Effect of amplitude and wavelength in the cooperative motion of Taylor lines

Abstract

In the present study, we have modeled the clustering of binary Taylor line swimmers in a Newtonian fluid. The fluid is modeled using the particle-based simulation method multiparticle collision dynamics, while for the Taylor line, we use a bead spring arrangement with a sine wave passing through it using a bending wave potential. The binary swimmers have the same propulsion speed, but they differ from each other in the shape of the Taylor line ensured by different amplitudes and lengths. We observe that an optimal amplitude exists for the Taylor line swimmer leading to large clusters formation. The size distribution of the clusters was observed to follow a power-law behavior followed by an exponential cutoff. We also calculated the probability of finding a bead of the swimmer as a function of the fractional distance from the center of the bounding circle and observed that when the amplitude is close to the optimal value, the swimmer forms clusters closer to the walls; otherwise, the swimmer stays almost uniformly distributed around the bounding area. When the ratio of the amplitude is high, the clusters formed at the center of the bounding area become stable and have a wedge-shape. By calculating the speed of the swimmer as a function of the fractional distance from the center of the bounding area, we show that the swimmers speed increases with the maximum at the walls. The simulation with a smaller system has revealed that the maximum clustering happens for an amplitude parameter of ∼0.17.