### Abstract

The work is devoted to stationary streaming flows resulting from standing capillary waves at interfaces between two immiscible liquids and their effect on the mass transfer rate of a passive scalar. In particular, oscillating liquid droplets immersed in another immiscible liquid are considered. Secondary streaming flows in the Stokes layers near the interface are calculated,as well as the corresponding vortical flows arising in the bulk. It is shown that the vortices can drastically enhance the mass transfer rate of a passive scalar which is to be extracted by one liquid from the other. The corresponding Sherwood number is of the order of [u_{int}a/D_{1}]^{1/2}, where u_{int} is the magnitude of the interfacial streaming velocity, a is the droplet radius, and D_{1} is the diffusion coefficient in liquid 1 (inside the droplet). This means that the effective diffusion coefficient is of the order of D_{1} [U_{int}a/D_{1}]^{1/2}, which is two orders of magnitude higher than D_{1}. The results obtained show that such flows can be of potential interest for novel bioseparator devices.

Original language | English |
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Pages (from-to) | 321-342 |

Number of pages | 22 |

Journal | Journal of Fluid Mechanics |

Volume | 444 |

DOIs | |

Publication status | Published - 2001 Oct 10 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

**Stationary d.c. streaming due to shape oscillations of a droplet and its effect on mass transfer in liquid-liquid systems.** / Yarin, Alexander.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Stationary d.c. streaming due to shape oscillations of a droplet and its effect on mass transfer in liquid-liquid systems

AU - Yarin, Alexander

PY - 2001/10/10

Y1 - 2001/10/10

N2 - The work is devoted to stationary streaming flows resulting from standing capillary waves at interfaces between two immiscible liquids and their effect on the mass transfer rate of a passive scalar. In particular, oscillating liquid droplets immersed in another immiscible liquid are considered. Secondary streaming flows in the Stokes layers near the interface are calculated,as well as the corresponding vortical flows arising in the bulk. It is shown that the vortices can drastically enhance the mass transfer rate of a passive scalar which is to be extracted by one liquid from the other. The corresponding Sherwood number is of the order of [uinta/D1]1/2, where uint is the magnitude of the interfacial streaming velocity, a is the droplet radius, and D1 is the diffusion coefficient in liquid 1 (inside the droplet). This means that the effective diffusion coefficient is of the order of D1 [Uinta/D1]1/2, which is two orders of magnitude higher than D1. The results obtained show that such flows can be of potential interest for novel bioseparator devices.

AB - The work is devoted to stationary streaming flows resulting from standing capillary waves at interfaces between two immiscible liquids and their effect on the mass transfer rate of a passive scalar. In particular, oscillating liquid droplets immersed in another immiscible liquid are considered. Secondary streaming flows in the Stokes layers near the interface are calculated,as well as the corresponding vortical flows arising in the bulk. It is shown that the vortices can drastically enhance the mass transfer rate of a passive scalar which is to be extracted by one liquid from the other. The corresponding Sherwood number is of the order of [uinta/D1]1/2, where uint is the magnitude of the interfacial streaming velocity, a is the droplet radius, and D1 is the diffusion coefficient in liquid 1 (inside the droplet). This means that the effective diffusion coefficient is of the order of D1 [Uinta/D1]1/2, which is two orders of magnitude higher than D1. The results obtained show that such flows can be of potential interest for novel bioseparator devices.

UR - http://www.scopus.com/inward/record.url?scp=0035840903&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035840903&partnerID=8YFLogxK

U2 - 10.1017/S0022112001005493

DO - 10.1017/S0022112001005493

M3 - Article

AN - SCOPUS:0035840903

VL - 444

SP - 321

EP - 342

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -