Crystal Content Viscosity Correction

Apply caller Krieger–Dougherty suspension correction below packing to independently supplied melt viscosity; distinct from existing Arrhenius melt-viscosity calculation, not a yield-stress or crystal-shape universal model.

Description

Suspended crystals can increase melt viscosity as their concentration approaches a packing limit.

Suspended crystals can increase melt viscosity as their concentration approaches a packing limit. The Krieger–Dougherty relation models that calibrated effect.

When to use Crystal Content Viscosity Correction

Use this tool to apply caller Krieger–Dougherty suspension correction below packing to independently supplied melt viscosity; distinct from existing Arrhenius melt-viscosity calculation, not a yield-stress or crystal-shape universal model.

Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.

How to use Crystal Content Viscosity Correction and understand its results

Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
Enter meltViscosityPaSeconds, crystalVolumeFraction, maximumPackingFraction, intrinsicViscosity using the field table and calculation rules, then run the tool.
Read relativeViscosityMultiplier, effectiveViscosityPaSeconds. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
meltViscosityPaSeconds	Melt viscosity Pa seconds	number	Required
crystalVolumeFraction	Crystal volume fraction	number	Required
maximumPackingFraction	Maximum packing fraction	number	Required
intrinsicViscosity	Intrinsic viscosity	number	Required

Use positive melt viscosity, intrinsic viscosity and packing fraction at most one. Require crystal fraction nonnegative and strictly below packing. Evaluate with log1p and multiply by melt viscosity.^[1]

relative viscosity = (1 − crystal fraction/packing fraction)^(−intrinsic viscosity × packing fraction)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
relativeViscosityMultiplier	Relative viscosity multiplier	number
effectiveViscosityPaSeconds	Effective viscosity Pa seconds	number

json

{
  "input": {
    "meltViscosityPaSeconds": 100,
    "crystalVolumeFraction": 0.2,
    "maximumPackingFraction": 0.4,
    "intrinsicViscosity": 2.5
  },
  "output": {
    "relativeViscosityMultiplier": 2,
    "effectiveViscosityPaSeconds": 200
  }
}

Limitations and assumptions

Crystal shape, yield stress and temperature-dependent melt viscosity are separate assumptions.

Numbers and computed results must be finite; overflow produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Bingham Yield Strength Lava: Infer Bingham yield intercept and plastic viscosity from measured yielded shear pairs; negative intercept or nonpositive slope is rejected instead of asserting a physical yield law. For a complementary task, use Melt Fraction Solidus Liquidus Interpolation: Interpolate a supplied monotone melt-fraction/temperature calibration, preserving a nonlinear liquidus/solidus curve without extrapolation; not a universal rock phase diagram.

References

Crystal Content Viscosity Correction — tool.io

Similar or alternative tools

Bingham Yield Strength Lava
Infer Bingham yield intercept and plastic viscosity from measured yielded shear pairs; negative intercept or nonpositive slope is rejected instead of asserting a physical yield law.
Melt Fraction Solidus Liquidus Interpolation
Interpolate a supplied monotone melt-fraction/temperature calibration, preserving a nonlinear liquidus/solidus curve without extrapolation; not a universal rock phase diagram.