For the first time, a measurement of the viscosity of microparticles composed of Newtonian fluids has been made over a range of 12 orders of magnitude (10 À3 to 10 9 Pa s), extending from dilute aqueous solutions to the solid-like behaviour expected on approaching a glass transition. Using holographic optical tweezers to induce coalescence between two aerosol particles (volume <500 femtolitres), we observe the composite particle relax to a sphere over a timescale from 10 À7 to 10 5 s, dependent on viscosity. The damped oscillations in shape illustrate the interplay of surface capillary forces and bulk fluid flow as the relaxation progresses. Viscosity values estimated from the extrapolation of measurements from macroscopic binary aqueous solutions of sucrose are shown to diverge from the microparticle measurements by as much as five orders of magnitude in the limit of ultrahigh solute supersaturation and viscosity. This is shown to be a consequence of the sensitivity of the viscosity to the composition of the particles, specifically the water content, and the often incorrect compositional dependence on water activity that are assumed to characterise aerosols and amorphous phases under dry conditions. For ternary mixtures of sodium chloride, sucrose and water, the measured viscosities similarly diverge from model predictions by up to three orders of magnitude. The Stokes-Einstein treatment for relating the diffusivity of water in sucrose droplets to the particle viscosity is found to depart from the measured viscosities by more than one order of magnitude when the viscosity exceeds 10 Pa s and up to six orders of magnitude at the highest viscosities accessed. Coalescence is shown to proceed with unit efficiency even up to the highest accessible viscosity. These measurements provide the first comprehensive account of the change in a material property accompanying a transition from a dilute solution to an amorphous semi-solid state using aerosol particles to probe the change in rheological properties.

Radiation pressure is associated with the momentum of light 1,2 , and it plays a crucial role in a variety of physical systems 3-6 . It is usually assumed that both the optical momentum and the radiation-pressure force are naturally aligned with the propagation direction of light, given by its wavevector. Here we report the direct observation of an extraordinary optical momentum and force directed perpendicular to the wavevector, and proportional to the optical spin (degree of circular polarization). Such an optical force was recently predicted for evanescent waves 7 and other structured fields 8 . It can be associated with the 'spin-momentum' part of the Poynting vector, introduced by Belinfante in field theory 75 years ago 9-11 . We measure this unusual transverse momentum using a femtonewton-resolution nano-cantilever immersed in an evanescent optical field above the total internal reflecting glass surface. Furthermore, the measured transverse force exhibits another polarization-dependent contribution determined by the imaginary part of the complex Poynting vector. By revealing new types of optical forces in structured fields, our findings revisit fundamental momentum properties of light and enrich optomechanics.Since Euler's studies of classical sound waves, the wave momentum has been naturally associated with the propagation direction of the wave, that is, the normal to wavefronts, or the wavevector. This idea was mathematically formulated by de Broglie for quantum matter waves: p = k, where p is the momentum, k is the wavevector and is the reduced Planck constant. In both classical and quantum cases, the wave momentum can be measured by means of the pressure force on an absorbing or scattering detector. In agreement with this, Maxwell claimed in his celebrated electromagnetic theory that 'there is a pressure in the direction normal to the waves' 1 . However, pioneering works by Poynting introduced the electromagnetic momentum density as a cross product of the electric and magnetic field vectors 2,12 :P∝ E × B. Unlike the straightforward de Broglie formula, the Poynting momentum is not obviously associated with the wavevector k. It is indeed aligned with the wavevector in the simplest case of a homogeneous plane electromagnetic wave. However, in more complicated yet typical cases of structured optical fields 13,14 (for example, interference, optical vortices, or near fields) the direction of P can differ from the wavevector directions 7,8 .Notably, the origin of this discrepancy between the Poynting momentum and wavevector lies within the framework of relativistic field theory (Supplementary Information). The conserved momentum of the electromagnetic field is associated with the translational symmetry of spacetime through Noether's theorem 10,15 . Applied to the electromagnetic field Lagrangian, this theorem produces the so-called canonical momentum density P can . In the quantum-field framework, the canonical momentum generates spatial translations of the field, in the same way as the de Broglie formula is...

Precise measurements of the surface tension and viscosity of airborne picolitre droplets can be accomplished using holographic optical tweezers.

Advances in optical tweezers, coupled with the proliferation of 2-photon polymerisation systems, mean that it is now becoming routine to fabricate and trap non-spherical particles. The shaping of both light beams and particles allows fine control over the flow of momentum from the optical to mechanical regimes. However, understanding and predicting the behaviour of such systems is highly complex in comparison with the traditional optically trapped microsphere. In this paper we present a conceptually new and simple approach, based on the nature of the optical force density. We illustrate the method through the design and fabrication of a shaped particle capable of acting as a passive force clamp; we demonstrate its use as an optically trapped probe for imaging surface topography. Further applications of the design rules highlighted here may lead to new sensors for probing bio-molecule mechanics, as well as to the development of optically actuated micro-machines.It is well known that the high intensity gradients generated in a tightly focused laser beam can be used to trap and manipulate micron-sized particles [1]. An optically trapped sphere is an elegant example of a microscopic harmonic oscillator, capable of measuring fN-scale forces, which has proved invaluable for the study of molecular motors and single biopolymer mechanics [2]. However, there are other desirable features of a force field that can only be introduced by modifying the particle shape or dielectric structure beyond that of a simple homogeneous sphere [3,4]. For example, optical torques can be applied to a particle whose symmetry has been lowered either by shape modification With increasing complexity of shape, the problem of predicting, and optimising, the 2 force profile of the trapped particle becomes ever more challenging. Although specialised software packages are available to compute the optical forces [13], their use is not routine.In this paper, therefore, we address this problem and describe a straightforward method for predicting the optical forces acting on extended dielectric particles of general shape. We support the description with rigorous 3-dimensional T-matrix calculations. To illustrate the approach, we describe the design and fabrication of a passive force clamp based on a tapered cylinder and capable of applying a constant force over displacements of several microns. We demonstrate its use in an optically-controlled scanning probe microscope for ultra-low force imaging. Potential future applications of this device may include the imaging of sensitive biological membranes. Results Background theory