Numerical Investigation of Effects of the Gas–Liquid Viscosity Ratio on the Rheological Properties of Bubbly Suspensions

The bubbly suspension is a gas–liquid mixture such that the bubbles are dispersed in a continuous liquid phase; it is widely used in industrial applications. When the bubbles happen to deform under shear, the flow structure of suspensions is altered. In turn, this can further change the rheological properties of bubbly suspensions. In this paper, the effects of the capillary number Ca and the gas–liquid viscosity ratio λ on bubble deformation and rheological properties are investigated based on a three-dimensional parallel plate Couette flow model using the volume-of-fluid method. When Ca = 0.05 and 0.1, the deformation parameter D is less affected by λ, D ≈ 0.05 and 0.1, so after stabilization the bubble shape is approximately spherical. When Ca is in the range of 0.4–2.5, D first increases and then decreases with increase in λ, and its deflection angle decreases first and then remains stable. For large viscosity ratios (λ = 5 and 10), the effect of Ca on D is small. As λ decreases (i.e., λ ≤ 2), the effect of Ca on D increases. At a small λ, the deformation parameter D gradually increases as the capillary number Ca increases. However, when Ca is large enough to reach a certain value of D ≈ 1, the bubble shape does not show a significant change. The relative viscosity of bubbly suspension η_r is closely related to the bubble shape (characterized by Ca) and the viscosity of gas inside the bubble (characterized by λ). When λ is certain, η_r decreases with increase in Ca (in the range of 0.05–2.5), and the larger Ca is, the smaller η_r. For 1 < λ < 10, although η_r decreases with increase in Ca, the minimum value of η_r is always greater than 1. As λ decreases, η_r is closer to 1. When λ ≤ 0.5, η_r decreases with increase in Ca, and the minimum value of η_r is less than 1. When Ca is certain, the shear stress at the gas–liquid interface increases as λ becomes large, and the resistance to the flow of the surrounding fluid increases; and thus the larger λ, the larger η_r. The injection of bubbles changes the rheological properties of suspensions and causes the first normal stress N₁. The first normal stress N₁ follows the distribution pattern of increasing first and then decreasing. At the same Ca, the larger λ, the smaller N₁.