AbstractWe consider the sharp interface limit of a convective Allen–Cahn equation, which can be part of a Navier–Stokes/Allen–Cahn system, for different scalings of the mobility $$m_\varepsilon =m_0\varepsilon ^\theta $$
m
ε
=
m
0
ε
θ
as $$\varepsilon \rightarrow 0$$
ε
→
0
. In the case $$\theta >2$$
θ
>
2
we show a (non-)convergence result in the sense that the concentrations converge to the solution of a transport equation, but they do not behave like a rescaled optimal profile in normal direction to the interface as in the case $$\theta =0$$
θ
=
0
. Moreover, we show that an associated mean curvature functional does not converge to the corresponding functional for the sharp interface. Finally, we discuss the convergence in the case $$\theta =0,1$$
θ
=
0
,
1
by the method of formally matched asymptotics.