Effect of passive particle shape on effective force in active bath

Abstract

<sec>In active matter, the effective force between passive objects is crucial for their structure and dynamics, which is the basis for understanding the complex behaviors within active systems. Unlike equilibrium states, the factors such as the surface configuration, size, and confinement strength significantly influence the effective forces between passive particles. Previous studies have shown that the shapes of passive particles affect the aggregation of active particles, leading to different forces experienced by passive particles with different shapes. However, recently, a long-range attractive force between passive platelike particles, caused by the bacterial flow field instead of the direct bacterium-plate collisions in active bacterial suspensions, has been found. This raises an intriguing question: how does hydrodynamics affect the forces on passive particles of different shapes in different ways?</sec><sec>In this work, we investigate the effective forces exerted on passive spherical and plate-like particles immersed in bacterial suspensions by optical-tweezers experiments. The effective force between passive particles can be calculated from the formula, <inline-formula><tex-math id="M1">\begin{document}$ {F_{{\text{eff}}}} = {\text{ }}k\left\langle {\Delta d} \right\rangle /2 $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M1.png"/></alternatives></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}$ \left\langle {\Delta d} \right\rangle $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M2.png"/></alternatives></inline-formula> represents the difference in distance between the passive particles in the bacterial bath and those in the solution without bacteria, <inline-formula><tex-math id="M3">\begin{document}$ k $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M3.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M3.png"/></alternatives></inline-formula> is the effective stiffness of optical traps. The <inline-formula><tex-math id="M5">\begin{document}$ {{{F}}}_{{\mathrm{e}}{\mathrm{f}}{\mathrm{f}}} > 0 $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M5.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M5.png"/></alternatives></inline-formula> indicates a repulsive force between passive particles, and the <inline-formula><tex-math id="M6">\begin{document}$ {F_{{\text{eff}}}} \lt {\text{ }}0 $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M6.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20240650_M6.png"/></alternatives></inline-formula> represents an effective attractive force between passive particles. Our results demonstrate that the passive spherical particles experience short-range repulsion, while plate-like particles are subjected to long-range attraction. This highlights the substantial effect of particle shape on their effective forces.</sec><sec>The forces on passive particles are mainly attributed to two factors: direct bacterium-particle collisions and the bacterial flow field. The analysis of the bacterial concentration and orientation distribution around passive particles reveals that for spherical particles, the concentration of bacteria between particles is higher than that outside the particles, but there is almost no difference in the orientation order between bacteria inside and outside the particles. This suggests that the effective repulsion between spherical particles is mainly due to the direct bacterial collisions. Conversely, for plate-like particles, the long-range attraction is primarily influenced by the bacterial flow field rather than their direct collisions, which is evidenced by the higher bacterial density and orientation order inside the two plates compared with those outside the two plates. This study provides strong evidence that the effective force between passive particles is shape dependent in active bath, and offers new insights into controlling active-directed assembly.</sec>