  The cellular environment, characterized by its intricate composition and
spatial organization, hosts a variety of organelles, ranging from
membrane-bound ones to membraneless structures that are formed through
liquid-liquid phase separation. Cells show precise control over the position of
such condensates. We demonstrate that organelle movement in external
concentration gradients, diffusiophoresis, is distinct from the one of colloids
because fluxes can remain finite inside the liquid-phase droplets and movement
of the latter arises from incompressibility. Within cellular domains
diffusiophoresis naturally arises from biochemical reactions that are driven by
a chemical fuel and produce waste. Simulations and analytical arguments within
a minimal model of reaction-driven phase separation reveal that the directed
movement stems from two contributions: Fuel and waste are refilled or extracted
locally, resulting in concentration gradients, which (i) induce product fluxes
via incompressibility and (ii) result in an asymmetric forward reaction in the
droplet's surroundings (as well as asymmetric backward reaction inside the
droplet), thereby shifting the droplet's position. We show that the former
contribution dominates and sets the direction of the movement, away from or
towards fuel source and waste sink, depending on the product molecules'
affinity towards fuel and waste, respectively. The mechanism thus provides a
simple means to organize condensates with different composition. Particle-based
simulations and systems with more complex reaction cycles corroborate the
robustness and universality of this mechanism.
