Drop collision with a solid particle is a ubiquitous phenomenon in a wide range of applications, including rain, spray coating, cooling or cleaning, particle encapsulation, inkjet printing, and additive manufacturing. Understanding the dynamics of drop collision is essential for optimizing these processes. In this study, we present a comprehensive experimental and analytical investigation of non-axisymmetric as well as axisymmetric drop impact on a solid particle. We use a high-speed video system to visualize the drop profile during the impact, and measure the drop height and spreading diameter for different liquid viscosities, ratios of the target to drop diameters, offsets, and various other impact parameters. We then develop a theoretical model for drop spreading on a solid spherical particle that relies on the formulation of a remote asymptotic solution for the inviscid flows, generated by non-axisymmetric drop impact. Next, the viscous effects in a thin viscous boundary layer are considered, which allows the formulation of an expression for the residual lamella thickness and maximum spreading. The theoretically predicted evolution of the lamella thickness, the residual film thickness, and the maximum spreading angle agree well with the experimental data presented in this work and the literature. Finally, we present a novel approach for in situ measurement of liquid viscosity, drop impact viscometry, at high shear rates via a single drop impact experiment, with potential application in industries where non-Newtonian drops play a major role, such as pesticide spraying, paint droplet spreading, blood drop impact and fuel injectors.

Three-dimensional non-rotating odd viscous liquids give rise to Taylor columns and support axisymmetric inertial-like waves (J. Fluid Mech., vol. 973, 2023, A30). When an odd viscous liquid is subjected to rigid-body rotation however, there arise in addition a plethora of other phenomena that need to be clarified. In this paper, we show that three-dimensional incompressible or two-dimensional compressible odd viscous liquids, rotating rigidly with angular velocity $\varOmega$, give rise to both oscillatory and evanescent inertial-like waves or a combination thereof (which we call of mixed type) that can be non-axisymmetric. By evanescent, we mean that along the radial direction, typically when moving away from a solid boundary, the velocity field decreases exponentially. These waves precess in a prograde or retrograde manner with respect to the rotating frame. The oscillatory and evanescent waves resemble respectively the body and wall-modes observed in (non-odd) rotating Rayleigh–Bénard convection (J. Fluid Mech., vol. 248, 1993, pp. 583–604). We show that the three types of waves (wall, body or mixed) can be classified with respect to pairs of planar wavenumbers $\kappa$ which are complex, real or a combination, respectively. Experimentally, by observing the precession rate of the patterns, it would be possible to determine the largely unknown values of the odd viscosity coefficients. This formulation recovers as special cases recent studies of equatorial or topological waves in two-dimensional odd viscous liquids which provided examples of the bulk–interface correspondence at frequencies $\omega <2\varOmega$. We finally point out that the two- and three-dimensional problems are formally equivalent. Their difference then lies in the way data propagate along characteristic rays in three dimensions, which we demonstrate by classifying the resulting Poincaré–Cartan equations.

Two-dimensional turbulence transfers its energy towards the lowest mode in the domain, but domain geometry exerts a powerful control. On the sphere, with its three axes of rotational symmetry, angular momentum conservation prevents energy from entering the three lowest modes – those corresponding to the spherical harmonics $Y_1^0$ and $Y_1^{\pm 1}$ – because the amplitudes of these three modes are proportional to the three conserved components of the angular momentum vector. Non-spherical ellipsoids partly or completely break the rotational symmetry corresponding to angular momentum conservation. The flow on spheroids, which have only one axis of rotational symmetry, conserves only a single component of angular momentum. If the axis of symmetry is taken to be the $z$-axis, then only the $z$-component of angular momentum is conserved. Energy can flow into the other two lowest modes. The general triaxial ellipsoid breaks all rotational symmetries, thus angular momentum is not conserved, and energy can flow into any mode. We describe numerical experiments that confirm these predictions.

The effectiveness of utilizing heating patterns as a drag-reduction tool in sloping channels is analysed. The usefulness of heating is judged by determining the pressure gradient required to maintain the same flow rate as in the isothermal case. The key to reducing pressure loss is the formation of separation bubbles, although these bubbles are washed away at relatively large Reynolds numbers. The bubbles reduce the direct contact between the stream and the side walls, thereby reducing the friction experienced by the flow. Moreover, the fluid inside the bubbles tends to rotate, a motion provoked by longitudinal temperature gradients. This rotation also seems to reduce the resistance. On the other hand, the existence of the bubbles tends to obstruct the stream, increasing the flow resistance. In general, channels oriented close to horizontal experience a relatively small pressure loss, but this loss grows markedly as the channel inclines towards the vertical. When modest heating is applied, the pressure loss is approximately proportional to the square of the associated Rayleigh number. It is also shown that if the heating wavelength is too short or too long, the heating loses its effectiveness. In certain circumstances, it turns out that the theoretical pressure-gradient reduction achieved by judicious heating is so large that it exceeds the pressure gradient required to drive the flow in the isothermal problem. The conclusion is that in these instances, a pressure gradient of the opposite sign must be applied to prevent flow acceleration.

High-frequency observation data, including all three components of instantaneous fluctuating velocity, temperature, as well as particulate matter 10 ($PM_{10}$), collected from the unstable atmospheric surface layer at $z/L = -0.11$ and $-$0.12, $L$ being the Obukhov length, during sand and dust storms (SDS), were used to explore the scaling of vertical coherence and the logarithmic energy profile for wall-attached eddies. The present results demonstrate good agreement with the self-similar range of the wall-attached features for velocity and temperature components, as well as for $PM_{10}$ at lower heights ($z<15$ m) during SDS. Following the idea depicted by Davenport (Q. J. R. Meteorol., vol. 372, 1961, pp. 194–211), an empirically derived transfer kernel comprises implicit filtering via a scale-dependent gain and phase, parametrically defined as $|H_L^2(f)|=\exp (c_1-c_2\delta /\lambda _x)$, where $c_1$ and $c_2$ are parameters, $\delta$ is the boundary layer thickness and $\lambda _x$ is the streamwise wavelength. Linear coherence spectrum analysis is applied as a filter to separate the coherent and incoherent portions. After this separation procedure, the turbulence intensity decay for wall-attached eddies is described in a log–linear manner, which also identifies how the scaling parameter differs between the measured components. These findings present abundant features of wall-attached eddies during SDS which further are used to improve/enrich existing near-wall models.