### Abstract

The work deals with stationary (dc) streaming flows resulting from standing capillary waves at the interface between two immiscible liquid layers, and with their effect on the mass transfer rate of a passive scalar (for example, a protein). Planar layers in a narrow channel are considered. Secondary streaming flows in the Stokes layers near the interfaces are calculated, as well as the corresponding vortical flows arising in the bulk. It is shown that the vortices can significantly 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 order [u^{*}
_{int}λ/D_{1}]^{1/2}, where u^{*}
_{int} is the magnitude of the interfacial streaming velocity, λ is the wavelength, and D_{1} is the diffusion coefficient in liquid 1. This means that the effective diffusion coefficient is of order

Original language | English |
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Pages (from-to) | 79-102 |

Number of pages | 24 |

Journal | Fluid Dynamics Research |

Volume | 31 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2002 Aug 1 |

Externally published | Yes |

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### Keywords

- Mass transfer at liquid-liquid interface
- Standing capillary waves
- Stationary de streaming
- Two-layer system

### ASJC Scopus subject areas

- Mechanical Engineering
- Statistical and Nonlinear Physics

### Cite this

*Fluid Dynamics Research*,

*31*(2), 79-102. https://doi.org/10.1016/S0169-5983(02)00089-8