  Janus particles self-propel by generating local tangential concentration
gradients along their surface. These gradients are present in a thin layer
whose thickness is small compared to the particle size. Chemical asymmetry
along the surface is a prerequisite to generate tangential chemical gradient,
which gives rise to diffusioosmotic flows in a thin region around the particle.
This results in an effective slip on the particle surface. This slip results in
the observed "swimming" motion of a freely suspended particle even in the
absence of externally imposed concentration gradients.Motivated by the
chemotactic behaviour of their biological counterparts(such as sperm cells,
neutrophils, macrophages, bacteria etc.), which sense and respond to external
chemical gradients, the current work aims at developing a theoretical framework
to study the motion of a Janus particle in an externally imposed linear
concentration gradient. The external gradient along with the self-generated
concentration gradient determines the swimming velocity and orientation of the
particle.The dominance of each of these effects is characterised by a
non-dimensional activity number A. The surface of Janus particle is modelled as
having a different activity and mobility coefficient on the two halves.Using
Lorentz Reciprocal theorem, an analytical expression for the rotational and
translational velocity is obtained. The analytical framework helps us divide
the parameter space of surface activity and mobility into four regions where
the particle exhibits different trajectories.
