# Modelling Extraction in Microchannels with Stratified Flow: Channel Geometry, Flow Configuration and Marangoni Stresses

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### Cites background from "Modelling Extraction in Microchanne..."

...However, in a recent study, we have shown that this effect is not strong enough to impact the primary pressure driven flow for practical fluid–solute systems (Picardo et al. 2015)....

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...For dilute solutions these boundary conditions read as (Picardo et al. 2015) −η′xc′1,x + c′1,y =Dr(−η′xc′2,x + c′2,y), (2.4) c′1 =Kc′2....

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...However, in a recent study, we have shown that this effect is not strong enough to impact the primary pressure driven flow, for practical fluid solute systems (Picardo et al. 2015)....

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...For dilute solutions these boundary conditions read as (Picardo et al. 2015):...

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...It consists of a solute transport equation in each fluid and two interface boundary conditions that enforce equality of flux and local equilibrium at the interface (Picardo et al. 2015)....

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##### References

1,082 citations

### "Modelling Extraction in Microchanne..." refers background in this paper

...This will result in stresses that act along the interface, directed towards regions of high interfacial tension, called Marangoni stresses [24]....

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...The changes in interfacial concentration are governed by the interface species transport equation, which accounts for the adsorption–desorption processes, as well as transport along the interface [24], [25]....

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...This leads to a lubrication approximation of the flow field, which is often used to describe flow in narrow gaps of varying width and flow of thin films [24]....

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818 citations

### "Modelling Extraction in Microchanne..." refers background in this paper

...Examples include mass transfer between a slowly moving drop and a stationary fluid [28–30] and mass transfer between stationary fluid layers [26, 31, 32]....

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...The simplified model can be written in terms of bulk phase concentrations alone, if the interfacial tension is known empirically in terms of the bulk phase concentrations of the solute [26]....

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376 citations

### "Modelling Extraction in Microchanne..." refers background in this paper

...In fact, there has been speculation in the literature about the possible influence of Marangoni stresses and how they might affect the system’s output [8, 27]....

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