期刊
MICROFLUIDICS AND NANOFLUIDICS
卷 22, 期 6, 页码 -出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10404-018-2084-y
关键词
Film thickness; Droplet velocity; Pressure drop; Lubrication theory; Numerical simulations
资金
- ERC [SIM-COMICS 280117]
- Swedish Research Council [2015-06334]
- Swedish Research Council [2015-06334] Funding Source: Swedish Research Council
The aim of this study is to derive accurate models for quantities characterizing the dynamics of droplets of non-vanishing viscosity in capillaries. In particular, we propose models for the uniform-film thickness separating the droplet from the tube walls, for the droplet front and rear curvatures and pressure jumps, and for the droplet velocity in a range of capillary numbers, Ca, from to 1 and inner-to-outer viscosity ratios, , from 0, i.e. a bubble, to high-viscosity droplets. Theoretical asymptotic results obtained in the limit of small capillary number are combined with accurate numerical simulations at larger Ca. With these models at hand, we can compute the pressure drop induced by the droplet. The film thickness at low capillary numbers () agrees well with Bretherton's scaling for bubbles as long as . For larger viscosity ratios, the film thickness increases monotonically, before saturating for to a value times larger than the film thickness of a bubble. At larger capillary numbers, the film thickness follows the rational function proposed by Aussillous and Qu,r, (Phys Fluids 12(10):2367-2371, 2000) for bubbles, with a fitting coefficient which is viscosity-ratio dependent. This coefficient modifies the value to which the film thickness saturates at large capillary numbers. The velocity of the droplet is found to be strongly dependent on the capillary number and viscosity ratio. We also show that the normal viscous stresses at the front and rear caps of the droplets cannot be neglected when calculating the pressure drop for Ca > 10(-3).
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