  We numerically study the coalescence dynamics of two sessile droplets with
radii $R_0$. The droplets are placed on top of a rigid substrate with a contact
angle of $\theta_{eq.} = \pi/9$. Having a highly wettable substrate
($\theta_{eq} \ll \pi/2$) theory predicts that the bridge height ($h_0$) scales
according to $h_0(t) \sim t^{2/3}.$ This behavior can be altered with e.g.
surface tension gradients ($\partial_x\gamma \neq 0$). These gradients appear
for example with heat transfer, surfactants or having different but miscible
liquids. Instead of coalescence, these gradients can lead to a stable two
droplet state. In this work, we focus on two aspects of this problem. The first
one is the concrete choice of the surface tension, therefore making it
spatially correlated. The second one is the reduction of scale towards a regime
in which the disjoining pressure becomes important. We find that coalescence
can be suppressed, given that there is a sharp gradient in surface tension. If
this gradient is smeared, we find an intermediate agreement with the $2/3$
power-law. In the limit of large smearing width, we observe an asymmetric
coalescence.
