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If capillary effects are not high 

LaTeX Math Inline
bodyP_c \rightarrow 0
or saturation does not vary along the streamline substantially 
LaTeX Math Inline
body\displaystyle \frac{\partial s_w}{\partial r} \rightarrow 0
  then 
LaTeX Math Inline
body\displaystyle \frac{\partial P_c}{\partial r} = \dot P_c \cdot \frac{\partial s_w}{\partial r} \approx 0
.

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