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Topics in Nonlinear Mechanics and Physics pp 255–276Cite as

Drops and Bubbles as Controlled Traveling Reactors and/or Carriers Including Microfluidics Aspects

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Abstract

Provided here is a succinct survey of significant features of theory and experiments dealing with drops or bubbles which may act as traveling reactors or mere carriers of appropriate payloads in microfluidic flows and devices. The units could be the seat of inner or surface reactions, internal heat generation, phase transformations or the like that provoke interfacial tension inhomogeneity and eventually controlled, directed or self-propelled motion (Marangoni effect).

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Notes

  1. 1.

    Micro = 10−6, nano = 10−9, pico = 10−12, femto = 10−15; microfluidic drops/picoliter volumes with sizes up to 100 μm, velocities in the range 1–10 μm/s (or higher). The molecular volume of a “hard” sphere is about 11.25 Angstroms, a water molecule is about 30 Angstroms (1 Å = 10−10 m = 0.1 nm, 1 nl = (102 μm)3), a typical colloidal particle radius is 0.1 m having 1012 times the mass of a water molecule, a typical pollen grain radius is 10−5 m with a density 1 g/cm3. Warning: for sizes below 1 μm, Brownian motion becomes significant eventually dominating the evolution (a further comment on this below). There is also nanofluidics coming in with fluids moving along, e.g., 102 nm and lower scale channels handling items in the range 1 Å–102 nm.

  2. 2.

    Warnings: when drops approach each other in the hundred nanometer and lower separation range, the carrier liquid may also prevent coalescence and rather foster aggregation of drops (ruling out or just counteracting Ostwald ripening) if surface forces (Derjaguin-Casimir pressure, DLVO theory, see, e.g., [38, 39] play a significant role (aggregation leading to a solid-like behavior of the compound seems to physicochemically underly ALS and Alzheimer diseases).

  3. 3.

    Warning: though low Reynolds number means that viscous drag is paramount this is compatible with the carrier fluid itself being only of small viscosity.

  4. 4.

    One more warning: please note that, for a given fluid, the ratio \( \eta^{2} /\rho \) has units of force and any object acted upon by such force will experience a Reynolds number of unity, independently of its size. A drop or other, moving at low Reynolds number therefore experiences forces smaller than \( \eta^{2} /\rho \) which for water is about one nN. And yet another warning: continuous curved flows in (particularly rectangular or the like) micro channels where the fluid tends to move outward around the curve, with most of the times secondary flows arising, deserve a specific analysis not done here.

  5. 5.

    Warnings: when using surfactants acting on drops it must be taking into account that size matters. As a drop reduces its size the surfactant concentration tends also to diminish with the scale imposed by the ratio of surface to volume and there would be less and less surfactant molecules at its surface so that their role may become negligible. Also to be noted is that when a drop moves, in a gas or air, evaporation may occur. If this is the case its radius evolves with a rate as the inverse square (a−2) so that evaporation tends to proceed faster as size diminishes.

  6. 6.

    Warning: for a sessile drop or a drop sliding on another liquid or on a solid substrate (disregard now spreading) the wettability conditions like wettability gradient/difference in contact angles, using magnetic fields or other agents as well as degree of hydrophilicity (wettability or hydrophobicity/no wettability) [8, 24] and not solely surface tension difference is of utmost importance and hence the inhomogeneity (chemical, mechanical) of the substrate becomes significant. To the above we must add the dominant role that the mentioned Derjaguin-Casimir forces (DLVO theory) can play.

  7. 7.

    Warning: the case of a highly viscous drop η2 ≫η1 moving in a Hele-Shaw channel deserves separate consideration not done here; a typical transverse scale is about 102 μm and caged drops can be safely considered as pancaked rather than spherical.

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Acknowledgements

This work was funded in part by EU under Marie Curie ITN CoWet (Grant Number 607861) and by MINECO under grants FIS-2014-62005-EXP and CTQ-2016-78895-R.

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Authors and Affiliations

  1. Instituto Pluridisciplinar, UCM, Paseo Juan XXIII, 1, 28040, Madrid, Spain

    Manuel G. Velarde, Yuri S. Ryazantsev, Ramon G. Rubio, Eduardo Guzman & Francisco Ortega

  2. Departamento de Quimica Fisica, UCM, Ciudad Universitaria, s/n, 28040, Madrid, Spain

    Ramon G. Rubio, Eduardo Guzman & Francisco Ortega

  3. Departamento de Quimica y Fisica, Universidad de Almeria, 04120, Almeria, Spain

    Antonio Fernandez-Barbero

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  1. Manuel G. Velarde
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Correspondence to Manuel G. Velarde .

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  1. Faculty of Sciences Ain Chock, University Hassan II - Casablanca, Casablanca, Morocco

    Mohamed Belhaq

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Velarde, M.G., Ryazantsev, Y.S., Rubio, R.G., Guzman, E., Ortega, F., Fernandez-Barbero, A. (2019). Drops and Bubbles as Controlled Traveling Reactors and/or Carriers Including Microfluidics Aspects. In: Belhaq, M. (eds) Topics in Nonlinear Mechanics and Physics. Springer Proceedings in Physics, vol 228. Springer, Singapore. https://doi.org/10.1007/978-981-13-9463-8_13

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