In many research areas, it is common to model advection-diffusion problemswith Lagrangian particle methods. This is the same as solving a stochasticdifferential equation, with drift and diffusion coefficients derived from theadvection-diffusion equation. But there is also a necessary condition for theparticle method to be equivalent to the Eulerian advection-diffusion equation,is that it satisfies the well-mixed condition (Thomson, 1987), which says thatif particles are well mixed, they have to stay well mixed later on. This is just astatement with respect to second law of thermodynamics, which is entropy. Acommonly used implementation of reflecting boundary conditions for particlemethods is analysed. We find that in some cases, this reflecting scheme willgive rise to oscillations in concentration close to the boundary, which we callthe boundary artifact.We analyse the reflection scheme in the Lagrangian model, and compareit to Neumann boundary conditions in the Eulerian model. We find that ifthe diffusivity has a non-zero derivative at the boundary, this violates one ofthe conditions for equivalence with the advection-diffusion equation, whichis that the drift coefficient in the SDE must be Lipschitz continuous. Thisseems to be the origin of the boundary artifact. We analyse the artifactfurther, and describe two different types of boundary artifact.We suggest different approaches to dealing with the problem, and findthat the problem can in practice be handled by adjusting the diffusivityclose to the boundary. Support and motivation for such a change is found inthe concept of the ”unresolved basal layer” (Wilson & Flesch, 1993), which isa pragmatic idea stating that closer than some distance from the boundary,we simply cannot know the details of the turbulent motion.