Buoyancy-Driven Motion of Viscous Drops through Cylindrical Capillaries at Small Reynolds Numbers

Motion of an Elastic Capsule in a Trapezoidal Microchannel Under Stokes Flow Conditions

Even though the research interest in the last decades has been mainly focused on the capsule dynamics in cylindrical or rectangular ducts, channels with asymmetric cross-sections may also be desirable especially for capsule migration and sorting. Therefore, in the present study we investigate computationally the motion of an elastic spherical capsule in an isosceles trapezoidal microchannel at low and moderate flow rates under the Stokes regime. The steady-state capsule location is quite close to the location where the single-phase velocity of the surrounding fluid is maximized. Owing to the asymmetry of the trapezoidal channel, the capsule's steady-state shape is asymmetric while its membrane slowly tank-treads. In addition, our investigation reveals that tall trapezoidal channels with low base ratios produce significant off-center migration for large capsules compared to that for smaller capsules for a given channel length. Thus, we propose a microdevice for the sorting of artificial and physiological capsules based on their size, by utilizing tall trapezoidal microchannels with low base ratios. The proposed sorting microdevice can be readily produced via glass fabrication or as a microfluidic device via micromilling, while the required flow conditions do not cause membrane rupture.

Dewetting film dynamics inside a capillary using a micellar nanofluid

An experimental study was performed in which hexadecane was displaced by a micellar nanofluid in a glass capillary. Experiments have shown that a thick film was formed on the capillary wall after hexadecane was displaced by the nanofluid. The thick hexadecane film is unstable, and over time it breaks and forms a thin film. Once the thick film ruptures, it retracts and forms an annular rim (liquid ridge) that collects liquid. As the volume of the annular rim increases over time, it forms a double-concave meniscus across the capillary and dewetting stops. The thin film on the right side of the double-concave meniscus then breaks and the contact angle increases. The process repeats until the droplets build up all along the capillary wall. Finally, the droplets are displaced from the capillary wall by the nanofluid and spherical droplets appear inside the capillary. This is a novel phenomenon because we did not observe any film formation when we used a solution without micelles. The theoretical model based on the lubrication approximation using the capillary pressure gradient was developed to estimate the annular rim dewetting velocity. The predicted dewetting velocity is found to be in fair agreement with the experimentally measured value.

Viscosity-ratio-based scaling for the rise velocity of a Taylor drop in a vertical tube

Simulations of a silicon oil Taylor drop rising in a tube filled with a glycerol-water mixture are performed to investigate the viscosity ratio effects on the rise velocity of the Taylor drop. By varying the viscosity ratio λ between the drop and the suspending liquid from O(0.1) to O(10), a simple relationship of the nondimensional terminal velocity, the Froude number (Fr), is revealed as Fr ∝ λ(-0.27). This scaling is further confirmed by recently published experimental data [Hayashi, Kurimoto, and Tomiyama, Int. J. Multiphase Flow 37, 241 (2011)]. The simulated drop shapes also compare well with the experiments. Increasing the viscosity ratio elongates the drop and tends to make the tail bulge out. The correlation applies to small Reynolds numbers and finite viscosity ratios.

Coalescence of Bubbles Translating through a Tube

The results of an experimental study of the interaction and coalescence of two air bubbles translating in a cylindrical tube are presented. Both pressure- and buoyancy-driven motion of the two bubbles in a Newtonian suspending fluid within the tube are considered. The close approach of the two bubbles is examined using image analysis, and measurements of the coalescence time are reported for various bubble size ratios and capillary numbers. For pressure-driven motion of bubbles, coalescence is found to occur in an axisymmetric configuration for all bubble size ratios considered in the experiments. For buoyancy-driven motion, on the other hand, the disturbance flow behind the leading bubble causes the trailing bubble to move radially out toward the tube wall when the trailing bubble size becomes very small compared to the size of the leading bubble. In that case, coalescence occurs in a nonaxisymmetric configuration, with a time scale for coalescence that is substantially larger than that for coalescence in the axisymmetric configuration. When the imposed flow is in the direction of the buoyancy force, coalescence time is independent of bubble size ratio, and decreases as the capillary number increases. Experimental measurements of the radius of the thin liquid film separating the two bubbles are used in conjunction with a simple film drainage model to predict the dependence of the coalescence time on the bubble size ratio.

Surfactant Effect on the Buoyancy-Driven Motion of Bubbles and Drops in a Tube

The effect of surfactants on the buoyancy-driven motion of bubbles and drops in a vertical tube is experimentally examined. The terminal velocities of fluid particles are measured and their steady shapes are quantitatively characterized in systems with various bulk-phase concentrations of surfactant. In the case of air bubbles, the presence of surfactant retards the motion of small bubbles due to the development of adverse Marangoni stresses, whereas it enhances the motion of large bubbles by allowing them to deform away from the tube wall more easily. For viscous drops, the surfactant-enhanced regime of particle motion becomes more pronounced in the sense that the terminal velocity becomes more sensitive to surfactant concentration, whereas the surfactant effect in the surfactant-retarded regime becomes weaker.