A New Model for Predicting the Maximum Gas Entrapment Concentration in a Yield Stress Fluid

Summary Gas entrapment is a typical phenomenon in gas-yield stress fluid two-phase flow, and most of the related research focuses on the entrapped condition of the single bubble. However, the amount of entrapped gas, which is more meaningful for engineering, is rarely involved. In this paper, a theoretical model for calculating the maximum gas entrapment concentration (MGEC) is established for the first time. The critical distance between horizontal and vertical entrapped bubbles was determined by the yielded region caused by the buoyancy and the coupled stress field around the multiple bubbles. The MGEC is the ratio of a single bubble volume to its domain volume, which is calculated from the distance between the vertical and the horizontal bubbles. By comparing with the experimental results, the average error of MGEC calculated by this model is 4.42%, and the maximum error is 7.32%. According to the prediction results of the model, an empirical equation that can be conveniently used for predicting MGEC is proposed.

Flow onset for a single bubble in a yield-stress fluid

We use computational methods to determine the minimal yield stress required in order to hold static a buoyant bubble in a yield-stress liquid. The static limit is governed by the bubble shape, the dimensionless surface tension ( $\gamma$ ) and the ratio of the yield stress to the buoyancy stress ( $Y$ ). For a given geometry, bubbles are static for $Y > Y_c$ , which we determine for a range of shapes. Given that surface tension is negligible, long prolate bubbles require larger yield stress to hold static compared with oblate bubbles. Non-zero $\gamma$ increases $Y_c$ and for large $\gamma$ the yield-capillary number ( $Y/\gamma$ ) determines the static boundary. In this limit, although bubble shape is important, bubble orientation is not. Two-dimensional planar and axisymmetric bubbles are studied.

A Printable and Conductive Yield-Stress Fluid as an Ultrastretchable Transparent Conductor

In contrast to ionically conductive liquids and gels, a new type of yield-stress fluid featuring reversible transitions between solid and liquid states is introduced in this study as a printable, ultrastretchable, and transparent conductor. The fluid is formulated by dispersing silica nanoparticles into the concentrated aqueous electrolyte. The as-printed features show solid-state appearances to allow facile encapsulation with elastomers. The transition into liquid-like behavior upon tensile deformations is the enabler for ultrahigh stretchability up to the fracture strain of the elastomer. Successful integrations of yield-stress fluid electrodes in highly stretchable strain sensors and light-emitting devices illustrate the practical suitability. The yield-stress fluid represents an attractive building block for stretchable electronic devices and systems in terms of giant deformability, high ionic conductivity, excellent optical transmittance, and compatibility with various elastomers.

Clouds of bubbles in a viscoplastic fluid

Viscoplastic fluids can hold bubbles/particles stationary by balancing the buoyancy stress with the yield stress – the key parameter here is the yield number $Y$ , the ratio of the yield stress to the buoyancy stress. In the present study, we investigate a suspension of bubbles in a yield-stress fluid. More precisely, we compute how much is the gas fraction $\phi$ that could be held trapped in a yield-stress fluid without motion. Here the goal is to shed light on how the bubbles feel their neighbours through the stress field and to compute the critical yield number for a bubble cloud beyond which the flow is suppressed. We perform two-dimensional computations in a full periodic box with randomized positions of the monosized circular bubbles. A large number of configurations are investigated to obtain statistically converged results. We intuitively expect that for higher volume fractions, the critical yield number is larger. Not only here do we establish that this is the case, but also we show that short-range interactions of bubbles increase the critical yield number even more dramatically for bubble clouds. The results show that the critical yield number is a linear function of volume fraction in the dilute regime. An algebraic expression model is given to approximate the critical yield number (semi-empirically) based on the numerical experiment in the studied range of $0\le \phi \le 0.31$ , together with lower and upper estimates.