Direct transport of particles in two-dimensional asymmetric periodic time-shift corrugated channel
Authors: Xie Tian-Ting  , Deng Ke  , Luo Mao-Kang  ,   Department of Mathematics, Sichuan University, Chengdu 610064, China;,   Department of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China
Published: December 2020

Studies on direct transport of particles not only attribute to understand many processes in the fields of biology, physics, chemistry, etc., but also to provide suitable methods to artificially control particles and micro-devices. In recent decades, direct transport in channels has aroused the interest of an increasing number of researchers. However, the current researches on direct transports in channels mainly focus on static boundary situations. Considering the fact that the time-variable channels exist widely in reality, the corresponding studies in time-variable channels are of distinct value and significance.
Therefore, in this paper, direct transport of particles in two-dimensional (2D) asymmetric periodic time-shift corrugated channel is discussed. Firstly, the corresponding Langevin equation describing the motion of particles in a 2D time-shift corrugated channel is established. The channel discussed here is periodic and symmetric in space but follows a periodic and asymmetric time-shift law. Secondly, the transport mechanism and properties of the above model are analyzed by numerical simulation. The average velocity of particles is chosen to evaluate the transport performance. The relationships between the average velocity and typical systematic parameters are discussed in detail.
According to the research, the transport mechanism is analyzed as follows. The asymmetric shift of the channel along the longitudinal direction will cause the distribution disparity of particles along the section direction, which can influence the bound effect of the channel on the motion of particles. Specifically, higher concentration of the particles along the section direction implies weaker bound effect of the channel walls, and vice versa. As a result, the particles exhibit different diffusive behaviors along the positive and negative longitudinal directions, thus inducing a direct current.
By investigating the relationships between the average velocity and typical systematic parameters, the conclusions are derived as follows. 1) The average current velocity is proportional to the asymmetric degree of channel since increasing asymmetric degree can increase the bound effect disparity, and thus promoting the direct transport behavior. 2) Higher temporal frequency can increase the directional impetus number in a certain period of time, but makes the distribution of particles more concentrated simultaneously. The competition between these two effects leads to generalized resonance transport behavior as the temporal frequency varies. 3) Wider channels allow particles to diffuse freely in larger space. Therefore, as the channel width increases, the bound effect is weakened and the direct transport is hindered, resulting in a decline in average velocity of particles. 4) The average current velocity exhibits generalized resonance behavior as the spatial frequency varies, which is caused by the competition between the diffusion scale of particle and the spatial period of channel. 5) With the growth of the noise intensity, the current velocity will first increase and then decrease, which means that adding proper noise to the system can enhance the direct transport phenomenon.