Dynamic Contact Angles
If you compare a static two-phase system with a moving two-phase system, you will observe that the interface, defined by the contact line, between the fluids is deformed in the moving system. A simple example would be a water drop running down a wall. The strength of this deformation scales with the Capillary Number
where is the viscosity, is the contact line speed, and is the surface tension. It is the ratio of viscous forces to surface tension forces. For capillary numbers near 0 flow through porous media is dominated by capillary forces, while for higher values the viscous forces dominate.
SatuDict with static contact angles assumes that the capillary number is almost zero, which means that the velocity of the contact line is assumed to be almost zero, too (as the viscosity is always positive). Thus, stationary distributions of two fluids are considered.
When checking Use Dynamic Contact Angles for the Dynamic Pore Morphology Method in the Capillary Pressure command, non-zero capillary numbers are allowed.
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Know how! The option to use dynamic contact angles is new in GeoDict 2026! |
This means the velocity of the contact line is not zero anymore which leads to an advancing contact angle (maximum angle when the contact line moves forward) and a receding contact angle (minimum angle when it retreats). Both differ from the static contact angle because viscous stresses bend the interface as it slides over the solid while the surface tension tries to maintain the equilibrium shape. Thus, we now have dynamic contact angles which depend on the velocity of the contact line and thus on the capillary number.
If you want to use the dynamic contact angles, you need to enter additional input in the options dialog compared to the static contact angles.
To define the velocity of the contact line you have to give the flow rate on a flow area in the Saturation Experiment tab. Additionaly, you need to predefine the viscosity of the fluids in the Constituent Materials tab. SatuDict always takes the viscosity of the denser fluid, e.g., for both Air-Water and Oil-Water systems, the viscosity of Water is taken.
To determine the phase distributions SatuDict computes the resulting dynamic contact angle. As shown by R.L. Hoffmann (1974) by plotting measured dynamic contact angles, the dynamic contact angle can be written as a function of the capillary number and a shift factor related to the static contact angle .
The fact that for the static and dynamic contact angles have to be the same, yields that has to be the inverse function of . The function is called the Hoffmann function and the dynamic contact angle can now be written as
with being the inverse function of .
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Important! Hoffmann’s correlation matches well at low to moderate capillary numbers (e.g., ) but can deviate at higher velocities (e.g., due to inertial effects) which was found in experimental studies. |
There are two methods implemented to determine the dynamic contact angle based on the above described input parameters. They are developed by Kistler (1993) and Cox (1986) and depend on the aggregate state of the two incorporated fluids.
