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On the effects of liquid-gas interfacial shear on slip flow through a parallel-plate channel with superhydrophobic grooved walls
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10.1063/1.3493641
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Affiliations:
1 Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong
2 Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
a) Author to whom correspondence should be addressed. Electronic mail: cong@hku.hk.
Phys. Fluids 22, 102002 (2010)
/content/aip/journal/pof2/22/10/10.1063/1.3493641
http://aip.metastore.ingenta.com/content/aip/journal/pof2/22/10/10.1063/1.3493641

## Figures

FIG. 1.

Flow through a plane channel with grooved walls; longitudinal flow is normal to the plane, while transverse flow is along the -axis. The coordinates and length dimensions are normalized with respect to half the period of the wall pattern. The liquid-gas interface is a flat surface in alignment with the top of the ribs.

FIG. 2.

Streamwise velocity profiles of the liquid phase on the liquid-gas interface for (a) longitudinal flow, (b) transverse flow, where , , , and (solid), 0.01 (dashed), 0.02 (dashed-dotted). The channel height is , except in one case, , as specified in (b). The symbols are the results adopted from previous studies: Teo and Khoo (Ref. 6) (crosses), Maynes et al. (Ref. 11) (squares and circles), and Davies et al. (Ref. 10) (triangles and inverted triangles).

FIG. 3.

Longitudinal slip length as a function of the channel height and gas area fraction of the wall , where , , and (a) , (b) . The dashes are for ideal gas .

FIG. 4.

Longitudinal slip length as a function of the channel height and gas area fraction of the wall , where , , and (a) , (b) . The dashes are for ideal gas .

FIG. 5.

Longitudinal slip length as a function of the viscosity ratio and gas area fraction of the wall , where , and (a) , , (b) , . The dotted lines are the limits for ideal gas .

FIG. 6.

Longitudinal slip length as a function of the groove depth , for , where , , and .

FIG. 7.

Transverse slip length as a function of the channel height and gas area fraction of the wall , where , , and (a) , (b) . The dashes are for ideal gas .

FIG. 8.

Transverse slip length as a function of the channel height and gas area fraction of the wall , where , , and (a) , (b) . The dashes are for ideal gas .

FIG. 9.

Transverse slip length as a function of the viscosity ratio and gas area fraction of the wall , where , , and (a) , (b) . The dotted lines are the limits for ideal gas .

FIG. 10.

For , , and , (a) transverse slip length as a function of the intrinsic slip length , for , 0.005, 0.01, and 0.02, where the dotted lines are the values computed by the approximation formula (36); (b) reciprocal of the gas slip length as a function of the intrinsic slip length , for , 0.005, 0.01, and 0.02.

FIG. 11.

Comparison between the modeling values of effective slip length, , and the predictions (a) using the formula (38), (b) using the formula (39). The symbols denote the following groups: (i) squares for and , (ii) diamonds for and , (iii) circles for and , (iv) triangles for and , and (v) inverted triangles for and . Each group contains the following cases: , , . The data points lying near the lower left corner of the graphs are those cases with , while the others are those with .

FIG. 12.

Ratio of the effective transverse to longitudinal slip lengths, , as a function of the gas area fraction of the wall, , for , , , and . The dashes are for ideal gas .

## Tables

Table I.

Approximate values representing the deviation of the effective longitudinal and transverse slip lengths based on gas viscosity from the corresponding values based on ideal inviscid gas for and . The upper and lower limits are for and , respectively. The values can be extended to other values of by linear interpolation as long as . Recall that all length dimensions are normalized by half the pitch of the wall micropattern.

/content/aip/journal/pof2/22/10/10.1063/1.3493641
2010-10-28
2014-04-16

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