In this paper, we explore the electrokinetics in the complex two-dimensional geometries via conformal mapping and experimental comparison. A general theoretical frame of conformal mapping is provided for the application in electrokinetics, and three geometries are taken as an example to derive concentration polarization, potential, and electric field. For an eccentric annulus, the theoretical calculation of limiting current remarkably agrees with the experimental measurement, indicating that conformal mapping as a powerful approach is applicable for the ion transport. In the overlimiting current, the asymmetric electroconvection and deionization shock in experiments are qualitatively consistent with the asymmetric slip velocity associated with the electric field from conformal mapping. Then for the concentric ellipse geometry, when the inner ellipse squashes into a finite stripe, the local electric field at the tips tends to form a singularity, driving the electro-osmotic instability of concentration enrichment. Additionally, for a corner geometry, the intensity of the electric field is analyzed for different shapes. Hence, conformal mapping as a theoretical tool potentially inspires more future work for the electrokinetics in the complicated geometries, while the experimental findings, particularly the stronger concentration depletion induced by eccentricity, hold the promising applications, such as the shock electrodialysis for the deionization and water treatment, and electrophoresis for the particle manipulation in microfluidic devices.

In the quasiclassical regime of quantum turbulence, it has long been hypothesized that there exist coherent vortical structures, made up of bundles of quantized vortices. More recently, there has been significant experimental evidence that points to their presence. Here, we perform a quantitative study of the reconnection of bundles of quantized vorticity and show that the approach and separation of bundles during a reconnection is consistent with the symmetric $\delta \sim t^{1/2}$ scaling which is consistent with studies of individual quantized vortex reconnection and classical vortex reconnections. We also examined the phenomena of “bridge” structures that form between the vortex bundles during the reconnection process and have also been observed during the reconnection of classical vortices. We study their persistence and suggest that their dissipation is driven by vortex-vortex interactions within the bridge itself.

Cablelike bodies play a key role in many interdisciplinary systems but are hard to simulate. Asymptotic theories, called slender-body theories, are effective but apply in specific regimes and can be hard to extend beyond leading order. In this paper we develop an exact slender-body-like theory for the surface traction of cablelike bodies in viscous flow. This theory expresses the traction as a series of solutions to a well-behaved one-dimensional Fredholm integral equation of the second kind. This process can be simply generalized to other systems.

The capillary rise in vertically situated open microchannels can be severely limited by liquid evaporation. Here we quantitatively study the rise dynamics using a combination of experiment and theory. On evaluating the effects of the enhanced evaporation near the solid-liquid-gas contact line on the mass transfer rate from liquid in a microchannel, we set up a differential equation for the temporal evolution of rise height by considering mass conservation of evaporating viscous liquid drawn against gravity via capillarity. It is found that there exists an optimal channel width that maximizes the equilibrium rise height under a given channel depth, unlike nonevaporative rise whose equilibrium height monotonically increases with the reduction of channel width. Our work can lay a foundation for understanding the evaporative capillary rise dynamics occurring in various porous media of biological, natural, and artificial settings.

In this study, the disturbance energy budget is analyzed on the derived disturbance energy norm in hypersonic and high-enthalpy boundary layers with thermal-chemical nonequilibrium (TCNE) effects. The disturbance growth rate is decomposed to quantitatively evaluate the contribution from various classified terms. Hypersonic flat-plate flows are investigated with various free-stream Mach numbers, free-stream temperatures, and wall temperatures. The linear and nonlinear evolutions of disturbances are predicted using linear stability theory and parabolized stability equations. The results show that in the first-mode region, the disturbance growth rates are determined by the production term (destabilizing) and the viscous term (stabilizing), while the former nearly offset the latter. In the second-mode region, the viscous term decreases to the minimum, resulting in the dominance of the second mode. The disturbance of the TCNE source term has a stabilizing effect on the second mode, but at most it reduces the growth rate by $6\%$ in a Mach 10 adiabatic case with the highest free-stream temperature of $900\mathrm{K}$. The production term is mainly responsible for the second-mode growth rate difference between the TCNE flow and calorically perfect gas flow. TCNE changes the disturbance characteristics mainly through the mean flow modification. In the oblique-mode breakdown case, the intensive energy transfer between the selected modes and their harmonic waves is found to occur where they interact strongly with the mean flow.

We performed an experimental study on water microjets of 100 microns in radius ablated in air by both green (532 nm) and near infrared (1064 nm) nanosecond laser pulses with up to 1100 mJ per pulse. We show this affordable and accessible experimental apparatus captures the essence of the water jet response after being ablated by an intense laser pulse. The results reveal that $\sim 3.5\%$ of laser pulse energy enters the water jet and half reaches the nozzle orifice as far as 50 times the jet diameter away from the ablation point through internal reflections. The energy density absorbed by the nozzle orifice exceeds the damage threshold of stainless steel, causing microexplosions and formation of a liquid sheet near the nozzle orifice.

Lubrication flow of a gas in a microscale gap between coaxial circular cylinders is studied on the basis of kinetic theory. The stationary inner cylinder is a Maxwell-type boundary with a nonuniform accommodation coefficient in the circumferential direction, and the outer cylinder is a diffuse reflection boundary rotating at a constant speed. The dimensionless curvature, defined as the gap size divided by the radius of the inner cylinder, is small, and the Knudsen number based on the gap size is arbitrary. The Boltzmann equation is studied analytically using the slowly varying approximation, with special attention being paid to the characteristics of the equation. Two macroscopic lubrication models of the Reynolds-type equations are derived: one consisting of the solutions for plane Couette and Poiseuille flows (plane lubrication model), and the other consisting of cylindrical Couette flow and a curved Poiseuille flow (improved lubrication model). For an assessment of the models, a direct numerical analysis of the flow is also conducted for the Bhatnagar-Gross-Krook-Welander kinetic equation using a hybrid finite-difference method. It is demonstrated that the use of the plane lubrication model leads to a non-negligible error when the Knudsen number is sufficiently large. This error is caused by neglect of the fact that the number of molecules arriving from the outer cylinder is greater than that from the inner one by an amount proportional to the square root of the dimensionless curvature. It is also demonstrated that the improved lubrication model provides an excellent approximation to the direct numerical solution over the whole range of the Knudsen number.

We consider the diffusiophoresis of a suspension of charged colloidal particles in the presence of a nonuniform solute concentration, where each species experiences Taylor dispersion from spanwise velocity gradients. We describe the two-dimensional evolution of both solute and particle concentration fields in a narrow channel with background Poiseuille flow by applying the lubrication approximation along with the assumption of constant particle $\zeta$ potential. We compare the theoretical predictions with the results of numerical simulations for fixed particle $\zeta$ potential, demonstrating good agreement. Finally, we comment on three-dimensional effects, long-time dynamics, and the validity of the constant particle $\zeta$ potential assumption for our model. We perform additional simulations with a simple variable-$\zeta$ potential model that treats the particle $\zeta$ potential as a logarithmic function of solute concentration. The results show good qualitative and quantitative agreement, supporting the use of the constant particle $\zeta$ potential assumption for this system under certain circumstances.

Partially wetting drops are ubiquitous in nature and industry and are often subject to a combined forcing by wind and gravity. In particular, the stability of water drops under the combination of wind and other external forces is relevant in numerous applications that include aircraft de-icing, heat exchangers, and fuel cells. In this paper, we investigate the onset of droplet depinning from a solid substrate when a partially wetting water droplet is simultaneously exposed to high-Reynolds-number airflow and to gravity. We first develop simple scaling arguments which explain that the critical flow velocity for depinning, $U_{\mathrm{cr}}$, and the droplet volume, $V$, scale as $U_{\mathrm{cr}}\sim V^{-1/6}$ in the absence of gravitational effects, in good agreement with the existing experimental data. We then develop a two-dimensional model for a unidirectional flow over a slender drop under two scenarios: aligned with (downwind) or opposing the gravitational body force (upwind). Our results show a clear deviation in $U_{\mathrm{cr}}$ between the upwind and downwind cases as the droplet size is increased. The differences between these two regimes are further manifested in the distinct droplet shapes at the critical onset of depinning. Finally, we investigate the role of flow separation from the leeward side of the drop by systematically increasing the slope of the droplet surface at the separation point. Our results point to more pronounced effects of the flow separation in the upwind regime.

Accurately predicting the force experienced by particles within a random bed during shock traversal is a challenging problem. In this paper, particle-resolved inviscid simulations of shock propagation over randomly distributed beds are performed, with the goal of quantifying the force on individual particles. Water was considered the continuum material, and then results were compared with previous research completed in air and the differences resulting from these different mediums were examined. Simulations were conducted for four different combinations of incident Mach number and bed volume fraction with the particles remaining stationary. Time-resolved streamwise and transverse force coefficients were calculated for each particle in the bed. It was observed that while the average force coefficient was similar to that of an isolated particle, the force on individual particles was substantially different. An important observation was that the inviscid drag force on some particles remained consistently positive, but others consistently negative even long after the passage of the shock. This persistent force on the particle was attributed to the potential flow fields that result from neighbors' specific locations upstream and downstream. Similar behavior was observed in the transverse force, with particles experiencing sustained force in the same lateral direction. These persistent forces are inviscid quasisteady contributions which with the viscous counterpart will play an essential role in the particle's long-term dispersion if allowed to move in response to the force.

Recent studies have shown that enveloped viruses contained in airborne respiratory droplets lose infectability fastest at intermediate ambient relative humidities $H_r$. However, the precise physicochemical mechanisms that generate such least-favorable conditions for the virus are not fully understood yet. Studying the evaporation dynamics of respiratory-like droplets in air experimentally and analytically, we reveal that at high $H_r$, the salt dissolved in respiratory drops inhibits their evaporation indefinitely. Conversely, at low $H_r$ the drop evaporates leaving a porous solid residue, inside which virions may remain dormant for long times. We conclude that the optimal relative humidity for minimal infectability should coincide with droplets containing the maximum concentration of salt for longest periods of time.

We combine extended proper orthogonal decomposition (EPOD) together with the Fukagata-Iwamoto-Kasagi (FIK) identity to quantify the role of individual coherent structures on the wall mass transfer in a turbulent pipe flow. Direct numerical simulation at a Reynolds number of 5300 (based on bulk velocity) is performed with the passive scalar released at the pipe inlet. The proper orthogonal decomposition (POD) eigenvalues show that the scalar field can be described by a more compact set of modes compared to the velocity field, and that these modes are skewed towards higher azimuthal wave numbers. POD modes for the scalar and EPOD modes for the velocity are visualized in the cross-stream plane to infer the capacity of each mode to transport scalar to and from the wall. A form of the FIK identity is derived for the wall mass transfer coefficient (Sherwood number, Sh) and employed to separate the contributions of the mean and fluctuating velocity and scalar fields. The FIK decomposition shows that the turbulent velocity/scalar correlations account for up to 65.8% of the total Sh. The contribution of each POD and EPOD mode to the Sh number is also computed; it is found that, using azimuthal wave numbers $m=1–15$ and POD modes $n=1–10$, it is possible to reconstruct $49\%$ of the turbulent component of Sh, with the velocity modes containing only $31\%$ of the turbulent kinetic energy. Quadrant analysis shows that these modes are related to ejection and sweep events near the wall, with the ejection events dominating.

The effects of thermal fluctuations on nanoscale flows are captured by a numerical scheme that is underpinned by fluctuating hydrodynamics. A stochastic lubrication equation (SLE) is solved on nonuniform adaptive grids to study a series of nanoscale thin-film flows. The Fornberg scheme is used for high-resolution spatial discretization and a fully implicit time-marching scheme is designed for numerical stability. The accuracy of the numerical method is verified against theoretical results for thermal capillary waves during the linear stage of their development. The framework is then used to study the nonlinear behavior of three bounded thin-film flows: (1) droplet spreading, where power laws are derived; (2) droplet coalescence, where molecular dynamics results are reproduced by the SLE at a fraction of the computational cost and it is discovered that thermal fluctuations decelerate the process, in contrast to previously investigated phenomena; and (3) thin-film rupture, where, in the regime considered, disjoining pressure dominates the final stages of rupture.

Reduction of fluid-solid friction utilizing the phenomenon of hydrodynamic slippage underlies a variety of energy-saving innovations. For simple demonstration of such ideas, the flow is often assumed to take place over a planar substrate. On the other hand, both roughness and intentionally textured topographies are ubiquitous in nature and engineering. Accordingly, a shear flow intrinsically slipping over a topography with small-amplitude corrugations is considered. Deriving scaling insights from a kinematic interpretation of the boundary conditions, a singular perturbation theory is developed for the multiscale interplay of the degree of intrinsic slip with the curvature of the surface along the slip velocity. Four distinct scaling regimes are identified. Especially for strongly (but not necessarily perfectly) slipping sinusoidal surfaces, unique analytical predictions with a wide intrinsic slip and amplitude range of numerical accuracy vis-à-vis finite element simulations are obtained, whereas the predictions on the small-slip scaling regimes corroborate findings from the literature. If the corrugation amplitude increases beyond a critical value, then strongly slipping surfaces suffer a slip-to-stick transition losing their lubricating properties. Unlike existing analytical predictions, the developed large-slip model can represent the slip-to-stick transition with reasonable accuracy, despite their rather simple analytical form. For extra accuracy, the predictions are readily extensible through computer algebra.

This work connects the attached eddies to the wall friction by relating the momentum transfer normal to the lower bound of the energetic range with the wall shear stress. Evidence is provided to show that this balance is the property of a specific layer, $l\approx 3\sqrt{{\text{Re}}_{\tau }}$, which coincides with the smallest attached eddies. As a result, our model predicts successfully the transition of the friction factor after the Blasius regime to the extreme Reynolds numbers range, and the resulting friction equation shows the same accuracy as the well-known logarithmic laws. This transition also affects the mean velocity profile. From the developed friction equation, a mean velocity profile is derived which is in accordance with the well-known log laws. Finally, it is conjectured that for high enough Reynolds numbers, both Prandtl's $1/7$ power law and the velocity profile approximate the mean velocity simultaneously, however at different distances from the wall.

We consider a model of two competing microswimming agents engaged in a pursue-evasion task within a low-Reynolds-number environment. Agents can only perform simple maneuvers and sense hydrodynamic disturbances, which provide ambiguous (partial) information about the opponent's position and motion. We frame the problem as a zero-sum game: The pursuer has to capture the evader in the shortest time, while the evader aims at deferring capture as long as possible. We show that the agents, trained via adversarial reinforcement learning, are able to overcome partial observability by discovering increasingly complex sequences of moves and countermoves that outperform known heuristic strategies and exploit the hydrodynamic environment.

Shear thickening of suspensions is studied by discrete-particle simulation, accounting for hydrodynamic, repulsive, and contact forces. The contact forces, including friction, are activated when the imposed shear stress $\sigma$ is able to overcome the repulsive force. The simulation method captures strong continuous and discontinuous shear thickening (CST and DST) in the range of solid volume fraction $0.54\le \varphi \le 0.56$ studied here. This work presents characteristics of the contact force network developed in the suspension under shear. The number of frictional contacts per particle $Z$ is shown to have a one-to-one relationship with the suspension stress, and the conditions for simple percolation of frictional contacts are found to deviate strongly from those of a random network model. The stress is shown to have important correlations with topological invariant metrics of the contact network known as $k$-cores; the $k$-cores are maximal subgraphs (“clusters”) in which all member particles have $k$ or more frictional contacts to other members of the same subgraph. Only $k\le 3$ is found in this work at solid volume fractions $\varphi \le 0.56$. Distinct relationships between the suspension rheology and the $k$-cores are found. One is that the stress susceptibility, defined as $\partial \sigma /\partial \dot{\gamma }$, where $\dot{\gamma }$ is the shear rate, is found to peak at the condition of onset of the 3-core, regardless of whether the system exhibits CST or DST. A second is that the stress per particle within cores of different $k$ increases sharply with increase of $k$ at the onset of DST; in CST, the difference is mild.

We formulate a data-driven, physics-constrained closure method for coarse-scale numerical simulations of turbulent fluid flows. Our approach involves a closure scheme that is nonlocal both in space and time, i.e., the closure terms are parametrized in terms of the spatial neighborhood of the resolved quantities but also their history. The data-driven scheme is complemented with a physical constraint expressing the energy conservation property of the nonlinear advection terms. We show that the adoption of this physical constraint not only increases the accuracy of the closure scheme but also improves the stability properties of the formulated coarse-scale model. We demonstrate the presented scheme in fluid flows consisting of an incompressible two-dimensional turbulent jet. Specifically, we first develop one-dimensional coarse-scale models describing the spatial profile of the jet. We then proceed to the computation of turbulent closures appropriate for two-dimensional coarse-scale models. Training data are obtained through high-fidelity direct numerical simulations. We also showcase how the developed scheme captures the coarse-scale features of the concentration fields associated with inertial tracers, such as bubbles and particles, carried by the flow but not following the flow. We thoroughly examine the generalizability properties of the trained closure models for different Reynolds numbers, as well as radically different jet profiles from the ones used in the training phase. We also examine the robustness of the derived closures with respect to the grid size. Overall, the adoption of the constraint results in an average improvement of $26\%$ for one-dimensional closures and $29\%$ for two-dimensional closures, being notably larger for flows that were not used for training.

By means of an asymptotic expansion, we derive an analytical expression for the stationary speed of a liquid droplet sliding down a ramp under the action of gravity. Our approximation holds in the limit of small Bond numbers. The dissipation is taken into account by means of an effective contact line viscosity. We show that if the latter has a gradient orthogonal to the gravity, the droplet drifts laterally in the direction opposite to the dissipation gradient, i.e., toward regions having lower dissipation. This lateral drift is a second-order effect in the Bond number, induced by the deformation of the contact line shape. These results are confirmed by a numerical calculation valid for arbitrary Bond numbers.

We investigate the deformation in a uniform water flow of thin sheets perforated with parallel cuts. Through combined experiments and theory, we show that deployment is governed by the competition between fluid forces and sheet stretchability, which is prescribed by the cut pattern. Importantly, fluid loading is modulated by the local three-dimensional geometry of pores that open upon stretching. This mesostructure offers a lever to influence macroscopic morphing, notably leading here to asymmetric deformations of symmetric planar sheets. It brings to the fore the kirigami cutting technique as a promising framework for the design of flow-responsive components.