Osmotic and phoretic competition explains chemotaxic assembly and sorting

Microscale objects responding to chemical gradients by migrating toward or away from a preferred species is a simple yet constitutive mechanism by which transport occurs in biological organisms. Synthetic chemotaxis provides key physical descriptions of simplified systems that can be used in biological models, or in the creation of advanced responsive material systems. In this article, we provide a quantitative framework for understanding synthetic chemotaxis of microparticles which involves a competition between phoresis and osmosis. We present separate quantitative measurements of phoresis and osmosis acting on individual taxing particles, finding that phoresis follows the long-predicted [Formula: see text] scaling while the osmotic contribution depends on the geometry and details of the system, and must be solved on a case-by-case basis. Through this, we are able to develop a more accurate picture of particle transport at the single particle level. Equipped with this approach, we go on to describe how high concentrations of particles in a symmetric chemical gradient grow close-packed hives that reach a steady-state size tunable through light intensity or particle size. Last, we demonstrate that mixed particles experiencing the same chemical gradient will selectively migrate toward or away depending on the nature of the particle surface, thereby locally sorting out a particular species. We anticipate these results will be important in describing both biological and synthetic chemotaxis in phoretic systems and should bring a wealth of studies that take advantage of competing osmotic flows to illicit unexpected dynamic active behavior.