Bubble Content Viscosity Reduction
Evaluate a supplied deformable-bubble viscosity-reduction power law only above its caller capillary applicability threshold; low-capillary bubbles can increase viscosity and are not handled by this reduction model.
Description
Deformable bubbles can reduce viscosity under a calibrated power law.
Deformable bubbles can reduce viscosity under a calibrated power law. Capillary number compares shear deformation with surface tension.
Evaluate a supplied deformable-bubble viscosity-reduction power law only above its caller capillary applicability threshold; low-capillary bubbles can increase viscosity and are not handled by this reduction model.
When to use Bubble Content Viscosity Reduction
Use this tool to evaluate a supplied deformable-bubble viscosity-reduction power law only above its caller capillary applicability threshold; low-capillary bubbles can increase viscosity and are not handled by this reduction model.
Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
How to use Bubble Content Viscosity Reduction and understand its results
- Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
- Enter bubbleFreeViscosityPaSeconds, bubbleVolumeFraction, callerReductionExponent, surfaceTensionNPerM, bubbleRadiusM, shearRatePerSecond, minimumCalibratedCapillaryNumber using the field table and calculation rules, then run the tool.
- Read capillaryNumber, 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 |
|---|---|---|---|
| bubbleFreeViscosityPaSeconds | Bubble free viscosity Pa seconds | number | Required |
| bubbleVolumeFraction | Bubble volume fraction | number | Required |
| callerReductionExponent | Caller reduction exponent | number | Required |
| surfaceTensionNPerM | Surface tension n per m | number | Required |
| bubbleRadiusM | Bubble radius m | number | Required |
| shearRatePerSecond | Shear rate per second | number | Required |
| minimumCalibratedCapillaryNumber | Minimum calibrated capillary number | number | Required |
Supply positive base viscosity, tension, radius and exponent, nonnegative shear and minimum capillary number, and bubble fraction below one. Reject capillary numbers below the supplied applicability minimum; equality is accepted.1
capillary number = viscosity × bubble radius × shear rate/surface tension; multiplier = (1 − bubble fraction)^exponent Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| capillaryNumber | Capillary number | number |
| relativeViscosityMultiplier | Relative viscosity multiplier | number |
| effectiveViscosityPaSeconds | Effective viscosity Pa seconds | number |
{
"input": {
"bubbleFreeViscosityPaSeconds": 100,
"bubbleVolumeFraction": 0.2,
"callerReductionExponent": 2,
"surfaceTensionNPerM": 0.1,
"bubbleRadiusM": 0.001,
"shearRatePerSecond": 10,
"minimumCalibratedCapillaryNumber": 1
},
"output": {
"capillaryNumber": 10,
"relativeViscosityMultiplier": 0.6400000000000001,
"effectiveViscosityPaSeconds": 64.00000000000001
}
}Limitations and assumptions
Low-capillary bubbles may increase viscosity and are outside this reduction model.
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 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. For a complementary task, use Newtonian Yield Stress Regime Checker: Screen caller negligible-yield approximation and ideal Bingham shear at applied stress; unyielded states return zero modeled shear, not a flow-safety determination.
References
-
Bubble Content Viscosity Reduction — tool.io
Similar or alternative tools
- 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.
- Newtonian Yield Stress Regime Checker
Screen caller negligible-yield approximation and ideal Bingham shear at applied stress; unyielded states return zero modeled shear, not a flow-safety determination.