text: the nanoparticles. 
  
  If the particle diffusivity is low, the front ‘collects’ the particles, resulting in a build up of the 
  
  particles at the front that itself is slowed down. This makes the front unstable and any ﬂuctuation 
  
  along the front will trigger a transverse instability that results in an evolving ﬁngering pattern. This 
  
  happens even when the particle-liquid and particle-particle attractive interactions do not favour 
  
  clustering (i.e. demixing of the liquid and the nanoparticles). In this regime, the instability is a 
  
  purely dynamic effect and energetics plays no role in determining the number of ﬁngers. We call 
  
  this the ‘transport regime’. 
  
  To illustrate the inﬂuence of energetics (characterized by the interaction parameters εij) on ﬁnger- 
  
  ing in Fig. 3 we display the dependence of the mean ﬁnger number on particle-liquid interaction 
  
  strength εnl. For εnl ≥ 1.5 the mean ﬁnger number < f > is nearly constant; this is the trans- 
  
  port regime. However, on decreasing εnl below 1.5, we observe a marked increase in the value 
  
  of < f >, indicating that energy plays an important role in determining the number of ﬁngers in 