Slip ratio (gas–liquid flow)

There are a number of correlations for slip ratio.

For homogeneous flow, S = 1 (i.e. there is no slip).

The Chisholm correlation[2][3] is:

${\displaystyle S={\sqrt {1-x\left(1-{\frac {\rho _{L}}{\rho _{G}}}\right)}}}$

The Chisholm correlation is based on application of the simple annular flow model and equates the frictional pressure drops in the liquid and the gas phase.

The slip ratio for two-phase cross-flow horizontal tube bundles may be determined using the following correlation:

${\displaystyle S=1+25.7{\sqrt {Ri\cdot Ca}}\cdot {\bigl (}P/D)^{-1}}$ where the Richardson and capillary numbers are defined as ${\displaystyle Ri={\frac {(\rho _{l}-\rho _{g})^{2}\cdot g\cdot y_{min}}{G^{2}}}}$ and ${\displaystyle Ca={\frac {\mu _{l}}{\sigma }}\left({\frac {x\cdot G}{\epsilon \cdot \rho _{g}}}\right)}$.[4]

For enhanced surfaces bundles the slip ratio can be defined as:

${\displaystyle S=6.71{\sqrt {(Ri\cdot Ca)}}}$[5]

Where:

• S – slip ratio, dimensionless
• P – tube centerline pitch
• D – tube diameter
• Subscript ${\displaystyle l}$– liquid phase
• Subscript ${\displaystyle g}$– gas phase
• g– gravitational acceleration
• ${\displaystyle y_{min}}$– minimum distance between the tubes
• G-mass flux (mass flow per unit area)
• ${\displaystyle \mu }$– dynamic viscosity
• ${\displaystyle \sigma }$– surface tension
• ${\displaystyle x}$– thermodynamic quality
• ${\displaystyle \epsilon }$– void fraction