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Register a new userSingle-file escape of colloidal particles from microfluidic channels
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Single-file diffusion is a ubiquitous physical process exploited by living and synthetic systems to exchange molecules with their environment. It is paramount quantifying the escape time needed for single files of particles to exit from constraining synthetic channels and biological pores. This quantity depends on complex cooperative effects, whose predominance can only be established through a strict comparison between theory and experiments. By using colloidal particles, optical manipulation, microfluidics, digital microscopy and theoretical analysis we uncover the self-similar character of the escape process and provide closed-formula evaluations of the escape time. We find that the escape time scales inversely with the diffusion coefficient of the last particle to leave the channel. Importantly, we find that at the investigated {bf microscale}, bias forces as tiny as $10^{-15};{rm N}$ determine the magnitude of the escape time by drastically reducing interparticle collisions. Our findings provide crucial guidelines to optimize the design of micro- and nano-devices for a variety of applications including drug delivery, particle filtering and transport in geometrical constrictions.
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The diffusion process of N hard rods in a 1D interval of length L (--> inf) is studied using scaling arguments and an asymptotic analysis of the exact N-particle probability density function (PDF). In the class of such systems, the universal scaling law of the tagged particles mean absolute displacement reads, <|r|>~ <|r|>_{free}/n^mu, where <|r|>_{free} is the result for a free particle in the studied system and n is the number of particles in the covered length. The exponent mu is given by, mu=1/(1+a), where a is associated with the particles density law of the system, rho~rho_0*L^(-a), 0<= a <=1. The scaling law for <|r|> leads to, <|r|>~rho_0^((a-1)/2) (<|r| >_{free})^((1+a)/2), an equation that predicts a smooth interpolation between single file diffusion and free particle diffusion depending on the particles density law, and holds for any underlying dynamics. In particular, <|r|>~t^((1+a)/2) for normal diffusion, with a Gaussian PDF in space for any value of a (deduced by a complementary analysis), and, <|r|>~t^((beta(1+a))/2), for anomalous diffusion in which the systems particles all have the same power-law waiting time PDF for individual events, psi~t^(-1-beta), 0<beta<1. Our analysis shows that the scaling <|r|>~t^(1/2) in a standard single file is a direct result of the fixed particles density condition imposed on the system, a=0.
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