text: over-damped stochastic equations of motion [80–83]. Here, we assume that Mn(ρl) = αΘs(ρl − 
  
  0.5), where Θs(x) is a continuous function that switches smoothly from the value 0 to the value 
  
  1 at x = 0 (i.e. it is essentially a smooth analogue of the Heaviside function). This ensures that 
  
  the nanoparticles are immobile when the local liquid density is small (dry substrate) and have a 
  
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              [html]<thead><tr><td>Comparison</td><td>For the evolution of the liquid density distribution we assume that the liquid is able to evaporate</td><td>from the surface into the vapour ( reservoir ) above the surface ( non - conserved dynamics ) and may</td>
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  15 