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A Hydrodynamic Instability Is Used to Create Aesthetically Appealing Patterns in Painting

Fig 8

Dispersion relation of the black/white layer.

The solid black line shows the results considering the values in Table 1 (At = 0.05). The dashed and dashed-dotted black lines show the influence of reducing the layer thickness: (− − −), H1 = 1 mm, H2 = 0.6 mm; (− ⋅ −), H1 = 0.4 mm, H2 = 0.2 mm. The red lines show the effect of changing the fluid viscosities, keeping the rest of the parameters fixed (layer thicknesses and densities). The red dashed line shows the prediction for smaller viscosities: μ1 = 5.79 Pa s, μ2 = 1.26 Pa s); the red dashed-dotted line shows the case for higher viscosities: μ1 = 23.14Pa s, μ2 = 5.04 Pa s). The blue lines show the effect of changing the density difference, keeping the rest of the parameters fixed. The blue dashed line shows the prediction for a smaller density difference (At = 0.02) produced by reducing the density of the top or bottom layer (ρ1 = 1002 kg/m3, ρ2 = 1050 kg/m3); the blue dashed dotted line corresponds also to a smaller density difference (At = 0.02) but by increasing the density of the bottom layer (ρ1 = 1050 kg/m3, ρ2 = 1110 kg/m3). The vertical gray line shows the experimental measurements of the mean blob size from Fig 5. Note that both n and k are shown in dimensionless form, considering, (g2 ρ1/μ1)−1/3 and (gρ12/μ12)1/3 respectively.

Fig 8

doi: https://doi.org/10.1371/journal.pone.0126135.g008