From breakup to coiling and buckling regimes in buoyant viscoplastic injections

Abstract

We study the injection flow of a heavy viscoplastic fluid into a light Newtonian fluid, via modelling and experiments. The injection is carried out downward, via an eccentric inner pipe inside a vertical closed-end outer pipe. This configuration results in a core viscoplastic fluid surrounded by an annular Newtonian fluid. The flow is structured and mixing is negligible. As the injection rate increases in a typical experiment, we observe three distinct flow regimes, associated with the core fluid behaviour, namely the breakup, coiling and buckling (bulging) regimes. In the breakup regime, the core fluid is yielded due to the extension caused by buoyancy, while in the buckling regime the yielding occurs due to the compression promoted by the pressure and the interfacial shear stress applied by the upward flow of the annular fluid. For the coiling regime, the core fluid remains largely unyielded until it exhibits a coiling behaviour. We develop a lubrication approximation model, using the Herschel–Bulkley constitutive equation, with dimensionless flow parameters including the Bingham number, the power-law index, the buoyancy number, the viscosity ratio, the diameter ratio, the eccentricity and the aspect ratio. Based on a reasonable prediction to the yielding onset, the model allows us to classify the flow regimes versus an elegant combination of the dimensionless numbers.

Viscoplastic fluid displacement flow in pipes : the effects of pipe axial

“…A wide angle lens digital camera (Basler acA2040 with 2 12 gray-scale levels) is utilized to capture the flow development, and it is connected to the computer to deliver/record the experimental images. To make the Carbopol solution, Carbopol powder is initially mixed with deionized water-sugar solution and then the mixture is neutralized with sodium hydroxide (NaOH), based on established methods [13]. A digital rheometer (DHR-3 TA Instrument) with a parallel-plate geometry with the diameter of 40 (mm) and the mean gap of 1 (mm) is utilized.…”

“…A digital rheometer (DHR-3 TA Instrument) with a parallel-plate geometry with the diameter of 40 (mm) and the mean gap of 1 (mm) is utilized. To avoid any wall slip effects at low shear rates, fine sandpapers are attached to the surface of the plates as rough surfaces [13] . The flow curve of the Carbopol solution, obtained from the rheometer measurements, is illustrated in Fig.…”

“…First, as previously mentioned, there is a general lack of knowledge regarding the effects of pipe rotation on displacement flows. Second, previous studies have largely focused on the displacement flow of viscoplastic fluids by Newtonian fluids [7], with only a few investigating the displacement of a Newtonian fluid by a viscoplastic fluid [12,13]. Given the poorly developed state of the literature on these two aspects, we seek to experimentally study the buoyant miscible displacement flow of a Newtonian fluid (water) by a viscoplastic fluid (Carbopol solution) in a vertical pipe with axial rotation, with potential applications in the primary well cementing process [1].…”

Tailoring Alginate-Gelatin Hydrogels to Precisely Modulate Osteogenesis in Dental Pulp Stem Cells While Preserving Other Cellular Behaviors

“…Circular hydrogels were obtained from crosslinked samples by puncturing the hydrogels with a steel hollow punch with an internal diameter of 20 mm. Sandpaper (80 grit) was pasted on the surface of the parallel plates to avoid the samples' slipperiness during the measurements [21]. Storage modulus (G') and loss modulus (G'') were measured on an amplitude sweep oscillatory test ranging from 0.1 to 10 % strain using an angular frequency of 1 rad/s at 37 °C.…”