  Enhanced diffusion is an emergent property of many experimental microswimmer
systems that usually arises from a combination of ballistic motion with random
reorientations. A subset of these systems, autophoretic droplet swimmers that
move as a result of Marangoni stresses, have additionally been shown to respond
to local, self-produced chemical gradients that can mediate self-avoidance or
self-attraction. Via this mechanism, we present a mathematical model
constructed to encode experimentally observed self-avoidant memory and
numerically study the effect of this particular memory on the enhanced
diffusion of such swimming droplets. To disentangle the enhanced diffusion due
to the random reorientations from the enhanced diffusion due to the
self-avoidant memory, we compare to the widely-used active Brownian model.
Paradoxically, we find that the enhanced diffusion is substantially suppressed
by the self-avoidant memory relative to that predicted by only an equivalent
reorientation persistence timescale in the active Brownian model. We attribute
this to transient self-caging that we propose is novel for self-avoidant
systems. Additionally, we further explore the model parameter space by
computing emergent parameters that capture the velocity and reorientation
persistence, thus finding a finite parameter domain in which enhanced diffusion
is observable.
