Thursday, February 3, 2011

Physical properties and data structures

Well, this week wasn't nearly as productive as I had hoped, but I have managed to setup a basic particle system data structure and am now incorporating in the code from Heckbert's report "Fast Surface Particle Repulsion." Basically it's the framework for a 3d spatial bucket-list style grid that allows for fast access to neighboring particles and will be useful for both layering the fluid simulation effects onto the particle system and later for quickly constraining floater particles to the implicit surface formulation.

In the process of setting up my particle data structure, I have been researching what physical properties of mercury to which I can put actual numbers.  So far, the most relevant properties of mercury I have been able to quantify:

 Behavioral Properties
  • Surface tension
  • Viscosity
  • Elasticity/Plasticity
  • Density
Rendering Properties
  • Reflectivity
  • Index of Refraction
Here is a brief overview of each property, how mercury exhibits it, and how my particle system will attempt to achieve the effect (see references below):

Surface Tension
Surface tension is the property exhibited by liquids that allows them to resist external forces due to the cohesive forces among liquid molecules which, while netting to zero within the liquid, result in a net internal force at the boundary. It turns out that surface tension is also responsible for the "blobby" feel of mercury as well as its tendency to form droplets or puddles instead of spreading all the way out (combined with mercury's lack of adherence to many solids), since the droplets are pulled into the spherical shape by the cohesive forces at the liquid surface. Note the blobby behavior of the high surface tension liquids in this movie (thanks to Joe for finding this one). Mercury's surface tension is extremely high: about 487 dyn/cm at 15 deg. Celsius, compared to water's suface tension of 71.97 dyn/cm at 25 degrees Celsius.
In order to simulate such a high surface tension, it's looking likely I might have to rely on more than the double density relaxation algorithm described in Particle-based viscoelastic fluid simulation where some amount of surface tension and smoothed surface is ensured but the amount is not directly controllable. I'm hoping I'll be able to fake the increased surface tension by applying an additional cohesive force to boundary particles, but this may result in asymmetry or instability, in which case I will need to think of a different approach.

Viscosity
The viscosity of mercury is slightly more viscous than water, but much less so than honey for example.  
While the actual viscosity of mercury falls at 1.526 mPa*s (compared to 0.894 for water and 2,000-10,000 for honey), I think to make the haptic interaction more interesting I will be want the user to be able to vary this
by making it more viscous. 

Elasticity/Plasticity
Elasticity is the property that brings the material back to its original shape after a deformation is applied then removed.  There is a linear relationship between the force applied (stress) and the relative deformation (strain).  Above the elastic limit for the material, the relationship becomes nonlinear and the material is said to exhibit plasticity, meaning the substance "forgets" its past shape.  Elastic modulus is the measure of an object's tendency to undergo an elastic non-permanent deformation when a force is applied to it and is defined as stress/strain.  The bulk modulus of a substance is a measure of its resistance to compression or its incompressibility.  Mercury has a very high Bulk Modulus (extremely incompressible) of 28.5 * 10^9 Pa, compared to water's Bulk Modulus of 2.15 * 10^9.
Like viscosity, elasticity/plasticity are part of the viscoelastic fluid formulation and can thus be worked into the system as variables that the users can change.

Density
Mercury has a density of  13,546 kg/m^3 at standard temperature and pressure, compared to water's density of 1000 kg/m^3 and gold's 19320.  The density might be useful in computing an appropriate force feedback.

Reflectivity
Mercury's reflectivity is relatively high at 73%.  I hope to simulate the reflectivity using basic environment mapping.

Index of Refraction 
Mercury has a low index of refraction at 1.000933 (compared to water which 1.33), which will result in essentially no refraction in a vacuum.  However, if there is time, I hope to parametrize this property as well, so there would have to be some perturbation of the environment map based on the amount of refraction.

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