Application of space-time image analysis for measuring viscoplastic fluid flow in open channel

Abstract This article presents a non-intrusive image-based velocimetry methodology for the experimental characterization of viscoplastic fluid flows, enabling the measurement of velocity profiles along the flow depth and the estimation of flow rates under controlled laboratory conditions. The approach is based on the analysis of space-time images (STIs) and introduces a two-dimensional continuous wavelet transform (2D CWT) framework for the automatic extraction of streak orientation and corresponding flow velocities. The novelty of the proposed methodology lies in the formulation of the STI orientation and velocity extraction problem within a fully two-dimensional, multiscale wavelet-based framework. In contrast to conventional STI-based velocimetry approaches, which typically rely on Fourier-based analyses, Gaussian filtering, correlation techniques, or gradient-based methods for orientation detection, the proposed methodology formulates the velocity estimation problem. Velocity information is obtained directly from the dominant inclination patterns identified in the STI images, providing a systematic and automated procedure for velocity profile reconstruction. The methodology is applied to an extensive experimental dataset obtained from predominantly laminar Carbopol 996 flows in an inclined rectangular open channel. The resulting velocity profiles capture key features of viscoplastic flows, including plug regions, sheared layers, and basal slip effects. For validation purposes, the experimental results are compared with theoretical predictions derived from lubrication theory for Herschel–Bulkley fluids. The proposed STI-2D CWT approach contributes to the advancement of STI velocimetry by extending existing methodologies toward a robust two-dimensional wavelet-based analysis, offering a complementary framework for the investigation of complex viscoplastic free-surface flows.