Use of the reflective background oriented schlieren technique to measure free surface deformations in a thin liquid layer non-uniformly heated from below

Abstract

To measure liquid film surface deformations, we use the Background Oriented Schlieren (BOS) technique with a reflective optical scheme, which includes a random dot pattern located above the liquid surface, and a camera that captures its reflection from the liquid interface. The substrate was covered with a special black coating to minimize stray light reflection, which allowed to provide clear visualization of the dot pattern reflected from the free surface even for very thin liquid films. Local slopes of the film surface cause the dot displacement on the pattern image relative to the pattern image captured in the absence of any free-surface deformations. Hence, the topography of the liquid film surface is encoded by the apparent displacement of the dot pattern. Using the cross correlation image processing, the displacement vector field was determined, which was then substituted in Poisson equation to reconstruct the free-surface profile of the liquid film. The main advantages of this technique are: applicability for liquids with surface temperature inhomogeneities, experimental simplicity, sensitivity and applicability for both transparent and opaque liquids. Using the reflective BOS technique and using substrate with black coating we measure the free-surface deformation field of a thin layer of silicone oil non-uniformly heated from below. Despite the fact that thermocapillary shear stresses tend to decrease the thickness of the liquid layer in hotter regions, in the experiment, a convex deformation of the liquid film surface was observed above the heater for a few seconds immediately after the start of heating. This phenomenon is explained by the expansion of the liquid induced by the heating, due to the dependence of the liquid density on temperature. The measurement results are compared with those obtained in a single point using the confocal sensor. A good agreement is achieved.