Measuring flux distributions for diffusion in the small-numbers limit

Area of Science:

• Physics
• Physical Chemistry
• Colloid Science

Background:

• Classical diffusion is described by Fick's law relating flux and concentration gradient.
• Experimental exploration of diffusion rate distributions for small particle numbers is lacking.

Purpose of the Study:

• To experimentally measure the distribution of diffusional fluxes for small numbers of colloidal particles.
• To investigate the validity of Fick's law at the single-particle level.
• To introduce and experimentally verify a new fluctuation theorem for particle fluxes.

Main Methods:

• Utilized a microfluidics device with a colloidal suspension of a small number of microspheres.
• Measured the distribution of diffusional fluxes and particle concentration gradients.

Main Results:

• Flux distribution follows a Gaussian function.
• Fick's law is valid for particle gradients as small as a single particle difference.
• Flux variance is proportional to the total number of particles.
• Observed backward flows against the concentration gradient.
• Introduced and quantitatively confirmed a new fluctuation theorem for fluxes.

Conclusions:

• Fick's law and statistical mechanics principles extend to small particle systems.
• The new fluctuation theorem provides insights into nonequilibrium systems.
• Microfluidics enables precise measurements of fundamental diffusion dynamics.