is raised slightly above their critical value, halting their descent and leaving them suspended in the fluid between the smaller droplets, which stay at the top, and the larger droplets, which settle at the bottom. The net effect is a clean isolation of any desired intermediate size.

The method even extends to droplets that are identical in size but differ in interfacial tension. In the simulations discussed so far, the maximum Bond number, which measures the ratio of acoustic to interfacial forces, is only 0.063, far below one, so surface tension keeps the droplets intact. When the interfacial force weakens, for example by adding surfactants to reduce the interfacial tension, the opposing acoustic forces within a large droplet can compete strongly enough to split it into daughter droplets. The authors demonstrate a two-step sorting scheme for two droplets of the same size: applying a high acoustic energy density splits the droplet with the weak interfacial tension into two daughters while the droplet with the strong interfacial tension remains whole, and then reducing the energy density to a value between the two critical levels lets the daughter droplets settle while the intact droplet suspends. Sorting by interfacial tension, through size-preserving splitting, thus becomes possible with the same acoustic hardware.

The theoretical findings hold promise for advanced droplet-sorting devices, but the authors are careful to spell out the practical hurdles. The acoustic energy densities and pressure amplitudes required are high enough that any experimental implementation would need pressurized systems to prevent cavitation, the formation of vapor bubbles that would otherwise disrupt the wavefield. The study also rests on simplifying assumptions: a predetermined acoustic energy density is employed without solving the first-order acoustic fields, and the acoustic body force is derived using a Boussinesq approximation in which density and sound speed variations are small. Solving the bidirectionally coupled equations of the fast-time acoustic fields and the slow-time hydrodynamic motion, with the divergence of the Reynolds stress tensor as the body force, would yield more accurate predictions of droplet dynamics. Even so, the work establishes a clear theoretical roadmap: by tuning frequency and acoustic energy density, researchers can now in principle hold droplets of any selected size, or any selected interfacial tension, motionless against gravity while everything around them falls, a capability that could reshape how emulsions, biological droplets, and encapsulated materials are sorted in the laboratory and beyond.

Subject of Research: A theoretical study of acoustic sorting of droplets beyond the Rayleigh limit under combined acoustic and gravity forces

Article Title: Sorting droplets beyond the Rayleigh limit under acoustic-gravity forces: a theoretical approach

Article References: Thirisangu, J., & Subramani, K. (2025). Sorting droplets beyond the Rayleigh limit under acoustic-gravity forces: a theoretical approach. Frontiers in Acoustics, 3, Article 1544464. https://doi.org/10.3389/facou.2025.1544464

Image Credits: AI Generated

DOI: 10.3389/facou.2025.1544464

Keywords: acoustofluidics, droplet sorting, Rayleigh limit, acoustic radiation force, gravity, interfacial tension, droplet splitting, microfluidics, Sorting, droplets, beyond, Rayleigh

The problem with flaxseed protein has always been structural. The conventional alkali extraction and acid precipitation methods used to isolate it are cheap and simple, but they leave the protein locked in a compact, rigid conformation. That rigidity limits how well the molecule can unfold and rearrange when it reaches an air-water or oil-water boundary, which is precisely what a protein must do to stabilize a foam or an emulsion. Flaxseed protein is also unusually rich in disulfide bonds, which knit its aggregates into a particularly stiff architecture, and it differs fundamentally from the soy proteins whose behavior food scientists have long used as a template.

The research team, led by Narisu Qin and colleagues, hypothesized that moderate ultrasonic treatment could loosen this molecular straitjacket. When ultrasound waves pass through a protein solution, they generate microscopic cavitation bubbles that collapse violently, producing localized shear forces, shock waves, and micro-jets. These forces batter the protein aggregates apart, disrupt intermolecular hydrogen bonds and hydrophobic interactions, and pry open buried structural segments, all without changing the protein’s covalent blueprint. Crucially, the team kept the treatment brief, just fifteen minutes in an ice-water bath, and verified with calorimetry exactly how much acoustic energy each power setting actually delivered to the sample.

The structural evidence was gathered across multiple scales. Laser diffraction showed the average particle diameter falling from 35.23 micrometers in the untreated control to 14.97 micrometers at 200 watts, before creeping back up at higher power. Atomic force microscopy and scanning electron microscopy revealed the same story visually: smooth, dense aggregates in the control gave way to rough, porous, loosened structures at moderate power. Yet SDS-PAGE gels showed the subunit composition remained untouched, confirming that ultrasound was rearranging non-covalent aggregates rather than breaking or welding covalent bonds.

Spectroscopy filled in the molecular picture. Infrared analysis of the amide bands revealed a shift away from rigid beta-sheet content toward alpha-helix, beta-turn, and random coil structures, a signature of a more pliable molecule. Fluorescence spectra red-shifted and intensified as cavitation exposed previously buried tryptophan residues to a more polar environment. Surface hydrophobicity and free sulfhydryl content both climbed, peaking at 300 watts, and proton NMR signals associated with hydrophobic group exposure strengthened in parallel. Every independent measurement pointed to the same conclusion: moderate ultrasound unfolds the protein and liberates its flexible segments.

The pivotal innovation of the study was treating conformational flexibility not as a vague descriptor but as a quantifiable mediator. The team measured flexibility indirectly through the protein’s susceptibility to trypsin digestion, reasoning that a floppier structure offers more enzymatic access points. The flexibility index rose from 0.25 in the untreated sample to 0.44 at 300 watts, then fell back to 0.33 at 400 watts as excessive cavitation drove the unfolded chains to re-aggregate and re-bury their exposed segments. This rise-and-fall pattern became the fingerprint against which all downstream functional gains were judged.

Interfacial measurements translated the molecular changes into macroscopic consequences. At the air-water boundary, interfacial tension plummeted from 45.87 to 25.74 millinewtons per meter across the power range, meaning the protein could spread faster and more completely across the surface. At the oil-water interface, adsorption kinetics fitted to a first-order model showed both diffusion and penetration rate constants peaking at 300 watts, and the dilational elastic modulus of the interfacial film, a measure of its viscoelastic strength, reached its maximum there as well. Contact angle measurements, which track how well a dried protein film resists water, rose from 55.17 to 81.53 degrees at 300 watts, reflecting the newly exposed hydrophobic groups.

The functional payoffs followed directly. Foaming capacity jumped from 50.56 percent in the control to 99.45 percent at 200 watts, with foam stability climbing from 53.84 to 84.93 percent, and microscopy showed the treated foams produced the smallest, most uniform bubbles. Emulsifying performance peaked slightly later, at 300 watts, where the emulsifying activity index reached 4.11 square meters per gram and the stability index hit 110.35 minutes, compared with 2.43 and 92.37 in the untreated protein. Confocal microscopy confirmed that emulsions made with the 300-watt protein had smaller, more even oil droplets. The slight offset between the optimal powers for foaming and emulsifying suggests the two functions demand somewhat different balances of flexibility, particle size, and film elasticity.

To move beyond anecdote, the researchers subjected the entire dataset to multivariate statistics. Principal component analysis captured 83.08 percent of the variance in two dimensions, with treated samples arrayed neatly along an axis of increasing ultrasound intensity. Pearson correlations tied foaming capacity positively to flexibility and contact angle and negatively to particle size and air-water interfacial tension, while emulsifying indices correlated strongly with flexibility, hydrophobicity, sulfhydryl content, and low interfacial tension. Partial least squares-discriminant analysis, validated by permutation testing, identified contact angle and interfacial tension as the most discriminating variables, elevating interfacial behavior from a side observation to a central mechanistic lever.

The authors are candid about the study’s limits. Flexibility was inferred from hydrolysis rates rather than measured directly, and the protein was extracted from degummed, low-temperature defatted meal, so residual mucilage polysaccharides and phenolics, which could otherwise complicate interfacial adsorption, were minimal. Long-term storage stability and performance in real food formulations remain untested, and future work combining hydrogen-deuterium exchange mass spectrometry with molecular dynamics simulations could resolve the unfolding process at atomic resolution. Even so, the framework stands: by quantifying how conformational flexibility mediates the link between ultrasound-induced structure changes and interfacial performance, the study offers a rational recipe for turning millions of tonnes of flaxseed meal into high-value foams, creams, and emulsions, one precisely tuned sound wave at a time.

Subject of Research: Ultrasound modification of flaxseed protein isolate and its effects on foaming and emulsifying properties

Article Title: Ultrasound-enhanced foaming and emulsifying properties of flaxseed protein isolate: mechanisms mediated by conformational flexibility and interfacial tension

Article References: Qin, N., Xu, W., Zhao, Z., & Huang, Y. (2026). Ultrasound-enhanced foaming and emulsifying properties of flaxseed protein isolate: mechanisms mediated by conformational flexibility and interfacial tension. Food Chemistry: X, Article 104619. https://doi.org/10.1016/j.fochx.2026.104619

Image Credits: AI Generated

DOI: 10.1016/j.fochx.2026.104619

Keywords: flaxseed protein, ultrasound, conformational flexibility, interfacial tension, foaming, emulsification, food chemistry, protein modification, cavitation, plant protein, food waste valorization, interfacial rheology

The research team, led by Yong Liang, Wei Wang, Kai Huang, Zhengxing Chen, and Tao Wang, began from a well-known obstacle. Rice proteins are nutritionally attractive because they offer a balanced profile of essential amino acids and low allergenicity, but as foam stabilizers they are notoriously difficult. They are largely insoluble in water and prone to severe aggregation, which prevents them from diffusing quickly to the air-water interface and forming a coherent film. Foams stabilized by plant protein particles alone often collapse within seconds or minutes, because these proteins tend to sit more comfortably in the air phase than in the liquid phase, leaving the foam vulnerable to rapid water drainage. Enhancing the water retention capacity of the interfacial film therefore became the central design goal of the work.

To solve the solubility problem, the researchers co-assembled rice proteins with soy protein isolates using a pathway of alkali solvation followed by acid precipitation. Both proteins were first unfolded at high pH, allowed to interact, and then refolded together into uniform, water-dispersible nanoparticles. Transmission electron microscopy showed that while rice proteins alone formed aggregates of roughly thirty-nanometer elementary particles, the co-assembled rice-soy protein nanoparticles, prepared at a one-to-one mass ratio, emerged as monodisperse particles of about forty nanometers. Zeta potential measurements revealed something unexpected: the complexes carried stronger surface charges than either protein alone, while their surface hydrophobicity was lower than that of either parent protein. This indicated that the hydrophobic groups of both proteins had been buried inside the co-assembled structures while the charged groups were exposed outward, a rearrangement driven by hydrophobic interactions, electrostatic attraction, and hydrogen bonding.

These nanoparticles already improved foaming. Soy protein isolates alone could generate foams filling seventy-five percent of the initial dispersion volume, but only five percent survived thirty minutes. The co-assembled rice-soy nanoparticles at optimal ratios reached one hundred percent foaming ability and pushed thirty-minute stability to roughly fifteen percent at higher concentrations, plateauing at fifty percent survival once the interface became saturated. That was progress, but more than eighty-five percent of the foam still vanished within half an hour. The team then turned to starch nanocrystals, rigid platelets produced by hydrolyzing waxy corn starch in sulfuric acid for seven days. These crystals carry abundant hydroxyl groups on their surfaces, making them strongly hydrophilic and mechanically robust, but they also aggregate heavily through hydrogen bonding between their faces.

When the protein nanoparticles and starch nanocrystals were simply mixed together, the two components associated into hybrid complexes the researchers call RSP@SNCs. Atomic force microscopy revealed that the aggregated starch crystals disaggregated and reappeared as sheet-like hybrid nanoparticles of one hundred to two hundred nanometers, a morphology distinct from either component. Intrinsic fluorescence spectroscopy provided quantitative evidence of close association: as starch nanocrystal concentration increased, the fluorescence of the protein’s aromatic amino acid residues was progressively quenched, following an apparent Stern-Volmer-type relationship with a mass-based quenching coefficient of 1.896 milliliters per milligram and a correlation coefficient of 0.9677. Fourier transform infrared spectroscopy showed no new absorption bands or significant shifts, confirming that the binding was non-covalent.

The molecular glue holding the complexes together turned out to be hydrogen bonding. In a clever chemical blocking experiment, the team repeated the complexation in the presence of sodium chloride, sodium dodecyl sulfate, or thiourea, which selectively disrupt ionic forces, hydrophobic attractions, and hydrogen bonding respectively. Thiourea dramatically weakened the protein-starch interactions and restored fluorescence, while the salt and surfactant had only minor effects. Because the starch nanocrystals self-aggregate primarily through hydrogen bonds between their hydroxyl groups, competition from protein-starch hydrogen bonding appears to reduce the surface energy of the crystals, suppressing their self-aggregation and yielding dispersed hybrids with balanced amphiphilic character, exactly what is needed to anchor at an air-water interface.

The foaming results were striking. Adding starch nanocrystals doubled the initial foam formation of the protein nanoparticles at the highest tested ratio of 1.2, while optical microscopy showed that bubbles became smaller and more homogeneous as the starch proportion rose. Confocal laser scanning microscopy, with proteins and starch labeled in different fluorescent colors, revealed that both components were jointly trapped at the air-water interface, forming a thick physical barrier around each bubble. In foams stabilized by protein alone, bubbles approached a millimeter in size with thin, patchy coverage; with the hybrids at a ratio of 0.8, bubble sizes dropped to hundreds of micrometers and the liquid-filled spaces between adjacent bubbles widened, reducing direct bubble contact and hindering coalescence.

The stabilization mechanism operates on three coupled fronts. First, the interfacial film itself: contact angle measurements showed starch nanocrystals are highly hydrophilic at forty degrees while rice-soy protein nanoparticles are more hydrophobic at seventy-nine degrees, and the hybrids strike a balance that wets both phases, lowers interfacial tension, and satisfies the Gibbs stability criterion against coarsening. Second, the bulk viscosity: shear rheology demonstrated that viscosity of the stabilizer dispersions increased with starch content, and cryo-scanning electron microscopy performed at minus 145 degrees Celsius revealed ordered hybrid structures arranged throughout the continuous phase, not just at the interface. These ordered microstructures elevated system viscosity, slowing bubble disproportionation and liquid drainage. Notably, the dispersions showed shear-thinning behavior, meaning that during the violence of whipping the mixture temporarily thins, allowing particles to race to the interface, after which viscosity rebuilds to lock the structure in place. Third, water retention: the hydrophilic starch crystals trap water in the interstitial spaces between bubbles, deterring the gravity-driven drainage that kills most foams.

The practical implications extend well beyond the laboratory. The authors point to applications in milky tea, lattes, and other foamed beverages where stability over hours rather than minutes would transform product quality, particularly for delivery and takeaway markets. Because every ingredient is edible and plant-derived, the system sidesteps the limitation of surfactant crystals, which can produce extraordinarily stable foams but are not food-grade. The work also demonstrates a broader design principle: rather than searching for a single miracle stabilizer, combining a diffusion-competent protein nanoparticle with a mechanically strong, hydrophilic nanocrystal produces synergy that neither component achieves alone. As demand grows for plant-based, low-calorie foods with indulgent textures, engineering the air-water interface with hybrid biocolloids may become a standard tool in the food engineer’s repertoire, turning one of the most fragile structures in cuisine into one of the most durable.

Subject of Research: Stabilization of aqueous food foams using rice and soy protein nanoparticles reinforced with starch nanocrystals

Article Title: Starch nanocrystals reinforce rice/soy protein-structured air-water interface to stabilize aqueous foams

Article References: Liang, Y., Wang, W., Huang, K., Chen, Z., & Wang, T. (2026). Starch nanocrystals reinforce rice/soy protein-structured air-water interface to stabilize aqueous foams. Journal of Agriculture and Food Research, Article 103352. https://doi.org/10.1016/j.jafr.2026.103352

Image Credits: AI Generated

DOI: 10.1016/j.jafr.2026.103352

Keywords: aqueous foams, starch nanocrystals, rice protein, soy protein isolate, food colloids, air-water interface, hydrogen bonding, foam stability, plant-based foods, Pickering stabilization, interfacial tension, food engineering