The motion of micro-swimmers over a cavity in a micro-channel.

This article combines the lattice Boltzmann method (LBM) with the squirmer model to investigate the motion of micro-swimmers in a channel-cavity system. The study analyses various influential factors, including the value of the squirmer-type factor (ß), the swimming Reynolds number (Rep), the size of the cavity, initial position and particle size on the movement of micro-swimmers within the channel-cavity system. We simultaneously studied three types of squirmer models, Puller (ß > 0), Pusher (ß < 0), and Neutral (ß = 0) swimmers. The findings reveal that the motion of micro-swimmers is determined by the value of ß and Rep, which can be classified into six distinct motion modes. For Puller and Pusher, when the ß value is constant, an increase in Rep will lead to transition in the motion mode. Moreover, the appropriate depth of cavity within the channel-cavity system plays a crucial role in capturing and separating Neutral swimmers. This study, for the first time, explores the effect of complex channel-cavity systems on the behaviour of micro-swimmers and highlights their separation and capture ability. These findings offer novel insights for the design and enhancement of micro-channel structures in achieving efficient separation and capture of micro-swimmers.

Temperature-controlled focusing of Brownian particles in a channel.

The preferential motion of Brownian particles in a channel with heated or cooled walls was numerically simulated using a direct numerical simulation method, that is, the fluctuating-lattice Boltzmann method. The resulting focusing of Brownian particles on the channel centerline induced by heated walls is the focus of this study. The effects of wall temperature, fluid thermal diffusivity, and particle size and density were considered in terms of both the focusing efficiency and performance of Brownian particles. It was revealed that the particle focusing process follows a quadratic relationship with time at high wall temperatures or a linear relationship at low wall temperatures. For a fixed wall temperature, the focusing efficiency (i.e., how fast the Brownian particles aggregate) is dominated by the Prandtl number, that is, the relative importance of the heat transfer and momentum transfer in the fluid. Meanwhile, the Lewis number, that is, the ratio of the fluid thermal diffusivity to the particle self-diffusivity, controls the focusing performance (i.e., to what extent Brownian particles aggregate). The possible mechanisms behind this are discussed. Finally, the negligible influence of particle density on both the focusing efficiency and performance was revealed.

Swimming Mode of Two Interacting Squirmers under Gravity in a Narrow Vertical Channel.

The swimming mode of two interacting squirmers under gravity in a narrow vertical channel is simulated numerically using the lattice Boltzmann method (LBM) in the range of self-propelling strength 0.1 ≤ α ≤ 1.1 and swimming type −5 ≤ ß ≤ 5. The results showed that there exist five typical swimming patterns for individual squirmers, i.e., steady upward rising (SUR), oscillation across the channel (OAC), oscillation near the wall (ONW), steady upward rising with small-amplitude oscillation (SURO), and vertical motion along the sidewall (VMS). The parametric space (α, ß) illustrated the interactions on each pattern. In particular, the range of oscillation angle for ONW is from 19.8° to 32.4° as α varies from 0.3 to 0.7. Moreover, the swimming modes of two interacting squirmers combine the two squirmers' independent swimming patterns. On the other hand, the pullers (ß < 0) attract with each other at the initial stage, resulting in a low-pressure region between them and making the two pullers gradually move closer and finally make contact, while the result for the pushers (ß > 0) is the opposite. After the squirmers' interaction, the squirmer orientation and pressure distribution determine subsequent squirmer swimming patterns. Two pushers separate quickly, while there will be a more extended interaction period before the two pullers are entirely separated.

Interaction between two unequal particles at intermediate Reynolds numbers: A pattern of horizontal oscillatory motion.

The two-dimensional lattice Boltzmann method (LBM) was used to study the motion of two interacting particles with different densities (ρ_{1} and ρ_{2}) and diameters (d_{1} and d_{2}), which were placed in a vertical channel under gravity. Both the density ratio (λ=ρ_{2}/ρ_{1}) and diameter ratio (r=d_{2}/d_{1}) between the particles were considered. The transition boundaries between the regime where the particles settle separately and the regime where the particles interact are identified by λ_{max}(r) and λ_{min}(r); they exhibit excellent power-law relationships with r. A pattern of horizontal oscillatory motion (HOM), characterized by a structure with a large (but light) particle right above a small (but heavy) one and strong oscillations of both particles in the horizontal direction, was revealed for r∼0.3 at intermediate Reynolds numbers. The results indicate that the magnitude of oscillations decreases with λ, whereas the frequency displays the opposite trend. A sudden increase in the terminal velocity of particles is seen, illustrating a transition from the classical pattern of drafting, kissing, and tumbling to the HOM at a certain λ. Upon increasing λ, the pattern of HOM may bifurcate into a vertical steady state at low Re or small r. Furthermore, the effects of the confinement ratio and particle-to-fluid density ratio were also examined. The existence of a critical confinement ratio is observed, beyond which the particles interact in a different manner.

Discontinuity in the sedimentation system with two particles having different densities in a vertical channel.

The two-dimensional lattice Boltzmann method was used to numerically study a sedimentation system with two particles having different densities in a vertical channel for Galileo numbers in the range of 5≤Ga≤15 (resulting in a Reynolds number, based on the settling velocity, approximately ranging between 0.6 and 7). Two types of periodic motion, differing from each other in terms of the size of the limit cycle, the magnitude of the time period, and their changes upon increasing the density difference between particles, are identified depending on whether there is a wake effect. The most prominent features of this system are discontinuous changes in the settling velocity (6.7≤Ga<9.7) and time period of oscillation (10.5≤Ga≤15) at a critical value of the density difference between particles. The first discontinuity results in an abrupt increase in the Reynolds number, associated with a Hopf bifurcation without the presence of vortex shedding. The second discontinuity is accompanied by the disappearance of "abnormal rotation" (referring to the situation in which a particle appears to roll up a wall when settling) of the heavy particle, which directly results from a sharp increase in the amplitude of oscillation induced by the enhanced wake effect at another critical density difference between particles. The wall effects on these discontinuous changes were also examined.

Grouping behavior of coaxial settling particles in a narrow channel.

Using numerical simulations, we studied the grouping behaviors of particles settling along their line of centers in narrow channels having a Reynolds number range of 5 ≤ Re ≤ 50. The calculations are based on our previously developed lattice Boltzmann direct-forcing-fictitious-domain method. We report the grouping behavior and investigate the dependence on the number of particles n, the initial interparticle separation h_{0}, and the Reynolds number Re. In particular, the mode of grouping is found to be independent of the number of particles when the Reynolds numbers is small. The two lowermost particles always come together first and form a vertical doublet and then the next two lowest particles form another doublet, and so on. Therefore, we observe n/2 doublets or (n-1)/2 doublets when n is even or odd, respectively. The uppermost particle is always left behind when n is odd. Furthermore, the separation between these doublets remains constant, displaying a power-law dependence decreasing from top to bottom.