ABSTRACT
We study here experimentally, numerically and using a lubrication approach, the shape, velocity and lubrication film thickness distribution of a droplet rising in a vertical Hele-Shaw cell. The droplet is surrounded by a stationary immiscible fluid and moves purely due to buoyancy. A low density difference between the two media helps to operate in a regime with capillary number Ca lying between 0.03 and 0.35, where Ca =µo Ud /γ is built with the surrounding oil viscosity γ0 , the droplet velocity Ud and surface tension γ. The experimental data show that in this regime the droplet velocity is not influenced by the thickness of the thin lubricating film and the dynamic meniscus. For iso-viscous cases, experimental and three-dimensional numerical results of the film thickness distribution agree well with each other. The mean film thickness is well captured by the Aussillous & Quéré (Phys. Fluids, vol. 12 (10), 2000, pp. 2367-2371) model with fitting parameters. The droplet also exhibits the 'catamaran' shape that has been identified experimentally for a pressure-driven counterpart (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501). This pattern has been rationalized using a two-dimensional lubrication equation. In particular, we show that this peculiar film thickness distribution is intrinsically related to the anisotropy of the fluxes induced by the droplet's motion.
ABSTRACT
Inertial microfluidics is an active field of research that deals with crossflow positioning of the suspended entities in microflows. Until now, the majority of the studies have focused on the behavior of rigid particles in order to provide guidelines for microfluidic applications such as sorting and filtering. Deformable entities such as bubbles and droplets are considered in fewer studies despite their importance in multiphase microflows. In this paper, we show that the trajectory of bubbles flowing in rectangular and square microchannels can be controlled by tuning the balance of forces acting on them. A T-junction geometry is employed to introduce bubbles into a microchannel and analyze their lateral equilibrium position in a range of Reynolds (1 < Re < 40) and capillary numbers (0.1 < Ca < 1). We find that the Reynolds number (Re), the capillary number (Ca), the diameter of the bubble (D[combining macron]), and the aspect ratio of the channel are the influential parameters in this phenomenon. For instance, at high Re, the flow pushes the bubble towards the wall while large Ca or D[combining macron] moves the bubble towards the center. Moreover, in the shallow channels, having aspect ratios higher than one, the bubble moves towards the narrower sidewalls. One important outcome of this study is that the equilibrium position of bubbles in rectangular channels is different from that of solid particles. The experimental observations are in good agreement with the performed numerical simulations and provide insights into the dynamics of bubbles in laminar flows which can be utilized in the design of flow based multiphase flow reactors.
