Rongxin Huang, Pinyu Wu, Ernst-Ludwig Florin
We demonstrate that the data presented in the manuscript by Y. Roichman et al. are not sufficient to show that the circulation of a trapped particle exists in a static optical trap.
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We demonstrate both experimentally and theoretically that a colloidal sphere trapped in a static optical tweezer does not come to equilibrium, but rather reaches a steady state in which its probability flux traces out a toroidal vortex. This non-equilibrium behavior can be ascribed to a subtle bias of thermal fluctuations by non-conservative optical forces. The circulating sphere therefore acts as a Brownian motor. We briefly discuss ramifications of this effect for studies in which optical tweezers have been treated as potential energy wells.
Collective operation of multiple engines to achieve a common objective is a vital step in the design of complex machines. Recent studies have reduced the length scales of engine design to micro and nanometers. While strategies to build complex machines from these remain to be devised, even the basic design principles remain obscure. Here, we construct and analyze the simplest collection of two engines from a pair of colloidal microspheres in optical traps at close separation. We demonstrate that at such proximity, non-conservative scattering forces that were hitherto neglected, affect the part…
We describe and implement a technique for extracting forces from the relaxation of an overdamped thermal system with normal modes. At sufficiently short time intervals, the evolution of a normal mode is well described by a one-dimensional Smoluchowski equation with constant drift velocity, v, and diffusion coefficient, D. By virtue of fluctuation-dissipation, these transport coefficients are simply related to conservative forces, F, acting on the normal mode: F = k_BT v/D. This relationship implicitly accounts for hydrodynamic interactions, requires no mechanical calibration, makes no assumpti…
The emergence of structure through aggregation is a fascinating topic and of both fundamental and practical interest. Here we demonstrate that self-generated solvent flow can be used to generate long-range attractions on the colloidal scale, with sub-pico Newton forces extending into the millimeter-range. We observe a rich dynamic behavior with the formation and fusion of small clusters resembling molecules, the dynamics of which is governed by an effective conservative energy that decays as $1/r$. Breaking the flow symmetry, these clusters can be made active.
Brownian vortexes are stochastic machines that use static non-conservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unl…
Recently, Huang, Wu and Florin posted a Comment (0806.4632v1) on our preprint (0804.0730v1) describing nonequilibrium circulation of a colloidal sphere trapped in a optical tweezer. The Comment suggests that evidence for toroidal probability currents obtained from experiments and simulations in the original posting should be considered inconclusive. The authors' concerns are based on two claims: (1) that Brownian dynamics simulations of the trapped particle's motions reveal no statistically significant circulation, and (2) that a realistic description of the radiation pressure acting on the tr…
When a rigid object approaches a soft material in a viscous fluid, hydrodynamic stresses arise in the lubricated contact region and deform the soft material. The elastic deformation modifies in turn the flow, hence generating a soft-lubrication coupling. Moreover, soft elastomers and gels are often porous. These materials may be filled with solvent or uncrosslinked polymer chains, and might be permeable to the surrounding fluid, which complexifies further the description. Here, we derive the point-force response of a semi-infinite and permeable poroelastic substrate. Then, we use this fundamen…
The concept of effective depletion forces between two fixed big colloidal particles in a bath of small particles is generalized to a non-equilibrium situation where the bath of small Brownian particles is flowing around the big particles with a prescribed velocity. In striking contrast to the equilibrium case, the non-equilibrium forces violate Newton's third law, are non-conservative and strongly anisotropic, featuring both strong attractive and repulsive domains.
A particle diffusing around a point of stable mechanical equilibrium in a static but non-conservative force field enters into a steady state characterized by circulation in the probability flux. Circulation in such a Brownian vortex is not simply a deterministic response to the solenoidal component of the force, but rather reflects an interplay between force-driven probability currents and diffusion. As an example of this previously unrecognized class of stochastic heat engines, we consider a colloidal sphere stably trapped in a conventional optical tweezer. Rather than coming into thermodynam…
When an external field drives a colloidal system out of equilibrium, the ensuing colloidal response can be very complex and obtaining a detailed physical understanding often requires case-by-case considerations. In order to facilitate systematic analysis, here we present a general iterative scheme for the determination of the unique external force field that yields a prescribed inhomogeneous stationary or time-dependent flow in an overdamped Brownian many-body system. The computer simulation method is based on the exact one-body force balance equation and allows to specifically tailor both gra…
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