Liquid Wall Contact Law

Description

This frictional contact law implements a friction-style contact between liquid and a wall where contact shear is related to shear rate, viscosity, and a scaling factor to vary from stick to slip contact. When the surfaces are in contact, the frictional sliding traction is

      [math]\displaystyle{ S_{slide} = k\ \eta(k\Delta v_t) \Delta v_t }[/math]

where k is a scaling factor (with units 1/length), [math]\displaystyle{ \eta(\dot\gamma) }[/math] is viscosity of a fluid (which may depend on shear rate), and [math]\displaystyle{ \Delta v_t }[/math] is the final difference in tangential velocities between fluid and the other material (usually a wall).

Note that k = 0 leads to zero sliding traction, which is the same as frictionless contact (and could be done using a Coulomb Friction Law with it's coeff = 0). As k get large, the law approaches stick contact having [math]\displaystyle{ \Delta v_t\to 0 }[/math] (and could be done using a Coulomb Friction Law with it's coeff = -1). All other values of k give partial-slip boundary conditions that depend on the liquid's viscosity and could be tailored to match experimental results.

After running some simulations for a range of k and at different resolutions, those results indicate that k is a material property. In other words, k is independent of grid cell size, or only weakly dependent of grid cell size. A possible physical interpretation is that 1/k is a "zone of influence" for the boundary region near a wall. If other problems show mesh dependence for k, it could (and then should) be varied with cell size.

Properties

The properties for this law are:

Property	Description	Units	Default
coeff	The scaling factor k in the contact law	1/length units	2
LiquidPhase	Enter the liquid phase material by ID (scripted files only) or by number	none	none

Note that this contact law uses the viscosity provided by the entered LiquidPhase material for all contact situations assigned to the law. Simulations that use this contact law must therefore insure that it only applies to contact involving that liquid material by setting default or custom contact laws as needed.

Examples

These commands create a liquid contact law for "MyLiquid" (using scripted commands) or material number 1 (using XML commands):

Material "LiquidContact","Liquid Contact Law","LiquidContact"
  LiquidPhase "MyLiquid"
  coeff 100
Done

<Material Type='64' Name='Liquid Contact Law'>
  <LiquidPhase>1</LiquidPhase>
  <coeff>100</coeff>
</Material>