Sources:
The choice of the dividing surface, strictly speaking, is arbitrary, however, it is very desirable to take into account the type of external potential . Otherwise, these expressions are at odds with the generally accepted concepts and common sense.
First,  must lie close to the transition layer (i.e., the region where the number density varies), otherwise it would mean the attribution of the bulk properties of one of the phase to the surface.
Second. In the case of weak adsorption, for example, when the potential is close to the stepwise, it is logical to choose  close to . (In some cases, choosing , where  is particle radius, excluding the "dead" volume.)
In the case of pronounced adsorption it is advisable to choose  close to the right border of the transition region. In this case all particles from the transition layer will be attributed to the solid, and  is always positive. Trying to put  in this case will lead to a strong shift of  to the solid body domain, which is clearly unphysical.
Conversely, if  (fluid on the left), it is advisable to choose  lying on the left side of the transition layer. In this case the surface particles once again refer to the solid and  is back positive.
Thus, except in the case of static membrane, we can always avoid the "negative adsorption" for one-component systems.