Capillary waves can be used to measure the fundamental fluid properties such as surface tension as well as, potentially, the viscosity of Newtonian fluids. This requires the measurement of various wave parameters, mainly wavelength, amplitude, and decay coefficient. However, the different scales of magnitudes make it a challenging task. Optical methods are well suited to analyze such problems due to their non-intrusive nature and high dynamic measurement resolution in both space and time. These methods are further categorized as point methods for a single probe measurement and space–time methods for transient measurement of the complete surface. Dynamic space–time methods are preferred despite the associated complex post-processing since they enable reconstruction of the wave surface. Some existing methods are discussed, and an improved method is then proposed to actually solve the associated inverse optics problem. In the method, an axisymmetric wave surface is re-constructed by analyzing the refracted laser sheet. The assumptions, simplifications, and constraints are taken to be compatible with experimental aspects for future validation. It is derived using the fundamental concepts in physics and the only major assumption of the axisymmetric nature of wave surface. The method exploits the underlying symmetry in the topography, making it more versatile, and suited for linear and non-linear capillary waves and waves with planar wavefront. The impact of parameters on the final result is determined through numerical simulations. Very low error (average and maximum) values are observed between reference and reconstructed topography for damped and undamped wave surfaces with a wide range of curvatures. Optimum values of critical parameters and associated reasoning are presented.

The displacement of a shear-thinning fluid by a denser and less viscous Newtonian fluid in a vertical duct is investigated using experiments and numerical simulations. We study how shear-thinning and increased viscosity contrast between the fluids affect the displacement. Our results show that the degree of shear-thinning significantly influences the development of interfacial patterns and the growth of perturbations. In the weakly shear-thinning regime, the displacement progresses as a stable displacement with no visible instabilities. Increasing the viscosity of the displaced fluids result in a Saffman–Taylor type instability with several finger-shaped channels carved across the width of the duct. In the strongly shear-thinning regime, a unique viscous finger with an uneven interface is formed in the middle of the displaced fluid. This finger eventually breaks through at the outlet, leaving behind considerably stagnant wall layers at the duct side walls. We link the onset of viscous fingering instability to the viscosity contrast between the fluids, and the stabilizing density difference, as expressed through a modified, unperturbed pressure gradient for the two fluids. Numerical simulations are performed with both an initial flat interface, and with a perturbed interface, and we find good qualitative agreement between experimental observations and computations.