From 026fa944b093e9b32ae310fe68a4a4de23785e23 Mon Sep 17 00:00:00 2001 From: marcocaggioni Date: Fri, 25 Sep 2026 23:54:53 -0400 Subject: [PATCH] Docs: HB vs TC walkthrough on 2% Carbopol in glycerin (issue #27) - New docs/walkthrough-carbopol-glycerin.md: HB and TC fits of the cp02_gly_20c_fc.json flow curve (2% Carbopol in glycerin, 20 C) - HB: sigma_y=0.674 Pa, K=13.65, n=0.713 (RedChi2 1.83e-3) - TC: sigma_y=0.376 Pa, gamma_dot_c=0.00182 1/s, eta_bg=3.71 Pa.s (RedChi2 3.55e-3) - Shows how the viscous continuous phase dominates above ~10 1/s and how TC's eta_bg isolates it (~2.6x pure glycerin viscosity) - Mermaid workflow diagram with committed SVG fallback for EPUB - Dataset archived under docs/walkthrough/ --- docs/index.md | 5 +- docs/walkthrough-carbopol-glycerin.md | 107 + docs/walkthrough/cp02_gly_20c_fc.json | 2826 +++++++++++++++++ docs/walkthrough/fig11_hb_tc_glycerin.png | Bin 0 -> 106339 bytes .../fig12_tc_decomposition_gly.png | Bin 0 -> 104590 bytes docs/walkthrough/fig13_viscosity_glycerin.png | Bin 0 -> 88729 bytes .../walkthrough_hb_tc_gly_workflow.svg | 1 + 7 files changed, 2938 insertions(+), 1 deletion(-) create mode 100644 docs/walkthrough-carbopol-glycerin.md create mode 100644 docs/walkthrough/cp02_gly_20c_fc.json create mode 100644 docs/walkthrough/fig11_hb_tc_glycerin.png create mode 100644 docs/walkthrough/fig12_tc_decomposition_gly.png create mode 100644 docs/walkthrough/fig13_viscosity_glycerin.png create mode 100644 docs/walkthrough/walkthrough_hb_tc_gly_workflow.svg diff --git a/docs/index.md b/docs/index.md index b487918..51f047d 100644 --- a/docs/index.md +++ b/docs/index.md @@ -124,7 +124,9 @@ runs it. Then see the **[wormlike-micelle + polymer case study](walkthrough-carr where the microstructure-informed `carreau_carreau` model resolves two relaxation times across a temperature series. And don't miss the **[polymer solution case study](walkthrough-carreau)**, where a Carreau fit meets the Cox–Merz and Delaware–Rutgers rules on amplitude, flow, and -frequency sweeps. Then browse the **[API reference](api)**. +frequency sweeps. For yield-stress fluids, the **[Carbopol in glycerin case study](walkthrough-carbopol-glycerin)** +pits Herschel–Bulkley against the three-component model and shows how a viscous continuous +phase rewrites the flow curve. Then browse the **[API reference](api)**. ## 🧪 Try it in your browser @@ -149,6 +151,7 @@ bottom of the page. walkthrough walkthrough-carreau-carreau walkthrough-carreau +walkthrough-carbopol-glycerin ``` ```{toctree} diff --git a/docs/walkthrough-carbopol-glycerin.md b/docs/walkthrough-carbopol-glycerin.md new file mode 100644 index 0000000..05f5c9d --- /dev/null +++ b/docs/walkthrough-carbopol-glycerin.md @@ -0,0 +1,107 @@ +# 🍯 Walkthrough: yield stress in a viscous sea — HB vs TC on 2% Carbopol in glycerin + +*Carbopol in water is the textbook yield-stress fluid. Put the same microgel in glycerin — +a continuous phase a thousand times more viscous — and the flow curve changes character. +This case study fits Herschel–Bulkley and the three-component (TC) model side by side and +shows how the TC decomposition isolates exactly what the viscous background is doing.* + +## 🧪 The dataset + +`cp02_gly_20c_fc.json` (attached to [issue #27](https://github.com/rheopy/rheofit/issues/27), archived here +as `walkthrough/cp02_gly_20c_fc.json`) holds an equilibrium flow curve of **2% Carbopol in +glycerin** at **20 °C**: 51 points from 0.001 to 100 s⁻¹. + +```python +import rheofit + +rheofit.print_steps("walkthrough/cp02_gly_20c_fc.json") +df = rheofit.load_step("walkthrough/cp02_gly_20c_fc.json", 0) # flow curve +``` + +Compare with the [original Carbopol case study](walkthrough) — same polymer, but there the +continuous phase was water (≈1 mPa·s) and here it is glycerin (≈1.41 Pa·s at 20 °C). That +single change rewrites the high-shear half of the flow curve. + +````{only} builder_html +```mermaid +flowchart TD + A["cp02_gly_20c_fc.json
2% Carbopol in glycerin, 20 °C
γ̇ = 0.001–100 s⁻¹"] + A --> B["Herschel–Bulkley fit
σ = σ_y + Kγ̇ⁿ"] + A --> C["TC fit
σ = σ_y + σ_y(γ̇/γ̇_c)½ + η_bgγ̇"] + B --> D["Compare:
RedChi², residuals,
parameter meaning"] + C --> D + D --> E["Decompose TC:
elastic / plastic / viscous"] + E --> F["✅ η_bg isolates the
viscous continuous phase"] +``` +```` + +```{only} not builder_html +![Analysis workflow: HB and TC fits of the Carbopol-in-glycerin flow curve, comparison, and TC decomposition](walkthrough/walkthrough_hb_tc_gly_workflow.svg) +``` + +## 🥊 Head-to-head: HB vs TC + +```python +hb = rheofit.fit(df, "herschel_bulkley", effort="thorough", seed=0) +tc = rheofit.fit(df, "tc", effort="thorough", seed=0) +``` + +| Model | σ_y (Pa) | 2nd param | 3rd param | RedChi² | cond | +|-------|----------|-----------|-----------|---------|------| +| Herschel–Bulkley | 0.674 ± 0.014 | K = 13.65 ± 0.12 Pa·sⁿ | n = 0.713 ± 0.004 | 1.83×10⁻³ | 3.5 | +| TC | 0.376 ± 0.021 | γ̇_c = 0.00182 ± 0.00027 s⁻¹ | η_bg = 3.71 ± 0.10 Pa·s | 3.55×10⁻³ | 16.2 | + +Both fits are clean and fully identified. Honestly, HB wins on statistics alone — but the +two models disagree on the *physics*, and that disagreement is the interesting part: + +![HB vs TC fits of the 2% Carbopol in glycerin flow curve, with relative residuals](walkthrough/fig11_hb_tc_glycerin.png) + +## 🔍 Reading the parameters: where the glycerin shows up + +**HB's exponent tells on the background.** In water, Carbopol thins hard (n ≈ 0.4–0.5). +Here n = 0.713 — the curve thins *less* steeply because a large Newtonian background props +up the high-shear stress. HB has no separate knob for that background, so it smears the +effect into K and n. + +**TC names the background.** The TC model splits the stress into three additive +contributions — a constant elastic term (the yield stress), a plastic term growing as +√γ̇, and a Newtonian viscous term: + +$$\sigma = \sigma_y + \sigma_y\left(\frac{\dot{\gamma}}{\dot{\gamma}_c}\right)^{1/2} + \eta_{bg}\,\dot{\gamma}$$ + +![TC three-term decomposition of the Carbopol-in-glycerin flow curve](walkthrough/fig12_tc_decomposition_gly.png) + +The decomposition shows the handoff directly: the plastic term carries the mid-range, and +above $\dot{\gamma} \approx$ 10 s⁻¹ the **viscous term $\eta_{bg}\dot{\gamma}$ dominates**. +The fitted background viscosity is **η_bg = 3.71 Pa·s** — about 2.6× the viscosity of +pure glycerin at 20 °C (≈1.41 Pa·s). The excess is the Carbopol microgel's own +contribution to the high-shear viscosity, riding on top of the solvent. + +**The two yield stresses differ, and TC's is the honest one.** HB reports σ_y = 0.67 Pa; +TC reports σ_y = 0.38 Pa. Part of what HB attributes to yielding is, in TC's accounting, +viscous stress from the glycerin background that is already present at low shear rates. +When the continuous phase is this viscous, "yield stress" from a two-parameter-style fit +is partly background in disguise. + +The viscosity view makes the same point from the other side: the data levels off toward +the TC background instead of thinning toward zero, and HB — with no plateau parameter — +is forced to keep bending downward. + +![Viscosity view: HB vs TC, with the TC background viscosity and pure-glycerin reference lines](walkthrough/fig13_viscosity_glycerin.png) + +## 🎯 Takeaways + +- **The continuous phase sets the high-shear story.** In water the background is + negligible; in glycerin it dominates above ~10 s⁻¹. Same microgel, different fluid. +- **HB fits slightly better here (RedChi² 1.8×10⁻³ vs 3.6×10⁻³) but explains less.** + Its n = 0.713 quietly absorbs the background viscosity into the power law. +- **TC's η_bg = 3.71 Pa·s isolates the physics the issue asked about**: a viscous + background ≈2.6× pure glycerin, with the microgel contributing the rest. +- **Yield stress is model-dependent when the background is viscous.** TC's σ_y = 0.38 Pa + vs HB's 0.67 Pa — the difference is background viscous stress that HB books as yield. + +## 📚 References + +- W. H. Herschel & R. Bulkley, "Konsistenzmessungen von Gummi-Benzollösungen", + *Kolloid-Z.* **39**, 291–300 (1926). [doi:10.1007/BF01432034](https://doi.org/10.1007/BF01432034) +- The TC (three-component) model is documented in rheofit's [TC model page](models/tc). diff --git a/docs/walkthrough/cp02_gly_20c_fc.json b/docs/walkthrough/cp02_gly_20c_fc.json new file mode 100644 index 0000000..634b0c7 --- /dev/null +++ b/docs/walkthrough/cp02_gly_20c_fc.json @@ -0,0 +1,2826 @@ +{ + "Schema": { + "Url": "https://software.tainstruments.com/schemas/TRIOSJSONExportSchema" + }, + "Operators": [], + "Sample": { + "Name": "cp02_gly_20c_fc", + "Density": { + "Value": 1000.0, + "Unit": { + "Name": "g/cm\u00b3" + } + } + }, + "Procedure": { + "Name": "FLowCurve_to_0.001", + "Steps": [ + { + "Name": "Flow-Sweep : \nTemperature 20 \u00b0C Inherit Set Point: Off \nSoak Time 0.0 s Wait For Temperature: Off \nLogarithmic sweep\nShear rate 100 to 1.0e-31/s\nPoints per decade 10 \nSteady state sensing: On Max. equilibration time 100.0 s \nSample period 10.0 s \n% tolerance 1.0 \nConsecutive within 3 \nScaled time 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"Torque_\u00b5N.m": 315.256096655503, + "Step time_s": 790.666076660156, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0009002685547, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.0559070967137814 + }, + { + "Displacement_rad": 1.81122004985809, + "Axial force_N": -0.0116560952737927, + "Gap_\u00b5m": 45.051499910187, + "Torque_\u00b5N.m": 269.250973360613, + "Step time_s": 831.714172363281, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0013999938965, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.0444085821509361 + }, + { + "Displacement_rad": 1.44139003753662, + "Axial force_N": -0.013427940197289, + "Gap_\u00b5m": 45.0088009529281, + "Torque_\u00b5N.m": 230.678822845221, + "Step time_s": 872.789245605469, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0041007995605, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.0352750681340694 + }, + { + "Displacement_rad": 1.14982998371124, + "Axial force_N": -0.0162887498736382, + "Gap_\u00b5m": 45.0119987362996, + "Torque_\u00b5N.m": 198.104680748656, + "Step time_s": 913.861389160156, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 20.00119972229, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.0280199348926544 + }, + { + "Displacement_rad": 0.904899001121521, + "Axial force_N": -0.012993773445487, + "Gap_\u00b5m": 45.0373008789029, + "Torque_\u00b5N.m": 170.301893376745, + "Step time_s": 954.915466308594, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 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"Temperature_\u00b0C": 20.0007991790771, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.00280200107954443 + }, + { + "Displacement_rad": 0.0912059023976326, + "Axial force_N": -0.0158459637314081, + "Gap_\u00b5m": 45.0525985797867, + "Torque_\u00b5N.m": 44.7170859843027, + "Step time_s": 1365.60559082031, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0044002532959, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.0022257047239691 + }, + { + "Displacement_rad": 0.0719583034515381, + "Axial force_N": -0.0146117433905602, + "Gap_\u00b5m": 45.0535007985309, + "Torque_\u00b5N.m": 39.9846139771398, + "Step time_s": 1406.69470214844, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0023002624512, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.00176794140134007 + }, + { + "Displacement_rad": 0.0573147982358932, + "Axial force_N": -0.015583286061883, + "Gap_\u00b5m": 45.0053012173157, + "Torque_\u00b5N.m": 35.9104087692685, + "Step time_s": 1447.77673339844, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0000991821289, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.00140433618798852 + }, + { + "Displacement_rad": 0.0456667989492416, + "Axial force_N": -0.0167847089469433, + "Gap_\u00b5m": 45.0373991043307, + "Torque_\u00b5N.m": 32.3856947943568, + "Step time_s": 1488.85681152344, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 19.9992008209229, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.00111558043863624 + }, + { + "Displacement_rad": 0.0449027009308338, + "Axial 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"Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0048007965088, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.000352663744706661 + }, + { + "Displacement_rad": 0.0142628997564316, + "Axial force_N": -0.0219563860446215, + "Gap_\u00b5m": 45.0242005172186, + "Torque_\u00b5N.m": 19.3927244254155, + "Step time_s": 1795.25256347656, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0030002593994, + "Procedure Step Id": "132ae93f-c758-4442-936a-7ccbd26444eb", + "Velocity_rad/s": 0.000280185369774699 + }, + { + "Displacement_rad": 0.0113482996821404, + "Axial force_N": -0.0221467334777117, + "Gap_\u00b5m": 45.0236002507154, + "Torque_\u00b5N.m": 18.0502065632027, + "Step time_s": 1846.31384277344, + "Results Step Id": "1fe0ced9-5160-47f4-bc46-07fb8f12b721", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 20.0041007995605, + "Procedure Step 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    cp02_gly_20c_fc.json
    2% Carbopol in glycerin, 20 °C
    γ̇ = 0.001–100 s⁻¹

    Herschel–Bulkley fit
    σ = σ_y + Kγ̇ⁿ

    TC fit
    σ = σ_y + σ_y(γ̇/γ̇_c)½ + η_bgγ̇

    Compare:
    RedChi², residuals,
    parameter meaning

    Decompose TC:
    elastic / plastic / viscous

    ✅ η_bg isolates the
    viscous continuous phase

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