An Experimental Study of 2D Radial Flow of a Yield Stress Fluid Between Parallel Disks

During the design phase in rock grouting applications (e.g. for tunnels), analytical and numerical techniques based on inputs from the rock mass characterization and grout flow properties are used to estimate the grout spread. The design process is complicated by the fact that the exact geometry (network of fractures) within the rock mass is not completely known. In addition, the rheological flow properties of commonly used cement-based grouts are complex due to thixotropy and hydration. In such cases, simplified one-dimensional (1D) and two-dimensional 2D fracture geometries are used as a basis for the design solution. As for cement grouts, their rheological behavior is normally described by simplified constitutive laws e.g. the Bingham model. Several analytical solutions for 1D channel flow and 2D radial flow of cement grouts have been presented in the literature describing the spread of grouts in fractures. Experimentally, only a limited amount of work has been carried out to study idealized yield stress fluid (YSF) flow between stationary parallel disks. The importance of such tests is that they facilitate the verification of analytical solutions and their limitations. Thus, in order to investigate in principle, the nature of 2D Bingham fluid velocity profiles in radial flow, we carried out for apparently the first time ultrasound velocimetry measurements within the constraints of an experimental model. The radial flow region was formed by the gap (aperture) between two parallel acrylic glass (Plexiglas) disks, each with a diameter of 1 meter and a thickness of 25 mm. The disk separation was attained from a variable height metallic spacer configuration. Ultrasound velocity profiling (UVP) was used for flow visualization through the measurement of velocity profiles of a model yield stress fluid (Carbopol) at different radial positions. The results are a comparison of the measured velocity profiles with those from analytical solutions. Of particular interest is the plug-flow region of the radial velocity profiles along the radial length (diameter) of the parallel disks. The current observations show a distinct plug region, coupled with wall slip effects for the Carbopol model YSF fluid that was used. The theoretically predicted velocity profiles are lower than the measured ones, however within a reasonably similar magnitude range. The main discrepancies between the theoretical predictions and measured data are then discussed. Future studies would then be targeted at improving the current experimental setup, for detailed measurements of the plug-flow region along the radial length, which remains a generally challenging issue for studies on YSFs and more specifically for rock grouting design. Moreover, considering roughened walls to significantly reduce wall slip that was present in the current study will also be part of the project's continuation.