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In this study, Brownian Dynamics simulations are implemented to investigate the motion of a bottom-heavy Janus particle near a wall under varying shear flow conditions and at small P\'eclet (Pe) numbers. The stochastic motion of the Janus particle impacted by surface forces is described using a set of coupled Langevin equations that takes into account the Janus particle orientation. Interactions arising from surface potentials are found to depend on the separation distance between the Janus particle and the wall, the properties of the surfaces involved, and the thickness of the Janus particle cap. When shear flow is introduced in the system, the dynamical behavior of the Janus particle is also governed by the strain rate. Furthermore, the effect of friction on the dynamical behavior of the Janus particle under shear flow is investigated and reveals that the rotational motion of the Janus particle slows down slightly when the particle is close to the surface. In summary, we demonstrate the ability to utilize Brownian Dynamics simulations to capture the rich dynamical behavior of a bottom-heavy Janus particle near a wall and under a range of shear flow conditions, cap thicknesses, and surface charges.

We propose a combined analytical-numerical strategy to predict the dynamics and trajectory of a microswimmer next to a curved spherical obstacle. The microswimmer is actuated by a slip velocity on its surface and a uniformly valid solution is provided by utilizing the Reynolds reciprocal theorem in conjunction with the exact hydrodynamic solution of translation/rotation of a sphere in an arbitrary direction next to a stationary obstacle. This approach permits the hydrodynamic interaction of the microswimmer and the obstacle to be consistently and accurately calculated in both far and near fields. Based on the analysis, it was shown that while the "point-singularity solution" is valid when the microswimmer is far from the obstacle, it fails to predict the correct dynamics when the swimmer is close to the obstacle (i.e. gap size is approximately twice the characteristic length of the microswimmer). Two different paradigms for propulsion, so-called "squirmer" and "phoretic" models, were examined and for each type of microswimmer, various types of trajectories are highlighted and discussed under which circumstances the swimmer can be hydrodynamically trapped or guided by the obstacle. The analysis indicates that it is always easier to capture a microswimmer in a closed circular orbit with a large sized obstacle ($\sim 20$-$40$ times larger than the microswimmer size) as in this case the magnitude of rotational velocity can be sufficiently large that the swimmer can adjust its distance and orientation vector with the obstacle.