Issue
Eur. Phys. J. Appl. Phys.
Volume 83, Number 1, July 2018
Materials for Energy harvesting, conversion and storage (Icome 2017)
Article Number 10903
Number of page(s) 4
Section Physics of Energy Transfer, Conversion and Storage
DOI https://doi.org/10.1051/epjap/2018180082
Published online 18 October 2018

© EDP Sciences, 2018

1 Introduction

If the insoluble particles are contained in droplets, they will form a certain deposition pattern on the surface of the substrate after evaporation. Different models can be applied in different fields, such as the coffee ring effect and the independent particle structure, which can be applied in the spray-ink printing [1] and the deposition process of DNA respectively. The potential application of sessile droplet evaporation in medicine is used for disease detection and diagnosis [2]. Brutin et al. studied the evaporation of whole blood droplets from different persons, obtaining diverse deposit pictures [3], and at the same time, the results of his study also pointed out that the mechanism of blood droplet evaporation could be used in forensic investigation [4]. Changing the internal parameters and external conditions are likely to produce a series of different deposition pattern, including the central aggregation type [5], combined structures and highly ordered organization of particles. Deegan et al. [6] found that for different experimental materials, the particles would move toward the edge, and form the cyclic deposition on the surface of substrate as long as three conditions were satisfied. The theoretical analysis and experimental study of Hu et al. [7] showed that the formation of deposition ring on the edge required not only the fixation of the contact line, but also the suppression of the Marangoni flow in the droplet.

Actually coffee ring pattern is formed due to the fixed contact line leading the particles radially outward flow in the suspension liquid [8,9]. The competition of the kinetics of evaporation and the interaction of the particles on the gas–liquid interface plays an important role in the formation of the uniform pattern [10]. Concentric ring is formed due to the fixation and movement of the triple-phase line [1113]. Bhardwaj et al. [14] proposed a phase diagram to predict how the deposit shapes resulting from the competition of three typical flow patterns. However, they did not make systematic experimental study or theoretical analysis of the effects of different substrate temperatures and the different droplets concentrations on the sedimentary patterns.

In this study, experimental work was performed. Besides, further analysis was made by quantitatively calculating the corresponding velocities of the radial flow [15], the Marangoni effect and Derjaguin–Landau–Verwey–Overbeek (DLVO) force.

2 Experimental method

The Al2O3–H2O nanofluid dispersion (Hangzhou Wanjing New Material Co. Ltd, an average diameter of 10 nm, a mass fraction of 20%) was diluted with deionized water into four different mass fractions of 0.05%, 0.2%, 1% and 3%. The nanofluids were stirred by the magnetic heating agitator (Jintan Zhongda Instrument Co. Ltd, 78-1) for one hour, and then vibrated by the ultrasonic cell disruptor (Nanjing Xianou Instrument Manufacturing Co. Ltd, XO-150) to make the particles well-dispersed. The droplets deposited on a slide glass surface whose temperature was controlled at 30 °C, 40 °C, 50 °C and 60 °C, respectively, with the thermostatic waterbath (Julabo, F12). The indoor temperature was 20 ± 0.2 °C, and the relative humidity was 30 ± 1%. The experiments with same parameters were repeated five times to ensure the reliability of the experiment.

The evaporation process of droplet was recorded by the droplet shape analyzer (KRUSS, DSA30), as shown in Figure 1, and then the evolution of contact angle and contact radius of the droplet with time were obtained by the measuring software.

After evaporation, the deposits were observed with the gem microscope (MOTIC, GM168, magnification 10–80 times) to get the whole deposit shapes.

thumbnail Fig. 1

The measurement equipment of the droplet in evaporation (DSA30 and Thermostatic Waterbath).

3 Results and discussion

3.1 Experimental results

Figure 2 shows 10 times larger pictures of deposition patterns taken by the gem microscope. For the lower concentration (0.05% and 0.2%), the coffee ring effect is more obvious, but for the higher concentrations (1% and 3%), concentric rings are formed. At the same temperature, the edge of the coffee ring becomes wide with the increasing of concentration, and for a constant concentration, the deposition of nanoparticles at the edge is more and more obvious with the increasing of substrate temperature.

thumbnail Fig. 2

The 10 times larger pictures of deposition patterns taken by the gem microscope.

3.2 Theoretical analysis

Based on the experimental data, the magnitude of three typical flow patterns is estimated by analytical relations. The flow and deposition of the nanoparticles at the three velocities are shown in the Figure 3 [14].

The dynamic viscosities of the nanofluid are given in Table 1 according to the computational formulas [1618].

thumbnail Fig. 3

Three convective mechanisms compete to form the deposit. In (1), a ring forms due to the radial flow caused by the maximum evaporation rate at the triple-phase line; in (2), a uniform deposit forms due to an attractive DLVO force between the particles and the substrate; in (3), a central bump forms due to a Marangoni recirculation loop.

Table 1

The dynamic viscosity of the nanofluid.

3.2.1 The radial flow

Deegan et al. [6] found there was a good agreement between experimental results and theoretical predictions for the vertically averaged radial flow velocity, which scaled as (1) where R is the contact radius [m], r is a radial distance from the center of the drop [m], and θ is the contact angle of the droplet [rad].

Figure 4 shows the average radial velocity Vrad − a> 101, the average value near the contact line Vrad − c> 102 and diverging at the contact line. The Vrad increases with time and diverges at the end of the evaporation according to the analysis of Deegan et al. [6]. The expression is based on the diffusion-limited theory not considering the influence of the substrate temperature. Obviously, the evaporation process will be accelerated with the increasing of the substrate temperature, then leading to the actual speed far greater than the above values.

thumbnail Fig. 4

The initial mean radial velocity with different concentrations at 50 °C (mean value of the entire radius Vrad − a and the average velocity Vrad − c of different positions R − r of 1, 10 and 100 μm (R > r > R/3)).

3.2.2 Marangoni circulation loop

An analytical expression for the typical loop velocity is provided by Hu and Larson [19] and scales as: (2)

In this equation (2), β is the gradient of surface tension with respect to the temperature (−0.1657 × 10−3 N/m·k), φ is the wetting angle of the drop [rad], μ is dynamic viscosity [Pa·s], and ΔT is the temperature difference between the edge and the top of the droplet [K].

From Figure 5, 10−2 < Vma < 100, as the evaporation goes on, the temperature difference between top and edge becomes smaller and smaller [20], and the contact angle also decreases with time, which result in Vma gradually decreasing over time, namely Marangoni effect gradually declining.

thumbnail Fig. 5

The variation curve of incipient Vma with temperatures and concentrations.

3.2.3 Attractive DLVO force

In this study, no hydrochloric acid or sodium hydroxide is added to the Al2O3 nanofluids, therefore, ignoring the electrostatic force, the VDLVO+ [14,21,22] scales as: (3) where A is the Hamaker constant, A = 2.43 × 10−20 J [23], αrtd is the retardation factor for the van der Waals force, taking 0.1 here [22], dp is diameter of particles (10 nm), and Z is the distance between the particle and the substrate [m].

The incipient VDLVO+ varies with the Z valued in proper order from 10 nm to h the highest point of the droplet for different concentrations as shown in Figure 6. (h = R − R cos θ)

Figure 6 shows the VDLVO+ is almost the same for different concentrations and increases dramatically with the decrease of Z, finally 10−27 < VDLVO+ < 10−4. Besides, the higher the temperature is, the bigger the VDLVO+ is.

Furthermore, 10−28 < VDLVO+/Vrad − a < 10−5, combined 10−3 < Vma/Vrad − a < 10−2, it can be concluded that the final deposition patterns should be based on the coffee ring and probably show a thin uniform layer inside the ring under the competition of the DLVO force and the Marangoni effect, which match the experimental results.

thumbnail Fig. 6

The variation of the incipient VDLVO+ with the Z for different concentrations.

4 Analysis of the concentric circular

For the approximate concentric circular pattern formed at the concentration of 1%, we added a set of experimental studies for the mass concentration of 3%, as shown in Figure 2.

The droplet evaporation model in this experiment is close to the stationary contact line until the final stage decreasing rapidly and sudden change to 0 shown in Figure 7.

The above analysis indicates that the radial flow plays a dominant role in the formation of the deposition pattern. Because the majority of the particles have moved to the edge during the fixed stage of the contact line, the remaining particles will form a inner ring following the triple-phase line for the higher concentration case. Meanwhile, since the radial velocity increases rapidly, even diverges at the end of the evaporation, a hollow internal circle is formed.

With the increase of temperature and the enhance of evaporation, the radial velocity is improved continuously, and most of the particles in the approximate fixed stage has deposited in the triple-phase line reducing the quantity of particles following the movement of contact line, so the concentration of internal concentric circle peters out.

It can be seen from the above deposition patterns that the concentration of nanoparticles is also an important factor affecting the combination of nanoparticles.

thumbnail Fig. 7

Profile evolution of 1% nanofluid sessile droplet on glass substrate of 30 °C.

5 Conclusion

Based on the above experimental and analytical results, the following conclusions can be obtained:

  • The experimental deposition patterns include the peripheral ring, the thin uniform layer with a thicker ring at the periphery and the concentric circular.

  • The magnitude of three typical flow patterns is estimated by analytical relations based on the experimental data, and the conclusion that the deposit patterns are based on the coffee ring coincides with the experimental results.

  • The radial flow caused by the maximum evaporation rate at the triple-phase line is dominant for the formation and variation of concentric circles.

Acknowledgment

The authors gratefully acknowledge financial support from the Foundation of Tianjin Education Committee (170018).

Author contribution statement

Tianying Li and Bin Liu contributed to the conception of the study. Tianying Li and Xiaoyan Ma performed the experiments. Tianying Li analyzed the data and wrote the manuscript. Bin Liu and Rachid Bennacer helped perform the analysis with constructive discussions. Rachid Bennacer and Xiaoyan Ma checked the expression and the grammar of English.

References

  1. L. Zhang, H. Liu, Y. Zhao, et al., Adv. Mater. 24, 436 (2012) [CrossRef] [PubMed] [Google Scholar]
  2. K. Sefiane, J. Bionic Eng. 7, S82 (2010) [CrossRef] [Google Scholar]
  3. D. Brutin, B. Sobac, B. Loquet, et al., Fluid Mech. 667, 85 (2011) [CrossRef] [Google Scholar]
  4. D. Brutin, B. Sobac, C. Nicloux, J. Heat Transf. 134, 061101 (2012) [CrossRef] [Google Scholar]
  5. C.T. Chen, F.G. Tseng, C.C. Chieng, Sens. Actuators A Phys. 130 (2006) [Google Scholar]
  6. R.D. Deegan, O. Bakajin, T.F. Dupont, et al., Phys. Rev. E 62, 756 (2000) [CrossRef] [Google Scholar]
  7. H. Hu, R.G. Larson, Phys. Chem. B 110, 7090 (2006) [CrossRef] [PubMed] [Google Scholar]
  8. R.D. Deegan, Phys. Rev. E 61, 475 (2000) [CrossRef] [Google Scholar]
  9. K. Sefiane, Adv. Colloid Interface Sci. 206, 372 (2014) [CrossRef] [PubMed] [Google Scholar]
  10. T.P. Bigioni, X. Lin, T.T. Nguyen et al., Nat. Mater. 5, 265 (2006) [CrossRef] [PubMed] [Google Scholar]
  11. J.R. Moffat, K. Sefiane, M.E. Shanahan, Phys. Chem. B 113, 8860 (2009) [CrossRef] [Google Scholar]
  12. D. Orejon, K. Sefiane, M.E. Shanahan, Langmuir 27, 34 (2011) [CrossRef] [PubMed] [Google Scholar]
  13. E. Adachi, A.S. Dimitrov, K. Nagayama, Langmuir 11, 1057 (1995) [CrossRef] [Google Scholar]
  14. R. Bhardwaj, X. Fang, P. Somasundaran et al., Langmuir 26, 7833 (2010) [CrossRef] [PubMed] [Google Scholar]
  15. J.M. Stauber, S.K. Wilson, B.R. Duffy, Langmuir 31, 3653 (2015) [CrossRef] [PubMed] [Google Scholar]
  16. Y. Xuan, Q. Li, Theory and Application of Nanofluid Energy Transfer (Science Press, Beijing, 2010) [Google Scholar]
  17. H.C. Brinkman, J. Chem. Phys. 20, 571 (1952) [Google Scholar]
  18. A. Einstein, Ann. Phys. 324, 289 (1906) [CrossRef] [Google Scholar]
  19. H. Hu, R.G. Larson, Langmuir 21, 3972 (2005) [CrossRef] [PubMed] [Google Scholar]
  20. T. Li, B. Liu, Q. Li, in Proceedings of the Academic Conference of China Engineering (Thermal Physics Society, Suzhou, 2017) [Google Scholar]
  21. M. Kobayashi, H. Nanaumi, Y. Muto, Colloids Surf. A 347, 2 (2009) [CrossRef] [Google Scholar]
  22. C. Tien, Granular Filtration of Aerosols and Hydrosols (Butterworths, Boston, 1989) [Google Scholar]
  23. P.C. Hiemenz, R. Rajagopalan, Principles of Colloid and Surface Chemistry, 3rd edn. (Marcel Dekker, New York, 1997) [Google Scholar]

Cite this article as: Tianying Li, Bin Liu, Xiaoyan Ma, Rachid Bennacer, Nanofluid Al2O3–H2O evaporation: energy and deposition patterns, Eur. Phys. J. Appl. Phys. 83, 10903 (2018)

All Tables

Table 1

The dynamic viscosity of the nanofluid.

All Figures

thumbnail Fig. 1

The measurement equipment of the droplet in evaporation (DSA30 and Thermostatic Waterbath).

In the text
thumbnail Fig. 2

The 10 times larger pictures of deposition patterns taken by the gem microscope.

In the text
thumbnail Fig. 3

Three convective mechanisms compete to form the deposit. In (1), a ring forms due to the radial flow caused by the maximum evaporation rate at the triple-phase line; in (2), a uniform deposit forms due to an attractive DLVO force between the particles and the substrate; in (3), a central bump forms due to a Marangoni recirculation loop.

In the text
thumbnail Fig. 4

The initial mean radial velocity with different concentrations at 50 °C (mean value of the entire radius Vrad − a and the average velocity Vrad − c of different positions R − r of 1, 10 and 100 μm (R > r > R/3)).

In the text
thumbnail Fig. 5

The variation curve of incipient Vma with temperatures and concentrations.

In the text
thumbnail Fig. 6

The variation of the incipient VDLVO+ with the Z for different concentrations.

In the text
thumbnail Fig. 7

Profile evolution of 1% nanofluid sessile droplet on glass substrate of 30 °C.

In the text

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