Droplet mobilization in actuated deformable tubes

TL;DR

The paper addresses controlled oil-droplet transport in a deformable, constricted tube by comparing hydrodynamic actuation and dynamic-wall actuation using a high-resolution NSCH–FSI framework. It reveals that oscillatory body forcing monotonically increases mobilization time with frequency while decreasing it with amplitude, whereas oscillatory follower-wall traction exhibits a resonance that minimizes mobilization time near the tube’s natural frequency, with amplitude primarily reducing time off-resonance. The work develops a rigorous axisymmetric, phase-field model including dynamic wettability and follower-load boundary conditions, and provides a phase diagram to guide actuation parameter selection for fast, intact droplet mobilization. These results offer actionable insights for microfluidic control, enhanced oil recovery, and SAW-based droplet manipulation, and suggest future exploration of adaptive, waveform-variant actuation and networks of deformable constrictions.

Abstract

We study the mobilization of an oil droplet in a deformable, actuated constricted tube subjected to two different actuation mechanisms: hydrodynamic actuation (oscillatory body force in the fluid) and dynamic wall actuation (oscillatory traction on the tube walls). Using high-resolution fluid-structure interaction simulations, we analyze the effects of actuation frequency and amplitude on droplet transport through the constriction. Our simulations show that hydrodynamic actuation leads to a monotonic increase in the droplet's mobilization time with increasing actuation frequency, and a decrease with increasing actuation amplitude. In contrast, dynamic wall actuation exhibits a resonance effect-the mobilization time reaches a minimum at a frequency near the tube's resonant frequency. Our study highlights the potential of actuation mechanisms in deformable tubes for precise control of droplet transport in bio-microfluidic applications.

Figures (11)

• Figure 1: Mobilization of a droplet in a constricted deformable capillary tube subjected to two distinct oscillatory actuation mechanisms. Panel (a) shows the hydrodynamic actuation mechanism via oscillatory forcing in the fluid (arrows shown in yellow). Panel (b) shows the dynamic wall actuation mechanism enabled by imposing a follower load on the tube wall (arrows shown in blue). In panels (a–b), the droplet’s initial position is shown in gray. The black dashed lines indicate the droplet’s position when the inertial component from the actuation is in the direction of the external pressure drop $\Delta \hat{p}_\text{v}$, whereas the black dotted lines denote its position when the inertial component from the actuation opposes $\Delta \hat{p}_\text{v}$. The white dotted line represents the centerline axis of the tube. The droplet size in the figure at different positions is not drawn to scale.
• Figure 2: Schematic of the two-dimensional axisymmetric computational domain, initial conditions and geometrical parameters used in our numerical simulations. The oscillatory fluid-forcing case is enabled by applying an oscillatory body force in the fluid (yellow arrows). The dynamic wall-actuation case is enabled by imposing a follower-load boundary condition on the tube wall (blue arrows).
• Figure 3: (a) Plot of droplet mobilization time ($t_\text{mob}$) in a soft constricted capillary tube versus forcing frequency $\overline{\omega}$, for both partial and complete droplet mobilization regimes. (b) Snapshots of the droplet motion for different values of $\overline{\omega}$. The bubble colored in white is shown by the level set $c = 0$ while the tube is shown in brown. The three-dimensional rendering is generated by revolving our two-dimensional axisymmetric simulation result about the symmetry axis. To illustrate the droplet movement, we show a sliced view of the three-dimensional tube.
• Figure 4: (a) Time evolution of the droplet's axial center of mass $\overline{z}_\text{d}$ for different values of forcing frequency $\overline{\omega}$. The black colored circular marker denotes the point of droplet breakup. However, the black colored square marker denotes the point when the droplet's contact separates from the tube walls. (b) Time variation of the primary droplet Taylor deformation parameter $D_\mathrm{ta}$. For $\overline{\omega} = 0.015$ (partial mobilization), $D_\mathrm{ta}$ is measured for the primary droplet until its breakup. For the other cases of $\overline{\omega}$ (complete mobilization), however, $D_\mathrm{ta}$ is computed until the droplet loses contact with the tube walls. The inset illustrates the definitions of droplet length ($L_\mathrm{d}$) and height ($H_\mathrm{d}$) used in Taylor deformation parameter ($D_\mathrm{ta}$), shown in a two-dimensional axisymmetric view of the tube.
• Figure 5: (a) Plot of droplet mobilization time ($t_\text{mob}$) in a soft constricted capillary tube versus forcing amplitude $\overline{H}_\omega$, for both partial and complete droplet mobilization regimes. (b) Snapshots of the droplet's motion for different values of $\overline{H}_\omega$. The bubble colored in white is shown by the level set $c = 0$ while the soft tube is colored in brown. The three-dimensional rendering is generated by revolving our two-dimensional axisymmetric simulation result about the symmetry axis. To illustrate the droplet movement, we show the sliced view of the three-dimensional tube.