Variation of translocation efficiency through constriction larger than the particle by Brownian motion

DNA molecules need to wait for entry into the nanopores of sequencers if the molecular length is larger than the pore width. Brownian motion explores diverse configurations randomly and some of them let the molecule pass through the nanopore. On the other hand, ink does not change its color when flowing through a pen where a constriction exists because the pigment particles are smaller than the channel width in the pen. The pigment particles are supposed to follow the streamlines of the dispersant fluid on average. However, we have found that a spherical particle can exhibit different transport efficiency due to Brownian motion when it translocates through a constriction even when the narrower part is still larger than the particle size. In particular, there is a maximum transport efficiency depending on the Péclet number, which is of great importance in the industrial context such as filtration with a huge pressure difference.