Additions and corrections

Wetting-induced formation of controllable monodisperse multiple emulsions in microfluidics

Nan-Nan Deng, Wei Wang, Xiao-Jie Ju, Rui Xie, David A. Weitz and Liang-Yin Chu

Lab Chip, 2013, 13, 4047–4052 (DOI: 10.1039/C3LC50638J). Amendment published 4th February 2014.

In the second paragraph of the “Theory and criterion” section, the assumption that “the engulfing process is determined by the three interfacial tensions and the sizes of drops” is not correct, which leads to a mathematical error in the derivation of eqn (1)–(4). The text in this paragraph after the sentence starting with “We assume that the engulfing process is…” should read:

“We assume that the engulfing process is determined by the three interfacial tensions; thus other factors such as gravity, fluid motion and forces between particles are ignored,²³ although we recognize these factors have effects on the behavior of drop engulfing, especially in conditions of flow. When two immiscible drops come into contact, one drop can completely engulf the other drop only because the total interfacial energies are reduced. For the case illustrated in Fig. 1a1–a3, drop A (radius R_A) completely engulfs drop B (radius R_B), and the relationship of interfacial energies fits in with eqn (1):^23,24

 γ_BC > γ_AC – γ_AB (1)

where γ_ij is the interfacial tension between fluids i and j.
The spreading coefficient is defined as

 S_A = γ_BC – (γ_AC + γ_AB) (2)”

Therefore, the calculations of the spreading coefficients in the “Results and discussion” section as well as in the ESI Supplementary Note are revised as follows.

Case 1 (Drop A1 engulfing drop B, as shown in Fig. 1a3)
For drop B and drop A1 dispersed in continuous phase C:

 γ_A1B = 0.18 mN m^–1, γ_BC = 3.07 mN m^–1, γ_A1C = 1.37 mN m^–1.

 So, S_A1 = γ_BC – (γ_A1C + γ_A1B) = 3.07 – (1.37 + 0.18) = 1.52 > 0

That is to say, drop A1 can completely engulf drop B according to the criterion (Fig. 1a3,d,f,g).

Case 2 (Drop B engulfing drop A2, as shown in Fig. 1a4)
For drop B and drop A2 dispersed in continuous phase C:

 γ_A2B = 0.58 mN m^–1, γ_BC = 3.07 mN m^–1, γ_A2C = 3.16 mN m^–1.

 So, S_B = γ_A2C – (γ_BC + γ_A2B) = 3.16 – (3.07 + 0.58) = –0.49 < 0, and S_A2 < 0, S_C < 0.

However, these results are not in accord with the criterion that drop B can completely engulf drop A2 when S_B > 0. We conjecture that there are two main causes to induce the complete engulfing: the first is that the two droplets are dispersed in the flowing stream of phase C within the microchannels. The fluid motion considerably changes the shapes of drops and the interfacial tensions of the systems, which could promote the drop engulfing. The second is that, when limS_B → 0^–, drop B also could wet drop A2 completely to form an A2/B/C double emulsion drop (for more details, please see: S. Toraz, PhD Thesis, Appendix I, McGill University, Montreal, 1969). In our experiments, we find S_B = –0.49. If reasonable experimental errors of interfacial tensions are considered, the limit of S_B is close to zero as well. This is, perhaps, why the prepared A2/B/C double emulsions still remain stable (Fig. 4g in the paper). In addition, we here clarify that the freshly prepared multiple emulsions whose system does not agree with the criterion (S_i > 0) may not be at their final equilibrium states, which may transform into other topologies due to dewetting.
The corrections do not change any of the conclusions in our paper, specifically that multiple emulsions are successfully created from wetting-induced drop-engulfing-drop phenomena by mixing lower-order emulsions together.

The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.

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