Abstract
Understanding the movement of drops and bubbles in microchannels isincreasingly important in the design and operation of microfluidicdevices that involve two-phase flows. Thus, Bretherton's analysis ofthe motion of long bubbles in tubes and the associated profile ofthe wetting film around it are relevant. In this work, steady motionof a long bubble through a cylindrical tube is revisited in the casewhere the wetting film between the bubble interface and thecapillary wall is non-Newtonian and described by the power-lawconstitutive relation. Using the standard lubrication analysis, theequation for the thickness of the wetting film as a function ofaxial distance is derived and integrated to find the film thickness.The film thickness and pressure drop across the bubble are found toscale with the capillary number as Ca2/3, with a proportionality factor that depends on the power-law index.
| Original language | English (US) |
|---|---|
| Article number | 36283 |
| Journal | Applied Mathematics Research eXpress |
| Volume | 2006 |
| DOIs | |
| State | Published - Dec 1 2006 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Computational Mathematics
- Applied Mathematics
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Confined motion of a long bubble through a power-law fluid. / Nadim, A.; Borhan, Ali.
In: Applied Mathematics Research eXpress, Vol. 2006, 36283, 01.12.2006.Research output: Contribution to journal › Article
TY - JOUR
T1 - Confined motion of a long bubble through a power-law fluid
AU - Nadim, A.
AU - Borhan, Ali
PY - 2006/12/1
Y1 - 2006/12/1
N2 - Understanding the movement of drops and bubbles in microchannels isincreasingly important in the design and operation of microfluidicdevices that involve two-phase flows. Thus, Bretherton's analysis ofthe motion of long bubbles in tubes and the associated profile ofthe wetting film around it are relevant. In this work, steady motionof a long bubble through a cylindrical tube is revisited in the casewhere the wetting film between the bubble interface and thecapillary wall is non-Newtonian and described by the power-lawconstitutive relation. Using the standard lubrication analysis, theequation for the thickness of the wetting film as a function ofaxial distance is derived and integrated to find the film thickness.The film thickness and pressure drop across the bubble are found toscale with the capillary number as Ca2/3, with a proportionality factor that depends on the power-law index.
AB - Understanding the movement of drops and bubbles in microchannels isincreasingly important in the design and operation of microfluidicdevices that involve two-phase flows. Thus, Bretherton's analysis ofthe motion of long bubbles in tubes and the associated profile ofthe wetting film around it are relevant. In this work, steady motionof a long bubble through a cylindrical tube is revisited in the casewhere the wetting film between the bubble interface and thecapillary wall is non-Newtonian and described by the power-lawconstitutive relation. Using the standard lubrication analysis, theequation for the thickness of the wetting film as a function ofaxial distance is derived and integrated to find the film thickness.The film thickness and pressure drop across the bubble are found toscale with the capillary number as Ca2/3, with a proportionality factor that depends on the power-law index.
UR - http://www.scopus.com/inward/record.url?scp=33846651644&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33846651644&partnerID=8YFLogxK
U2 - 10.1155/AMRX/2006/36283
DO - 10.1155/AMRX/2006/36283
M3 - Article
VL - 2006
JO - Applied Mathematics Research eXpress
JF - Applied Mathematics Research eXpress
SN - 1687-1200
M1 - 36283
ER -