Buoyancy-driven bubbly flows naturally have spatially dependent density fields, which allow for multiple definitions of the scale-dependent (or filtered) energy. A priori, it is not obvious which of these provide the most physically apt scale-by-scale budget. In the present study, we compare two such definitions, based on (i) filtered momentum and filtered velocity (Pandey et al., J. Fluid Mech., 2020, vol. 884, p. R6), and (ii) Favre-filtered energy (Aluie, Phys. D: Nonlinear Phenom., 2013, vol. 247, pp. 54–65; Pandey et al., Phys. Rev. Lett., 2023, vol. 131, p. 114002). We also derive a Kármán–Howarth–Monin relation using the momentum–velocity correlation function and contrast it with the scale-by-scale energy budget obtained in (i). We find that, for the volume fraction and Atwood number explored, irrespective of the definition, energy transfers due to the advective nonlinearity and surface tension are identical. However, discrepancies arise for the buoyancy and pressure contributions. We show that the Favre-filtered definition is the more appropriate choice, within which buoyancy injects energy, pressure transfers energy to large scales and both advective nonlinearity and surface tension transfer energy downscales where it is dissipated by viscosity.

The elastic properties of nanoscale extracellular vesicles (EVs) are believed to influence their cellular interactions, thus having a profound implication in intercellular communication. However, accurate quantification of their elastic modulus is challenging due to their nanoscale dimensions and their fluid-like lipid bilayer. We show that the previous attempts to develop atomic force microscopy-based protocol are flawed as they lack theoretical underpinning as well as ignore important contributions arising from the surface adhesion forces and membrane fluctuations. We develop a protocol comprising a theoretical framework, experimental technique, and statistical approach to accurately quantify the bending and elastic modulus of EVs. The method reveals that membrane fluctuations play a dominant role even for a single EV. The method is then applied to EVs derived from human embryonic kidney cells and their genetically engineered classes altering the tetraspanin expression. The data show a large spread; the area modulus is in the range of 4 to 19 mN/m and the bending modulus is in the range of 15 to 33 kBT, respectively. Surprisingly, data for a single EV, revealed by repeated measurements, also show a spread that is attributed to their compositionally heterogeneous fluid membrane and thermal effects. Our protocol uncovers the influence of membrane protein alterations on the elastic modulus of EVs.

We study the buckling of pressurized spherical shells by Monte Carlo simulations in which the detailed balance is explicitly broken - thereby driving the shell to be active, out of thermal equilibrium. Such a shell typically has either higher (active) or lower (sedate) fluctuations compared to one in thermal equilibrium depending on how the detailed balance is broken. We show that, for the same set of elastic parameters, a shell that is not buckled in thermal equilibrium can be buckled if turned active. Similarly a shell that is buckled in thermal equilibrium can unbuckle if sedated. Based on this result, we suggest that it is possible to experimentally design microscopic elastic shells whose buckling can be optically controlled.

We present direct numerical simulations (DNS) study of confined buoyancy-driven bubbly flows in a Hele-Shaw setup. We investigate the spectral properties of the flow and make comparisons with experiments. The energy spectrum obtained from the gap-averaged velocity field shows E(k) similar to k for k < k (d) , E(k) similar to k(-5) for k > k (d) , and an intermediate scaling range with E(k) similar to k(-3) around k similar to k(d) . We perform an energy budget analysis to understand the dominant balances and explain the observed scaling behavior. For k < k(d) , energy injection balances dissipation due to drag, whereas for k > k(d) , the net injection balances net dissipation. We also show that the Navier-Stokes equation with a linear drag can be used to approximate large scale flow properties of bubbly Hele-Shaw flow.

We investigate the spectral properties of buoyancy-driven bubbly flows. Using high-resolution numerical simulations and phenomenology of homogeneous turbulence, we identify the relevant energy transfer mechanisms. We find (a) at a high enough Galilei number (ratio of the buoyancy to viscous forces) the velocity power spectrum shows the Kolmogorov scaling with a power-law exponent -5/3 for the range of scales between the bubble diameter and the dissipation scale (η). (b) For scales smaller than η, the physics of pseudo-turbulence is recovered.