Dielectrophoretic Trapping of a Floating Liquid Marble

A liquid marble, a liquid droplet coated with hydrophobic powder, is an emerging digital microfluidic platform. It can potentially serve as a mixer or reactor for chemical and biological assays in the microscale. Automated manipulation of liquid marbles is essential for the implementation of more microfluidic functions in the technology platform of “lab in a marble”. We report the analytical and experimental results of trapping a floating liquid marble using dielectrophoresis in a nonuniform electric field. Liquid marbles with volumes ranging from 5 to $50\mu \mathrm{L}$ are effectively trapped by the dielectrophoretic force from a horizontal distance ranging from 10 to 60 $\mathrm{mm}$ and under an applied voltage ranging from 1.6 to 5 $\mathrm{kV}$. A one-dimensional analytical model is then proposed for the trapping process and agrees well with experimental data. Finally, based on the relationship between the static friction coefficient and the Bond number of a floating liquid marble, an operation map is derived for successful trapping of the liquid marble, providing a better insight into controlled manipulation of liquid marbles.

Figure 1

The experimental setup for DEP trapping of a floating LM.

Figure 2

Schematic of the DEP trapping concept and the corresponding electric field distribution from a 2D analytical model. (a) The free body diagram of a floating LM and an electrode under a nonuniform electric field in the cylindrical coordinate system. (b) The 2D axisymmetric electric field generated by the analytical model. (c) The curve of horizontal DEP force $F_{\mathrm{DEP}-r}$ versus LM position $r$ in the electric field.

Figure 3

The DEP trapping process of a floating LM (10-$\mu \mathrm{L}$ volume, 30-$\mathrm{mm}$ distance, and 4-$\mathrm{kV}$ applied voltage). (a) The position of the LM during the trapping process. (b) The corresponding velocity of the LM. (c) The corresponding acceleration of the LM. (d) The oscillation of the floating LM relative to the electrode and fitting with a DSHM solution (the starting point is set as the first time that the LM is trapped under the electrode center line).

Figure 4

The theoretical electric field distribution of DEP trapping of a floating LM and the corresponding force fitting (15-$\mu \mathrm{L}$ volume and 5-$\mathrm{kV}$ applied voltage). (a) The theoretical electric field distribution. (b) The corresponding real-time DEP force curve from experimental data (blue points) and nonlinear parameter fitting outcome (green solid line), as well as the simulation result from the theoretical model (red solid line).

Figure 5

The calculated DEP force from experimental data in various experiments and the corresponding theoretical data of the model as well as the static friction coefficient fitting. (a) DEP force versus marble volume (5–50 $\mu \mathrm{L}$) at 5-$\mathrm{kV}$ applied voltage and 10-$\mathrm{mm}$ distance. (b) DEP force versus the square of applied voltage (1.6–5 $\mathrm{kV}$) at 10-$\mu \mathrm{L}$ marble volume and 10-$\mathrm{mm}$ distance. (c) The relationship of the static friction coefficient and the Bond number of floating LMs in DEP trapping (logarithmic coordinates).

Figure 6

Operation maps of DEP trapping of floating LMs with various volumes. (a) 5-$\mu \mathrm{L}$ LM trapping. (b) 10-$\mu \mathrm{L}$ LM trapping. (c) 15-$\mu \mathrm{L}$ LM trapping. (d) 20-$\mu \mathrm{L}$ LM trapping. (e) 30-$\mu \mathrm{L}$ LM trapping. (f) 50-$\mu \mathrm{L}$ LM trapping. Blue solid points represent the successful trapping in experiments, while red solid triangles are unsuccessful experimental counterparts. Blue open circles and red open triangles represent the successful and unsuccessful trapping cases predicted by the analytical model, respectively.

Figure 7

(a),(b) Images of sessile and floating 10-$\mu \mathrm{L}$ LMs and (c),(d) sessile and floating 30-$\mu \mathrm{L}$ LMs.

Figure 8

Dynamic analysis on DEP trapping of floating LMs with various experimental parameters. (a) The trends of displacement, velocity, and acceleration with time of 10-$\mu \mathrm{L}$ LMs trapped from 10, 30, and 50-$\mathrm{mm}$ distances under 4-$\mathrm{kV}$ applied voltage. (b) The trends of displacement, velocity, and acceleration with time of 30-$\mu \mathrm{L}$ LMs trapped from 10, 30, and 50-$\mathrm{mm}$ distances under 4-$\mathrm{kV}$ applied voltage. (c) The trends of displacement, velocity, and acceleration with time of 50-$\mu \mathrm{L}$ LMs trapped from 10, 30, and 50-$\mathrm{mm}$ distances under 4-$\mathrm{kV}$ applied voltage. (d) The trends of displacement, velocity, and acceleration with time of 10-$\mu \mathrm{L}$ LMs trapped at 1.6- to 5-$\mathrm{kV}$ applied voltages from 50-$\mathrm{mm}$ distance.