High-speed images of driven sessile water drops recorded under frequency scans are analysed for resonance peaks, resonance bands and hysteresis of characteristic modes. Visual mode recognition using back-lit surface distortion enables modes to be associated with frequencies, aided by the identifications in Part 1 (Bostwick & Steen, J. Fluid Mech., vol. 760, 2014, pp. 5–38). Part 1 is a linear stability analysis that predicts how inviscid drop spectra depend on base state geometry. Theoretically, the base states are spherical caps characterized by their ‘flatness’ or fraction of the full sphere. Experimentally, quiescent shapes are controlled by pinning the drop at a circular contact line on the flat substrate and varying the drop volume. The response frequencies of the resonating drop are compared with Part 1 predictions. Agreement with theory is generally good but does deteriorate for flatter drops and higher modes. The measured frequency bands agree better with an extended model, introduced here, that accounts for forcing and weak viscous effects using viscous potential flow. As the flatness varies, regions are predicted where modal frequencies cross and where the spectra crowd. Frequency crossings and spectral crowding favour interaction of modes. Modal interactions of two kinds are documented, called ‘mixing’ and ‘competing’. Mixed modes are two pure modes superposed with little evidence of hysteresis. In contrast, modal competition involves hysteresis whereby one or the other mode disappears depending on the scan direction. Perhaps surprisingly, a linear inviscid irrotational theory provides a useful framework for understanding observations of forced sessile drop oscillations.

A vortex ring is a torus-shaped fluidic vortex. During its formation, the fluid experiences a rich variety of intriguing geometrical intermediates from spherical to toroidal. Here we show that these constantly changing intermediates can be ‘frozen' at controlled time points into particles with various unusual and unprecedented shapes. These novel vortex ring-derived particles, are mass-produced by employing a simple and inexpensive electrospraying technique, with their sizes well controlled from hundreds of microns to millimetres. Guided further by theoretical analyses and a laminar multiphase fluid flow simulation, we show that this freezing approach is applicable to a broad range of materials from organic polysaccharides to inorganic nanoparticles. We demonstrate the unique advantages of these vortex ring-derived particles in several applications including cell encapsulation, three-dimensional cell culture, and cell-free protein production. Moreover, compartmentalization and ordered-structures composed of these novel particles are all achieved, creating opportunities to engineer more sophisticated hierarchical materials.

In this work, we study the resonance behavior of mechanically oscillated, sessile water drops. By mechanically oscillating sessile drops vertically and within prescribed ranges of frequencies and amplitudes, a rich collection of resonance modes are observed and their dynamics subsequently investigated. We first present our method of identifying each mode uniquely, through association with spherical harmonics and according to their geometric patterns. Next, we compare our measured resonance frequencies of drops to theoretical predictions using both the classical theory of Lord Rayleigh and Lamb for free, oscillating drops, and a prediction by Bostwick and Steen that explicitly considers the effect of the solid substrate on drop dynamics. Finally, we report observations and analysis of drop mode mixing, or the simultaneous coexistence of multiple mode shapes within the resonating sessile drop driven by one sinusoidal signal of a single frequency. The dynamic response of a deformable liquid drop constrained by the substrate it is in contact with is of interest in a number of applications, such as drop atomization and ink jet printing, switchable electronically controlled capillary adhesion, optical microlens devices, as well as digital microfluidic applications where control of droplet motion is induced by means of a harmonically driven substrate.

Drawing parallels to the symmetry breaking of atomic orbitals used to explain the periodic table of chemical elements; here we introduce a periodic table of droplet motions, also based on symmetry breaking but guided by a recent droplet spectral theory. By this theory, higher droplet mode shapes are discovered and a wettability spectrometer is invented. Motions of a partially wetting liquid on a support have natural mode shapes, motions ordered by kinetic energy into the periodic table, each table characteristic of the spherical-cap drop volume and material parameters. For water on a support having a contact angle of about 60°, the first 35 predicted elements of the periodic table are discovered. Periodic tables are related one to another through symmetry breaking into a two-parameter family tree. droplet vibrations | sessile drop dynamics | meniscus motions | capillary ballistics | moving contact line D roplets and droplet motions surround us. Our harvests depend on rain drops. We sweat, we shower, and we drink. Our eyes make tears and our blood splats. Drops enable the protein content of our bodily fluids to be measured (1), our silicon chips to be fabricated (2), and complex parts to be additively sculpted by drop-on-demand processing (3,4). Water droplets in motion are shaped into objects of beauty by surface tension. Their images have become symbols of purity and cleanliness, selling beer, jewelry, clothing, and automobiles. However, despite more than a century of study, the motions of droplets on a support have resisted systematic classification. This paper introduces the periodic table classification of capillary-ballistic droplet motions.The capillary-ballistic model assumes an ideal fluid with surface tension acting on the deformable surface (SI Appendix). Capillary-ballistic motions are typical of thin liquids like water. Prototypical of dynamics of this kind are free drop vibrations, predicted by Rayleigh to have frequencies (5) λ kl as inwhere the corresponding deformation is Y l k ðθ, φÞ in spherical coordinates. Here, wavenumber k is the degree and l is the order of the spherical harmonic Y l k (6). Frequencies [1] and mode shapes Y l k constitute the so-called Rayleigh spectrum, predictions verified experimentally (7,8). Note that, in [1], different l′s share the same frequency. These degeneracies arise from the perfect symmetry of the spherical free drop. The introduction of a support typically breaks these degeneracies.Deformations of the supported drop (9), Fig. 1 (Bottom Row), break from the Y l k ðθ, φÞ shapes. The number of layers n (Top Row, in schematic) and of sectors l [Bottom Row: bold lines, rendered shape (Right)] characterize modal symmetry. Using k = l + 2ðn − 1Þ, symmetries are alternatively classified "mathematically" by wavenumber pairs ½k, l. Modes are either "symmetric" (short for axisymmetric), e.g., [6,0]leftmost, "star," e.g., [6,6]rightmost, or "layer" modes (short for layer sector), e.g., [6,2] and ½6,4middle two modes. Note that the Rayleigh spectrum [1] splits. That is, [...

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