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The understanding of forces is central to a comprehensive picture of physical reality. Nowadays it is becoming increasingly important to explore forces on micro- and nanoscopic length scales. Such forces are typically in the piconewton and femtonewton range. Apart from the technological challenge intrinsic to dealing with such minute forces, it is important to realize that the general concepts of everyday life cannot be simply scaled down to nanoscopic objects, due mainly to the thermal noise affecting the motion of small objects (Brownian motion).

For microscopic objects immersed in a liquid, viscous forces dominate by several orders of magnitude over inertial effects, that is, they are overdamped. This implies that a constant force leads to a constant terminal drift velocity , so that , with representing the friction coefficient. However, Brownian noise complicates the situation. Indeed, the presence of a spatially varying Brownian noise leads to the presence of apparent forces, which exist only because of the presence of thermal noise.

This Demonstration focuses on a paradigmatic case of a Brownian particle near a wall. You can explore the dependence of the spurious force term and the associated drift on the particle radius and distance from the wall in water as medium. The correction terms become more relevant for smaller distances and radii. While the drift reaches a constant value for , the spurious force diverges. For high values the force is indicated by a green arrow.

Note that in contrast to the drift, the force only depends on the particle radius and not on the viscosity of the medium.

[1] G. Volpe, L. Helden, T. Brettschneider, J. Wehr, and C. Bechinger, "Influence of Noise on Force Measurements," Phys. Rev. Lett., 104(17), 2010.