Motion of an active particle in linear concentration gradients

Janus particles are self-propelling bodies which generate local concentration gradients in a thin layer ($\delta$) compared to the size ($a$) of the particle($\delta \ll a$). Chemical assymetry along the surface is essential to generate chemical gradients. This generated concentration gradient gives rise to diffusioosmotic flows in the thin layer which is equivalent to a slip when seen from far, resulting in swimming of the particle even without any external concentration gradient.In realistic situations Janus particles can be in a fluid with concentration gradients. Therefore, in this work, we theoretically study the effect of external linear concentration gradient(electrolytic and non-electrolytic solutes) on Janus particle. The external gradient gives rise to a competition between the local concentration gradient and the external concentration gradient. We show that it can be captured by a non-dimensional activity number.The framework is general for any arbritrary angle $\beta $ between the direction of concentration gradient and the axis of self- propulsion. We see, for $\beta=0 $, only the translational velocity changes, subject to a change in strength of external concentration gradient. However, for other angles, the Janus particle undergoes rotation.