The prey-predator motion of the active droplets
Abstract
We present a generic solution for the relative motion of two diffusiophoretic prey-predator particles of arbitrary chemical activity Ai and radius Ri, where i = 1;2 refers to the predator and prey, respectively. Using the Lorentz reciprocal theorem, we investigate the impact of radius ratios and chemical reaction rates on the interaction between the particles. Our study reveals four distinct regimes of interaction, similar to the findings of Nasouri & Ramin (Phys. Rev. Lett., vol. 124, 2020, pp. 168003) for particles of identical sizes: (i) the prey particle escapes; (ii) two particles reach a stable equilibrium distance; (iii) two particles reach an unstable equilibrium distance where the prey is captured below it and escapes above it; (iv) the prey particle is captured. Unlike previous work, we differentiate between regimes with near-field and far-field interactions, which can be either attractive or repulsive, and find that the boundary between (i, iii) and (ii, iv) represents the transition from the attraction to repulsion in the far field, given by jA1=A2j = (R2=R1)2, while the transition between (i, ii) and (iii, iv) represents the interaction transition for particles in close proximity. We also perform three-dimensional simulations of prey-predator systems, which validate our theoretical predictions. Our study extends the applicability of the Lorentz reciprocal theorem to prey-predator system and quantitatively obtains interaction regime transition curves by distinguishing near-field and far-field interactions.
Related
- Stochastic predator-prey compartment model with cyclic and non-cyclic transition pathways and mortality
- Wave-driven contraction-deformation coupling enables the motility and revolving waves of active gel droplets
- Fluctuating chemically active droplets
- Active colloidal rafts perform swimming strokes that propel their host droplets
- Active Hydrodynamics Couples Polymer Organization, Shape Fluctuations, and Motility in Deformable Droplets
BibTeX
@misc{chen2026preypredator,
title = {{The prey-predator motion of the active droplets}},
author = {Yibo Chen and Kai Leong Chong and Roberto Verziccoa and Detlef Lohse},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05477},
eprint = {2609.05477},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05477},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The prey-predator motion of the active droplets
AU - Yibo Chen
AU - Kai Leong Chong
AU - Roberto Verziccoa
AU - Detlef Lohse
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.05477
UR - https://arxiv.org/abs/2609.05477
AB - We present a generic solution for the relative motion of two diffusiophoretic prey-predator particles of arbitrary chemical activity Ai and radius Ri, where i = 1;2 refers to the predator and prey, respectively. Using the Lorentz reciprocal theorem, we investigate the impact of radius ratios and chemical reaction rates on the interaction between the particles. Our study reveals four distinct regimes of interaction, similar to the findings of Nasouri & Ramin (Phys. Rev. Lett., vol. 124, 2020, pp. 168003) for particles of identical sizes: (i) the prey particle escapes; (ii) two particles reach a stable equilibrium distance; (iii) two particles reach an unstable equilibrium distance where the prey is captured below it and escapes above it; (iv) the prey particle is captured. Unlike previous work, we differentiate between regimes with near-field and far-field interactions, which can be either attractive or repulsive, and find that the boundary between (i, iii) and (ii, iv) represents the transition from the attraction to repulsion in the far field, given by jA1=A2j = (R2=R1)2, while the transition between (i, ii) and (iii, iv) represents the interaction transition for particles in close proximity. We also perform three-dimensional simulations of prey-predator systems, which validate our theoretical predictions. Our study extends the applicability of the Lorentz reciprocal theorem to prey-predator system and quantitatively obtains interaction regime transition curves by distinguishing near-field and far-field interactions.
ER -