PHYSICAL REVIEW E 102, 062602 (2020) Lattice model for active flows in microchannels Alessandro Ravoni 1 , * and Luca Angelani 2 1 Department of Mathematics and Physics, Roma Tre University, 00146 Rome, Italy 2 ISC-CNR, Institute for Complex Systems, and Dipartimento di Fisica, Università Sapienza, I-00185 Rome, Italy (Received 18 May 2020; revised 8 October 2020; accepted 10 November 2020; published 1 December 2020) We introduce a one-dimensional lattice model to study active particles in narrow channel connecting finite reservoirs. The model describes interacting run-and-tumble swimmers exerting pushing forces on neighboring particles, allowing the formation of long active clusters inside the channel. Our model is able to reproduce the emerging oscillatory dynamics observed in full molecular dynamics simulations of self-propelled bacteria [Paoluzzi et al., Phys. Rev. Lett. 115, 188303 (2015)] and allows us to extend in a simple way the analysis to a wide range of system parameters (box length, number of swimmers), taking into account different physical conditions (presence or absence of tumbling, different forms of the entrance probability into the channel). We find that the oscillatory behavior is suppressed for short channels length L < L ∗ and for high tumbling rates λ>λ ∗ , with threshold values L ∗ and λ ∗ which in general depend on physical parameters. Moreover, we find that oscillations persist by using different entrance probabilities, which, however, affect the oscillation properties and the filling dynamics of reservoirs. DOI: 10.1103/PhysRevE.102.062602 I. INTRODUCTION Active matter under confinement shows unexpected and counterintuitive behaviors [1,2]. A quite large variety of nonequilibrium phenomena has been observed in experiments and numerical simulations of self-propelled bacteria or active particles such as, for example, particles accumulation at walls [3–5], emergence of spontaneous flows in asymmetric envi- ronments [2,6], micro-objects actuation [7–10], self-trapping inside colloidal vesicles [11], just to cite a few. Of particular interest, especially in the biological realm, is the behavior of swimmers in microchannels. For not-too-narrow channels particle aggregation at channel walls, with the formation of transient clusters, and upstream swimming in the presence of external flow has been observed [12–17]. When the channel thickness becomes of the order of the particle size, single- file motion can set in, producing crowding effects [18–21]. In a recent study a quite surprising dynamical behavior has been found in a numerical simulation of bacteria confined in two microchambers connected by a very thin channel [22]. Swimmers alternately fill and empty the two containers, self -sustaining density oscillations in the system. The emergent oscillatory phenomenon was generated by the persistent char- acter of the active particle motion, together with the single-file condition in the narrow channel and the density-dependent swimmers motility in the chambers. To our knowledge, there are no experimental studies investigating such a mechanism. Moreover, a complete investigation of the role of swimmers properties and physical or geometrical parameters are still lacking. * alessandro.ravoni@uniroma3.it The aim of this work is to introduce a simplified model to study interacting swimmers inside a thin channel under the single-file condition, allowing us in a simple way to investigate a large variety of physical conditions. We devel- oped a model where the channel is a one-dimensional lattice that connects two microchambers which act as reservoirs from which the swimmers can come out with a certain probability. Inside the channel, the motion of the run-and-tumble particles depends both on their orientation and on that of the neighbor- ing swimmers. The paper is organized as follows. In Sec. II we introduce the dynamics of particles inside the channel and the mod- eling of microchambers. In Sec. III we present the results of our parametric study, obtained by varying the number of swimmers, the length of the channel, the entrance probability from the microchambers, and the tumbling rate of the run-and- tumble particles. Finally, we summarize our results in Sec. IV. II. THE MODEL The system we are interested in consists of two mi- crochambers (C α , α = 1, 2) connected by a thin microchannel (Fig. 1). We consider a discrete model for the channel, repre- sented by a one-dimensional lattice of r cells. The channel’s length is L = rl , where l is the linear dimension of a cell (in the following we consider units such as l = 1, so the value of L corresponds to the number of lattice cells). We consider single-file condition, i.e., each cell can be occupied at most by one swimmer. Each swimmer is represented by a run-and- tumble particle, i.e., a particle which moves at constant speed v and reorients its direction of motion with rate λ. We denote with θ =±1 the orientation of the particles in the channel, corresponding, respectively, to right or left swimming direc- tion. During the evolution of the system, swimmers can enter 2470-0045/2020/102(6)/062602(10) 062602-1 ©2020 American Physical Society