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SPICULEYield stress
FORMULATION · YIELD STRESS

Spicule Yield Stress
Criteria and test methods for keeping spicules suspended

Yield stress is the minimum stress a formula must receive before it starts to flow (unit: Pa, pascal). When the network inside a gel or cream can bear the weight of a single spicule, the spicule stays where it is. This page sets out the criteria and test methods used to design and check spicule formulas.

How to read the numbers on this page

Every number carries a label. “Calc · estimate” is a physical calculation trusted to its order of magnitude; “Calc · per-size recalc pending” will be recalculated for each spicule size; “Measured · test report” comes from an external laboratory report; “Literature range · estimate” is a general range from the literature. The yield stress of our own gel and cream has not been measured; it will be added here once measured.

Yield stress comes from the network inside the formula

Gels and creams contain a network. In a gel, neutralised carbomer particles swell and interlock; in a cream, fatty alcohol and emulsifier build stacked layers between the water (a lamellar gel network).

If the force a single spicule exerts under its own weight is smaller than the force this network can bear (the yield stress), the spicule stays where it is.

Yield stress comes from the network inside the formulaGelCreamSwollen carbomerLamellar gel layersSpiculeOil droplet
What breaks the network: high-speed mixing or homogenising after the spicules are added · divalent salts · low pH in a carbomer gel

Yield stress, not viscosity

  • Viscosity only slows settling; it cannot stop it. Even in a 10,000 mPa·s liquid with no yield stress, long spicules sink at about 0.1–0.2 mm/h (depending on orientation).Calc · per-size recalc pending
  • With a yield stress, spicules stop even when the viscosity is low.
  • Thickeners such as carbomer usually build a yield stress at the same time as they raise viscosity, which is why “thicker means no settling” has seemed true on the bench. The criterion to use is yield stress.
Viscosity only slows settling; yield stress stops itViscosity onlyWith yield stressStartStartAfter 7 dAfter 7 dSettled layerStays in place
Same spicules · upright clear bottles · room temperature. In a liquid with viscosity only, a settled layer forms at the bottom over time; in a gel or cream with a yield stress, the spicules stay in place.

How hard a spicule pulls on the network — orientation decides

The spicule true density is 2.0417 g/cm³, heavier than water, so without a network spicules sink. How hard a spicule loads the network depends on how it lies.Measured · test report

OrientationLying
Where the weight restsAlong the whole long side · Set by thickness
Yield stress needed to stop it≈ 0.01–0.015 PaCalc · per-size recalc pending
Sinking speed (relative to a sphere of equal volume)≈ 0.5Calc · per-size recalc pending
OrientationStanding
Where the weight restsOn the tip · Set by length
Yield stress needed to stop it≈ 0.23–0.35 PaCalc · per-size recalc pending
Sinking speed (relative to a sphere of equal volume)≈ 0.7Calc · per-size recalc pending

The orientation calculation was made for one spicule length. A per-size recalculation is in progress, and this table will be split by size when the values are ready.

  • Spicules have a large surface area, so they sink less than a sphere of the same volume. A lying spicule in particular loads the network very little.
  • Spicules are hollow, so when the axial canal fills with formula the effective weight is lower. The calculation above assumes a solid spicule, the safe side.

Design target

Yield stress of 1 Pa or moreCalc · per-size recalc pending

Worst case (standing) × safety factor 3

A design target built on calculation. It may be lowered by measurement.

Basis of the calculation: drag of slender particles (slender-body approximation) plus the literature stop criterion measured with round particles, Y = σy/(Δρ·g·d) ≈ 0.1–0.15. For needle shapes it is trusted to its order of magnitude only. The settling test is the check.Calc · estimate

Orientation decides how hard a spicule loads the networkLyingStanding≈ 0.01–0.015 Pa≈ 0.23–0.35 PaSet by thicknessSet by lengthCalc · per-size recalc pendingDesign target · τy ≥ 1 PaWorst case × safety factor 3
A lying spicule spreads its weight along its long side; a standing spicule concentrates it on the tip, the worst case. The design target is the worst case with a safety factor added.

How much is 1 Pa?

1 Pa is the force of about 100 g pressing on an area of 1 m². It is a very small force.Test condition · conversion

Analogy: one sheet of copy paper (80 g/m²) lying on a desk presses with ≈ 0.8 Pa. 1 Pa is a little more than one sheet of paper.

A single spicule is very light, so a network that bears only this much will hold it. By calculation it stops above about 0.35 Pa; 1 Pa is the safety line with a safety factor of 3.Calc · per-size recalc pending

Yield stress by product

ProductWater · toner
Yield stress (literature range · estimate)0 (no network)Literature range · estimate
ProductThin lotion · serum
Yield stress (literature range · estimate)0 to a few PaLiterature range · estimate
ProductCarbomer gel · cream
Yield stress (literature range · estimate)Tens of Pa or moreLiterature range · estimate
ProductKetchup · mayonnaise
Yield stress (literature range · estimate)Tens of PaLiterature range · estimate
ProductToothpaste
Yield stress (literature range · estimate)100 Pa or moreLiterature range · estimate

What it means: a well-made carbomer gel or cream is usually far above 1 Pa (estimate). Take care with thin lotion or serum types, with networks broken by high-speed mixing after the spicules are added, and with carbomer networks loosened by acid.

Unit conversion: raw-material suppliers sometimes give yield stress as “yield value, dyn/cm²”. 1 Pa = 10 dyn/cm², so the 1 Pa target equals 10 dyn/cm².Test condition · conversion

The actual values of our gel and cream have not been measured. Once measured, a measured column will be added next to this table.Not measured

How much is 1 Pa?One sheet of copy paper80 g/m² ≈ 0.8 Pa1 Pa ≈ 100 g / 1 m²Yield stress by productStop calc* 0.35 PaSafety line* 1 PaWater/tonerNo networkThin lotionCarbomer gelKetchup/mayoToothpaste0.11101001,000Yield stress (Pa · log scale)* Calc · per-size recalc pendingBars = Literature range · estimate
The paper-sheet analogy and yield stress by product (log scale). The stop calculation and safety line are pending per-size recalculation; the bars are literature ranges (estimate).

Pass criteria by formula type

FormulaGel · cream
SpiculesMust not settle (kept suspended)
PassYield stress of 1 Pa or more (when a rheometer is available) + no settled layer in the settling test
FormulaAmpoule · liquid
SpiculesMay settle · shake before use
PassAfter shaking, spreads evenly again and the bottom does not cake

Test methods

  1. Rheometer stress sweep
    At 25 ℃, raise the applied stress step by step and read the point where the sample starts to flow (yield stress τy). Result in Pa.
  2. Vane spindle yield test
    Fit a vane spindle to a Brookfield-type viscometer and read the yield value. Result in Pa. The alternative when no rheometer is available.
  3. Settling test (required for gels and creams · together with the rheometer result)
    Fill a clear bottle, seal it and stand it upright. At room temperature and at 45 ℃, record the settled layer at the bottom (mm) and the clear layer on top (mm) at 24 h · 3 d · 7 d. No settled layer = pass. Do not call it a pass on 24 h alone.Test condition · conversion
  4. Ampoule · liquid
    After the same bottle test, invert and shake by hand (record the number of shakes) and check whether it spreads evenly again and whether the bottom has caked.
How to measure yield stress, and how to judgeStress sweep · 25 ℃Yield stress τyNetwork holdsNetwork breaks, flowsApplied stress (Pa · log scale)Deformation · flowJudging gels · creamsRheometer available?YesNoτy ≥ 1 Pa · 25 ℃Settling test onlySettling test (both paths)Room temp. · 45 ℃ — 24 h · 3 d · 7 d
On a stress-sweep curve, the point where flow begins is the yield stress. Without a rheometer, judge by the settling test alone; the settling test is required on both paths.

Keeping the network intact during manufacture

  • Add spicules last, after cooling below 40 ℃. Do not use high-speed mixing or homogenising after adding them (the network breaks and loses viscosity and yield stress).
  • Using a divalent salt (for example Zinc PCA) in a carbomer gel can collapse the network.
  • Carbomer networks loosen at low pH. For acidic gels, use a thickener that keeps its network in acid, such as Polyacrylate Crosspolymer-6.
  • Gum and cellulose thickeners (Xanthan Gum · Cellulose Gum · Hydroxyethylcellulose, etc.) dull the spicule tingling sensation, so they are not used in spicule formulas.

Not measured — to be added after measurement

  • Measured yield stress of our gelNot measured
  • Measured yield stress of our creamNot measured
  • Spicule axial canal diameter (the calculation assumes a solid spicule)Not measured

These will be added here after the first settling observation and rheometer measurement. The 1 Pa design target is a goal built on calculation and may be lowered by measurement.

References

  1. Calculation: UNIZ LAB R&D physical calculation (drag of slender particles + literature stop criterion measured with round particles) · an estimate trusted to its order of magnitude
  2. True density: Protech Korea Co., Ltd. ((주)프로테크코리아) · Test report 2022-07-04~05 — AccuPyc II 1340 gas pycnometer · density 2.0417 g/cm³ (5 cycles, σ ±0.0016)

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