We study statistical properties of the pair dispersion of Lagrangian particles in transonic to supersonic compressible turbulence of an isothermal ideal gas in two dimensions, driven by large-scale solenoidal and irrotational stirring forces, via direct numerical simulations. We find that the scaling exponents of the order-p negative moments of the doubling and halving times of pair separations are nonlinear functions of p. Furthermore, the doubling- and halving-time statistics are different. The halving-time exponents are universal—they satisfy their multifractal model-based prediction, irrespective of the nature of the stirring. The doubling-time exponents are not. In the solenoidally stirred flows, the doubling-time exponents can be expressed solely in terms of the multifractal scaling exponents obtained from the structure functions of the solenoidal component of the velocity. Moreover, they depend strongly on the Mach number, Ma. In contrast, in the irrotationally stirred flows, the doubling-time exponents do not satisfy any known multifractal model-based relation, and are independent of Ma. Our work is a generalization of Richardson's law of pair dispersion to compressible turbulence.

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.

Elastic turbulence (ET), observed in flows of sufficiently elastic polymer solution at small inertia, is characterized by chaotic motions and power-law scaling of energy spectrum (E) in both wavenumber (k) and frequency (ω): E(k)∼k−α and E(ω)∼ω−β. Experiments of ET have obtained a vast range of values for the exponent β. In inertial turbulence, Taylor’s frozen-flow hypothesis implies α=β, i.e., spatial and temporal scales are linearly related to each other. In contrast, from high-resolution simulation in three different setups, a tri-periodic box, a channel, and a planar jet, we show that in ET α≈4 while β varies significantly. Our analysis shows that in general Taylor’s hypothesis does not hold in ET as there is no universal relation, linear or otherwise, between space and time. We thus clear the confusion of the different scaling exponents found in ET, and focus the attention of future research on understanding α. Our analysis also implies that waves-like dynamics with a linear dispersion relation (e.g., Alfvén waves) cannot play a role in determining the scaling behavior of ET. The techniques introduced here can be useful for studying smooth chaotic flows in general, e.g., active turbulence.

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 use the short-time inference scheme [Manikandan, Phys. Rev. Lett. 124, 120603 (2020)0031-900710.1103/PhysRevLett.124.120603], obtained within the framework of stochastic thermodynamics, to infer a lower bound to entropy production rate from flickering data generated by interference reflection microscopy of HeLa cells. We can clearly distinguish active cell membranes from their adenosine-triphosphate-depleted selves and even spatiotemporally resolve activity down to the scale of about 1 μm. Our estimate of activity is model independent.

Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds (Re) numbers. Our direct numerical simulations show that elastic turbulence, though a low Re phenomenon, has more in common with classical, Newtonian turbulence than previously thought. In particular, we find power-law spectra for kinetic energy E(k) ~ k−4 and polymeric energy Ep(k) ~ k−3/2, independent of the Deborah (De) number. This is further supported by calculation of scale-by-scale energy budget which shows a balance between the viscous term and the polymeric term in the momentum equation. In real space, as expected, the velocity field is smooth, i.e., the velocity difference across a length scale r, δu ~ r but, crucially, with a non-trivial sub-leading contribution r3/2 which we extract by using the second difference of velocity. The structure functions of second difference of velocity up to order 6 show clear evidence of intermittency/multifractality. We provide additional evidence in support of this intermittent nature by calculating moments of rate of dissipation of kinetic energy averaged over a ball of radius r, εr, from which we compute the multifractal spectrum.

Red blood cells (RBCs) are more deformable than most other cells in the body, and any change in the deformability of RBCs can have major physiological effects. Here, we report a high-throughput micro- fluidic device to determine the Young's modulus of single RBCs. Our device consists of a single channel opening into a funnel, with a semi-circular obstacle placed at the mouth of the funnel. As an RBC passes the obstacle, it deflects from its original path. Using populations of artificially stiffened RBCs, we show that the stiffer RBCs deflect more compared to the healthy RBCs. We then generate a calibration curve that maps each RBC trajectory to its Young's modulus, obtained using an atomic force microscope. Finally, we sort a mixed population of RBCs based on their deformability alone. Our device could potentially be further miniaturized to sort and obtain the elastic constants of nanoscale objects, such as exosomes, whose shape change is difficult to monitor by optical microscopy.

Adherent cells ensure membrane homeostasis during de-adhesion by various mechanisms, including endocytosis. Although mechano-chemical feedbacks involved in this process have been studied, the step-by-step build-up and resolution of the mechanical changes by endocytosis are poorly understood. To investigate this, we studied the de-adhesion of HeLa cells using a combination of interference reflection microscopy, optical trapping and fluorescence experiments. We found that de-adhesion enhanced membrane height fluctuations of the basal membrane in the presence of an intact cortex. A reduction in the tether force was also noted at the apical side. However, membrane fluctuations reveal phases of an initial drop in effective tension followed by saturation. The area fractions of early (Rab5-labelled) and recycling (Rab4-labelled) endosomes, as well as transferrin-labelled pits close to the basal plasma membrane, also transiently increased. On blocking dynamin-dependent scission of endocytic pits, the regulation of fluctuations was not blocked, but knocking down AP2-dependent pit formation stopped the tension recovery. Interestingly, the regulation could not be suppressed by ATP or cholesterol depletion individually but was arrested by depleting both. The data strongly supports Clathrin and AP2-dependent pit-formation to be central to the reduction in fluctuations confirmed by super-resolution microscopy. Furthermore, we propose that cholesterol-dependent pits spontaneously regulate tension under ATP-depleted conditions.

Lagrangian pair dispersion provides insights into mixing in turbulent flows. By direct numerical simulations (DNSs) we show that the statistics of pair dispersion in the randomly forced two-dimensional Burgers equation, which is a typical model of shock-dominated turbulence, is very different from its incompressible counterpart because Lagrangian particles get trapped in shocks. We develop a heuristic theoretical framework that accounts for this - a generalization of the multifractal model - whose prediction of the scaling of Lagrangian exit times agrees well with our DNS.

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.