Experiments in Fluids

, 59:141 | Cite as

Control of droplet movement on an inclined wall with sawtoothed wettability pattern by applying ultrasonic vibration

  • Kenji KatohEmail author
  • Hiroki Tamura
  • Eriko Sato
  • Tatsuro Wakimoto
Research Article


This study deals with the control of the movement of liquid droplets rolling down an inclined plate based on the differences in the wettability of the plate. We used a photoreactive polymer poly(7-methacryloyloxy coumarin) (PMC) whose molecular structure can be changed reversibly to realize different wettabilities by ultraviolet irradiation. We proposed employing sawtooth patterns at boundaries between areas with different contact angles to control the droplet trajectory. Furthermore, we experimentally observed that the droplet moves along a line inclined to the direction of gravity. The droplet behavior can be analyzed using a theoretical model based on the droplet dynamics wherein the surface tension acting on the contact line and the gravitational force are considered. The theoretical results suggest that inclination from the gravitational direction can be increased if the advancing contact angle is reduced. In the experiments conducted herein, ultrasonic vibration was applied to the inclined plate to reduce the contact angle hysteresis. The results showed that the advancing contact angle actually decreased and that the droplet trajectory was controlled to realize motion along a line with inclination angle almost twice of that realized without vibration.

Graphical abstract

A saw-tooth pattern of boundary between the areas with different contact angles was proposed to control the trajectory of a droplet rolling down on an inclined plate. As shown in the right figure, the droplet immediately diverges from the direction of gravity and moves in accordance with the target lines.

Roman symbols


Maximum width of a droplet [m]


Vector of the force applied to a droplet [N]


Gravitational acceleration [m/s2]


Ratio of straight part of contact line to the radius of the arc-like contact line [-]


Radius of arc-like contact line [m]


Liquid volume [m3]


Coordinate on the plate surface in the direction of gravity [m]


Coordinate on the plate surface in transverse direction [m]

Greek symbols

α (= 45°)

Oblique angle of the UV-irradiated area in Pattern A [°]


Inclination angle of moving droplet [°]


Variation in the contact angle [°]


Center angle of the arc-like contact line (advancing side, ref. Fig. 4) [°]


Contact angle [°]


Target inclination angle of droplet movement [°]


Liquid density [kg/m3]


Surface tension [N/m]


Inclination angle of the test plate [°]


Center angle of the arc giving the receding contact angle (receding side, ref. Fig. 4) [°]









Gravity direction on the plate surface


Transverse direction on the plate surface



A part of this research was supported by Japan Society for the Promotion of Science (JSPS) Grant Number 15K05802.

Supplementary material

Supplementary material 1 (MP4 598 KB)


  1. Abdelgawad M, Park P, Wheeler R (2009) Optimization of device geometry in single-plate digital microfluidics. J Appl Phys 105:094506. CrossRefGoogle Scholar
  2. Abgrall P, Gué AM (2007) Lab-on-chip technologies: making a microfluidic network and coupling it into a complete microsystem—a review. J Micromech Microeng 17:R15–R49. CrossRefGoogle Scholar
  3. Agapov RL, Boreyko JB, Briggs DP, Srijanto BR, Retterer ST, Collier CP, Lavrik NV (2014) Length scale selects directionality of droplets on vibrating pillar ratchet. Adv Mater Interfaces 1:1400337. CrossRefGoogle Scholar
  4. Bhaumik SK, Das S, Chakraborty S, Das Gupta S (2014) Droplet transport through dielectrophoretic actuation using line electrode. Microfluid Nanofluidics 16:597–603. CrossRefGoogle Scholar
  5. Chen JZ, Troian SM, Darhuber AA, Wagner S (2005) Effect of contact angle hysteresis on thermocapillary droplet actuation. J Appl Phys 97:014906. CrossRefGoogle Scholar
  6. Darhuber AA, Troian SM (2005) Principles of microfluidic actuation by modulation of surface stresses. Annu Rev Fluid Mech 37:425–455. MathSciNetCrossRefzbMATHGoogle Scholar
  7. Datta S, Das AK, Das PK (2015) Uphill movement of sessile droplets by electrostatic actuation. Langmuir 31:10190–10197. CrossRefGoogle Scholar
  8. Dong Y, Holmes HR, Böhringer KF (2017) Converting vertical vibration of anisotropic ratchet conveyors into horizontal droplet motion. Langmuir 33:10745–10752. CrossRefGoogle Scholar
  9. Fobel R, Fobel C, Wheeler AR (2013) Dropbot: an open-source digital microfluidic control system with precise control of electrostatic driving force and instantaneous drop velocity measurement. Appl Phys Lett 102:193513. CrossRefGoogle Scholar
  10. Gupta S, Ramesh K, Ahmed S, Kakkar V (2016) Lab-on-chip technology: a review on design trends and future scope in biomedical applications. Int J Bio-Sci Bio-Technol 5:311–322. CrossRefGoogle Scholar
  11. Higashine M, Katoh K, Wakimoto T, Azuma T (2008) Profiles of liquid droplets on solid plates in gravitational and centrifugal fields. J JSEM 8(Special Issue):49–54. Google Scholar
  12. Hutama TJ, Oleschuk RD (2017) Magnetically manipulated droplet splitting on a 3D-printed device to carry out a complexometric assay. Lab Chip 17:2640–2649. CrossRefGoogle Scholar
  13. Jain V, Devarasetty V, Patrikar R (2017) Effect of electrode geometry on droplet velocity in open EWOD based device for digital microfluidics applications. J Electrost 87:11–18. CrossRefGoogle Scholar
  14. Karapetsas G, Chamakos NT, Papathanasiou AG (2017) Thermocapillary droplet actuation: effect of solid structure and wettability. Langmuir 33:10838–10850. CrossRefGoogle Scholar
  15. Katoh K, Higashine M, Nakamoto N, Azuma T (2006) On the sliding down of liquid drops on inclined plates (1st report, Critical inclination angle of plates). Trans Jpn Soc Mech Eng Ser B 72:1287–1294. CrossRefGoogle Scholar
  16. Katoh K, Wakimoto T, Masuda R (2010) A new method to actuate a droplet on a plate by use of laser and ultrasonic oscillation. Trans Jpn Soc Mech Eng Ser B 76:2135–2142. CrossRefGoogle Scholar
  17. Katoh K, Tamura H, Sato E, Wakimoto T (2016) Control of droplet movement on an inclined wall by difference of wettability. Jpn J Multiph Flow 29:451–459. CrossRefGoogle Scholar
  18. Lahoon S, Rio OI, Cheng P, Neumann AW (1996) Axisymmetric drop shape analysis (ADSA). In: Neumann AW, Spelt JK (eds) Applied surface thermodynamics surfactant science Series 63, pp 441–508, CRC Press, Boca RatonGoogle Scholar
  19. Lee JL, Lee S, Kang KH (2012) Droplet jumping by electrowetting and its application to the three-dimensional digital microfluidics. Appl Phys Lett 100:081604. CrossRefGoogle Scholar
  20. Li W, Lynch V, Thompson H, Fox MA (1997) Self-assembled monolayers of 7-(10-Thio- decoxy)coumarin on gold: synthesis, characterization, and photodimerization. J Am Chem Soc 119:7211–7217. CrossRefGoogle Scholar
  21. Lu HW, Glasner K, Bertozzi AL, Kim CJ (2007) A diffuse interface model for electrowetting drops in a Hele–Shaw cell. J Fluid Mech 590:411–435. CrossRefzbMATHGoogle Scholar
  22. Morrison H, Curtis H, McDowell T (1966) Solvent effects on the photodimerization of coumarin1. J Am Chem Soc 88:5415–5419. CrossRefGoogle Scholar
  23. Nahar MM, Nikapitiya JB, You SM, Moon H (2016) Droplet velocity in an electrowetting on dielectric digital microfluidic device. Micromachines 7:71. CrossRefGoogle Scholar
  24. Obi M, Morino S, Ichimura K (1999) Factors affecting photoalignment of liquid crystals induced by polymethacrylates with coumarin side chains. Chem Mater 11:656–664. CrossRefGoogle Scholar
  25. Pratap V, Moumen N, Subramanian RS (2008) Thermocapillary motion of a liquid drop on a horizontal solid surface. Langmuir 24:5185–5193. CrossRefGoogle Scholar
  26. Sato E, Nagai S, Matsumoto A (2012) Reversible volume changes of polymer thin films and their application to wettability control. In: 8th coatings science international conference book of abstracts, pp 83–86Google Scholar
  27. Sato E, Nagai S, Matsumoto A (2013) Reversible thickness control of polymer thin films containing photoreactive coumarin derivative units. Prog Org Coat 76:1747–1751. CrossRefGoogle Scholar
  28. Shastry A, Case MJ, Böhringer KF (2006) Directing droplets using microstructured surfaces. Langmuir 22:6161–6167. CrossRefGoogle Scholar
  29. Suzuki K, Homma H, Murayama T, Fukuda S, Takanobu H, Miura H (2010) Electrowetting-based actuation of liquid droplets for micro transportation systems. J Adv Mech Des Syst 4:365–372. CrossRefGoogle Scholar
  30. Volpe CD, Maniglio D, Morra M, Siboni S (2002) The determination of a ‘stable-equilibrium’ contact angle on heterogeneous and rough surfaces. Colloids Surf A Physicochem Eng Asp 206:47–67. CrossRefGoogle Scholar
  31. Wakimoto T, Sato Y, Katoh K (2013) A new method to actuate a droplet on a plate by use of laser irradiation to improve wettability. J JSEM 13:19–26. Google Scholar
  32. Xi HD, Zheng H, Guo W, Gañán-Calvo AM, Ai Y, Tsao CW, Zhou J, Li W, Huang Y, Nguyenh NT, Tan SH (2017) Active droplet sorting in microfluidics: a review. Lab Chip 17:751–771. CrossRefGoogle Scholar
  33. Yeo LY, Friend JR (2014) Surface acoustic wave microfluidics. Annu Rev Fluid Mech 46:379–406. MathSciNetCrossRefzbMATHGoogle Scholar
  34. Zhang Y, Nguyen NT (2017) Magnetic digital microfluidics—a review. Lab Chip 17:994–1008. CrossRefGoogle Scholar
  35. Zhao Y, Liu F, Chen CH (2011) Thermocapillary actuation of binary drops on solid surfaces. Appl Phys Lett 99:104101. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringOsaka City UniversityOsakaJapan
  2. 2.Department of Applied Chemistry and BioengineeringOsaka City UniversityOsakaJapan

Personalised recommendations