diff --git a/docs/index.md b/docs/index.md index d52c0cc..b487918 100644 --- a/docs/index.md +++ b/docs/index.md @@ -122,7 +122,9 @@ New here? Read the **[Carbopol case study](walkthrough)** — a complete, reprod head-to-head of the TC model against Herschel–Bulkley on real data, run the way the skill runs it. Then see the **[wormlike-micelle + polymer case study](walkthrough-carreau-carreau)**, where the microstructure-informed `carreau_carreau` model resolves two relaxation times across -a temperature series. Then browse the **[API reference](api)**. +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)**. ## 🧪 Try it in your browser @@ -146,6 +148,7 @@ bottom of the page. walkthrough walkthrough-carreau-carreau +walkthrough-carreau ``` ```{toctree} diff --git a/docs/walkthrough-carreau.md b/docs/walkthrough-carreau.md new file mode 100644 index 0000000..ae2475c --- /dev/null +++ b/docs/walkthrough-carreau.md @@ -0,0 +1,146 @@ +# 🌀 Walkthrough: one polymer, three experiments — Carreau fitting meets Cox–Merz and Delaware–Rutgers + +*Steady shear says how a polymer solution flows; oscillation says how it relaxes. For a +high-molecular-weight linear polymer in water, the two stories should be the same story — +and with `rheofit` you can check, quantitatively, that they are.* + +## 🧪 The dataset + +`a_remake_dhr2.json` (attached to [issue #25](https://github.com/rheopy/rheofit/issues/25), archived here +as `walkthrough/a_remake_dhr2.json`) holds three equilibrium experiments on a **high molecular +weight linear polymer in aqueous solution** at **25 °C**: + +| # | Step | Range | Points | +|---|------|-------|--------| +| 0 | Amplitude sweep | strain 0.1 → 1000 % at ω = 1 rad/s | 41 | +| 1 | Flow sweep | shear rate 1000 → 0.01 s⁻¹ | 51 | +| 2 | Frequency sweep | ω = 100 → 0.1 rad/s at γ = 0.5 % | 31 | + +```python +import rheofit + +rheofit.print_steps("walkthrough/a_remake_dhr2.json") +flow = rheofit.load_step("walkthrough/a_remake_dhr2.json", 1) # flow curve +amp = rheofit.load_step("walkthrough/a_remake_dhr2.json", 0) # amplitude sweep +freq = rheofit.load_step("walkthrough/a_remake_dhr2.json", 2) # frequency sweep +``` + +````{only} builder_html +```mermaid +flowchart TD + A["a_remake_dhr2.json
high-MW linear polymer, 25 °C"] + A --> B["Amplitude sweep
γ₀ = 0.1–1000 % @ ω = 1 rad/s"] + A --> C["Flow sweep
γ̇ = 0.01–1000 s⁻¹"] + A --> D["Frequency sweep
ω = 0.1–100 rad/s @ γ = 0.5 %"] + B --> E["Delaware–Rutgers check
η′(γ₀ω) vs η(γ̇)"] + C --> E + C --> F["Carreau fit
η₀, λ, n"] + C --> G["Cox–Merz check
|η*(ω)| vs η(γ̇)"] + D --> G + E --> H["✅ steady & oscillatory agree"] + G --> H +``` +```` + +```{only} not builder_html +![Analysis workflow: three experiments feeding the Carreau fit, the Cox–Merz check, and the Delaware–Rutgers check](walkthrough/walkthrough_carreau_workflow.svg) +``` + +## 📐 The Carreau model + +The [Carreau](models/carreau) model describes a fluid with a zero-shear plateau that thins +toward a power law at high shear rates: + +$$\eta(\dot{\gamma}) = \eta_0 \left[1 + (\lambda \dot{\gamma})^2\right]^{(n-1)/2}$$ + +Each parameter has a direct physical reading: **η₀** is the zero-shear viscosity of the +fully entangled network, **λ** is the characteristic relaxation time (thinning sets in at +$\dot{\gamma}_c = 1/\lambda$), and **n** is the high-shear power-law exponent. Fitting the +flow curve is one line: + +```python +res = rheofit.fit(flow, "carreau", effort="thorough", seed=0) +``` + +| Parameter | Value | Rel. error | Physical meaning | +|-----------|-------|-----------|------------------| +| η₀ | 1.992 Pa·s | 1.3 % | zero-shear plateau | +| λ | 0.199 s | 6.2 % | relaxation time → thinning above γ̇ ≈ 5 s⁻¹ | +| n | 0.414 | 2.3 % | power-law exponent in the thinning regime | + +RedChi² = 3.85×10⁻³, condition number 9.5 — a clean, fully identified fit. The residuals +show a mild S-shape (±10 %), the honest signature of a real polymer solution against the +idealized Carreau form, not a fitting failure. + +![Carreau fit to the flow curve, with relative residuals](walkthrough/fig7_carreau_fit.png) + +## 🔁 Cox–Merz: the frequency sweep predicts the flow curve + +In 1958, Cox and Merz noticed something remarkable for polymer melts and solutions: the +**steady-shear viscosity equals the magnitude of the complex viscosity** when shear rate +and angular frequency are matched — + +$$\eta(\dot{\gamma}) = |\eta^*(\omega)|\Big|_{\omega=\dot{\gamma}}$$ + +— even though one is a nonlinear steady measurement and the other comes from small, +linear oscillations. No deep theory demanded it; the data did +([Cox & Merz, 1958](https://doi.org/10.1002/pol.1958.1202811812)). + +Plotting $|\eta^*(\omega)|$ from the frequency sweep directly onto $\eta(\dot{\gamma})$ +from the flow curve: + +![Cox–Merz superposition: complex viscosity from the frequency sweep overlaid on the steady-shear flow curve](walkthrough/fig8_cox_merz.png) + +The two curves coincide to within **2.3 %** (log-RMS) over three decades, 0.1–100 s⁻¹. +For this linear polymer solution, Cox–Merz holds essentially exactly — the small-amplitude +oscillatory measurement predicts the nonlinear flow curve with no adjustable parameters. + +## 📊 Delaware–Rutgers: the amplitude sweep predicts the flow curve too + +Doraiswamy and co-workers generalized Cox–Merz to *other* shear deformations: in a strain +sweep at fixed frequency, the **dynamic viscosity plotted against the strain-rate amplitude** +recovers the steady-shear viscosity — + +$$\eta(\dot{\gamma}) = \eta'(\gamma_0 \omega)\Big|_{\dot{\gamma}=\gamma_0\omega}$$ + +— known as the **Delaware–Rutgers rule** after the two university groups +([Doraiswamy et al., 1991](https://doi.org/10.1122/1.550184)). + +Here the amplitude sweep ran at ω = 1 rad/s, so $\gamma_0\omega$ spans 0.001–10 s⁻¹ — +right across the Carreau plateau and into the thinning regime: + +![Delaware–Rutgers superposition: dynamic viscosity from the amplitude sweep overlaid on the steady-shear flow curve](walkthrough/fig9_delaware_rutgers.png) + +Agreement within **9 %** (log-RMS). The slight shortfall at the highest strain rates is +expected: beyond $\gamma_0 \approx$ 10–25 % the material leaves the linear regime and +$\eta'$ begins its own nonlinear descent. + +That the comparison is legitimate at all needs one check — the frequency sweep must sit +*inside* the linear viscoelastic regime. The amplitude sweep confirms it: $G'$ and $G''$ +are strain-independent up to $\gamma_0 \approx$ 10–25 %, so the frequency sweep's +$\gamma = 0.5$ % is safely linear. + +![Amplitude sweep at 1 rad/s: G′ and G″ are strain-independent (linear regime) up to γ₀ ≈ 10–25%](walkthrough/fig10_amplitude_lve.png) + +## 🎯 Takeaways + +- **One model, three experiments.** The Carreau fit (η₀ = 1.99 Pa·s, λ = 0.199 s, + n = 0.414) describes the flow curve; Cox–Merz and Delaware–Rutgers show the oscillatory + experiments were measuring the same physics all along. +- **No adjustable parameters.** Both superposition rules are parameter-free predictions — + when they hold this well (2.3 % and 9 %), it is strong evidence the sample is a simple, + well-behaved linear polymer solution with no thixotropy, slip, or degradation during + the measurement. +- **Oscillation as a viscometer.** Where steady shear is hard — very low rates, very high + rates, fragile samples — a frequency or amplitude sweep plus the right rule gives you + the flow curve anyway. + +## 📚 References + +- P. J. Carreau, "Rheological equations from molecular network theories", + *Trans. Soc. Rheol.* **16**, 99–127 (1972). [doi:10.1122/1.549276](https://doi.org/10.1122/1.549276) +- W. P. Cox & E. H. Merz, "Correlation of dynamic and steady flow viscosities", + *J. Polym. Sci.* **28**(118), 619–622 (1958). [doi:10.1002/pol.1958.1202811812](https://doi.org/10.1002/pol.1958.1202811812) +- D. Doraiswamy, A. N. Mujumdar, I. Tsao, A. N. Beris, S. C. Danforth & A. B. Metzner, + "The Cox–Merz rule extended: A rheological model for concentrated suspensions and other + materials with a yield stress", *J. Rheol.* **35**, 647–685 (1991). [doi:10.1122/1.550184](https://doi.org/10.1122/1.550184) diff --git a/docs/walkthrough/a_remake_dhr2.json b/docs/walkthrough/a_remake_dhr2.json new file mode 100644 index 0000000..3f5d6a7 --- /dev/null +++ b/docs/walkthrough/a_remake_dhr2.json @@ -0,0 +1,7402 @@ +{ + "Schema": { + "Url": "https://software.tainstruments.com/schemas/TRIOSJSONExportSchema" + }, + "Operators": [], + "Sample": { + "Name": "A_remake_DHR2", + "Density": { + "Value": 1000.0, + "Unit": { + "Name": "g/cm\u00b3" + } + } + }, + "Procedure": { + "Name": "Basic_Cream", + "Steps": [ + { + "Name": "Conditioning-Sample : \nTemperature 25 \u00b0C Inherit Set Point: Off \nSoak Time 0.0 s Wait For Temperature: On \nWait for axial relaxation: Off\nPerform preshear: Off\nPerform equilibration: Off\n\n", + "Id": "ee6093a8-8d74-40d3-8e5a-c7ba51b31b86" + }, + { + "Name": "Oscillation-Amplitude : \nTemperature Inherit Set Point: On \nSoak Time 0.0 s Wait For Temperature: Off \nAngular frequency 1.0 rad/s\r\nLogarithmic 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"DisplayName": "Raw phase", + "ValueType": "Number", + "Unit": { + "Name": "\u00b0" + } + }, + "Procedure Step Id": { + "DisplayName": "Procedure Step Id", + "ValueType": "Uuid" + }, + "Results Step Id": { + "DisplayName": "Results Step Id", + "ValueType": "Uuid" + }, + "Displacement_rad": { + "DisplayName": "Displacement", + "ValueType": "Number", + "Unit": { + "Name": "rad" + } + }, + "Step time_s": { + "DisplayName": "Step time", + "ValueType": "Number", + "Unit": { + "Name": "s" + } + }, + "Axial force_N": { + "DisplayName": "Axial force", + "ValueType": "Number", + "Unit": { + "Name": "N" + } + }, + "Velocity_rad/s": { + "DisplayName": "Velocity", + "ValueType": "Number", + "Unit": { + "Name": "rad/s" + } + }, + "Torque_\u00b5N.m": { + "DisplayName": "Torque", + "ValueType": "Number", + "Unit": { + "Name": "\u00b5N.m" + } + }, + "Termination reason": { + "DisplayName": "Termination reason", + "ValueType": "Text" + }, + "Temperature_\u00b0C": { + "DisplayName": "Temperature", + 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"40470112-f83a-419a-922e-3ba43af61da7", + "Velocity_rad/s": -1.3038399515608E-07, + "Oscillation displacement_rad": 0.00111765926703811 + }, + { + "Axial force_N": -0.0308279003947973, + "Gap_\u00b5m": 30.0383999274345, + "Angular frequency_rad/s": 1.00000035762787, + "Raw phase_\u00b0": 80.0015754464416, + "Torque_\u00b5N.m": 0.000837357017058338, + "Step time_s": 238.762542724609, + "Results Step Id": "a52e9757-fc1f-4e6e-a95f-016d300e9ba3", + "Temperature_\u00b0C": 25.0083999633789, + "Oscillation torque_\u00b5N.m": 5.29985982211656, + "Procedure Step Id": "40470112-f83a-419a-922e-3ba43af61da7", + "Velocity_rad/s": 9.01517978491029E-07, + "Oscillation displacement_rad": 0.000886286434251815 + }, + { + "Axial force_N": -0.0297366008162498, + "Gap_\u00b5m": 30.0325991702266, + "Angular frequency_rad/s": 1.00000035762787, + "Raw phase_\u00b0": 79.9422074421759, + "Torque_\u00b5N.m": -0.000872230010440234, + "Step time_s": 248.739074707031, + "Results Step Id": 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"Raw phase_\u00b0": 80.5184158609365, + "Torque_\u00b5N.m": 0.00252391996191648, + "Step time_s": 338.203918457031, + "Results Step Id": "a52e9757-fc1f-4e6e-a95f-016d300e9ba3", + "Temperature_\u00b0C": 25.0023994445801, + "Oscillation torque_\u00b5N.m": 0.526310998338886, + "Procedure Step Id": "40470112-f83a-419a-922e-3ba43af61da7", + "Velocity_rad/s": 3.99535991846278E-07, + "Oscillation displacement_rad": 8.79824656294659E-05 + }, + { + "Axial force_N": -0.0286538992077112, + "Gap_\u00b5m": 30.0302999676205, + "Angular frequency_rad/s": 1.00000035762787, + "Raw phase_\u00b0": 80.1388076072455, + "Torque_\u00b5N.m": -0.00235592989561439, + "Step time_s": 348.172882080078, + "Results Step Id": "a52e9757-fc1f-4e6e-a95f-016d300e9ba3", + "Temperature_\u00b0C": 24.9834003448486, + "Oscillation torque_\u00b5N.m": 0.420575986481708, + "Procedure Step Id": "40470112-f83a-419a-922e-3ba43af61da7", + "Velocity_rad/s": -4.19093986181451E-08, + "Oscillation displacement_rad": 7.03718033037148E-05 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"a52e9757-fc1f-4e6e-a95f-016d300e9ba3", + "Temperature_\u00b0C": 25.0102005004883, + "Oscillation torque_\u00b5N.m": 0.168225000152233, + "Procedure Step Id": "40470112-f83a-419a-922e-3ba43af61da7", + "Velocity_rad/s": -5.49479004519071E-08, + "Oscillation displacement_rad": 2.81594911939465E-05 + }, + { + "Axial force_N": -0.0378790982067585, + "Gap_\u00b5m": 30.0547999358969, + "Angular frequency_rad/s": 1.00000035762787, + "Raw phase_\u00b0": 79.4441500478986, + "Torque_\u00b5N.m": 0.000291404012031649, + "Step time_s": 398.337890625, + "Results Step Id": "a52e9757-fc1f-4e6e-a95f-016d300e9ba3", + "Temperature_\u00b0C": 25.0069999694824, + "Oscillation torque_\u00b5N.m": 0.133368999399863, + "Procedure Step Id": "40470112-f83a-419a-922e-3ba43af61da7", + "Velocity_rad/s": 1.52736006953091E-07, + "Oscillation displacement_rad": 2.22591970668873E-05 + }, + { + "Displacement_rad": 227.417999267578, + "Axial force_N": 0.5273157954216, + "Gap_\u00b5m": 30.016599339433, + "Torque_\u00b5N.m": 4547.8199608624, + "Step time_s": 13.4054803848267, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0053005218506, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 17.7150993347168 + }, + { + "Displacement_rad": 181.800994873047, + "Axial force_N": 0.458596229553223, + "Gap_\u00b5m": 30.0116007565521, + "Torque_\u00b5N.m": 4250.0770650804, + "Step time_s": 26.6060638427734, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9997005462646, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 14.0715999603271 + }, + { + "Displacement_rad": 146.375, + "Axial force_N": 0.403480768203735, + "Gap_\u00b5m": 30.0105002679629, + "Torque_\u00b5N.m": 3962.23226562142, + "Step time_s": 39.7860946655273, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0062999725342, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 11.1775045394897 + }, + { + "Displacement_rad": 110.952003479004, + "Axial force_N": 0.343349784612656, + "Gap_\u00b5m": 30.0280007650144, + "Torque_\u00b5N.m": 3689.37407620251, + "Step time_s": 52.950740814209, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9992008209229, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 8.87858009338379 + }, + { + "Displacement_rad": 91.2203979492188, + "Axial force_N": 0.298511773347855, + "Gap_\u00b5m": 30.0142000924097, + "Torque_\u00b5N.m": 3432.25849792361, + "Step time_s": 66.1717987060547, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9988994598389, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 7.05250310897827 + }, + { + "Displacement_rad": 73.2509994506836, + "Axial force_N": 0.250595241785049, + "Gap_\u00b5m": 30.020399208297, + "Torque_\u00b5N.m": 3187.99493834376, + "Step time_s": 79.2605819702148, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0137004852295, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 5.60200357437134 + }, + { + "Displacement_rad": 55.8339996337891, + "Axial force_N": 0.210233196616173, + "Gap_\u00b5m": 30.0096999126254, + "Torque_\u00b5N.m": 2956.22716657817, + "Step time_s": 92.3411636352539, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0023994445801, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 4.44983005523682 + }, + { + "Displacement_rad": 45.8846015930176, + "Axial force_N": 0.175745233893394, + "Gap_\u00b5m": 30.0406009046128, + "Torque_\u00b5N.m": 2734.73188281059, + "Step time_s": 105.514572143555, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9937000274658, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 3.53462958335876 + }, + { + "Displacement_rad": 36.6559982299805, + "Axial force_N": 0.147812411189079, + "Gap_\u00b5m": 30.0282008538488, + "Torque_\u00b5N.m": 2523.55239354074, + "Step time_s": 118.673080444336, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9897994995117, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 2.80765962600708 + }, + { + "Displacement_rad": 28.4762001037598, + "Axial force_N": 0.121589176356792, + "Gap_\u00b5m": 30.0226001854753, + "Torque_\u00b5N.m": 2320.8458442241, + "Step time_s": 131.800903320313, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.993200302124, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 2.23019909858704 + }, + { + "Displacement_rad": 22.8495998382568, + "Axial force_N": 0.0998189151287079, + "Gap_\u00b5m": 30.0410993077094, + "Torque_\u00b5N.m": 2127.53610685468, + "Step time_s": 144.959426879883, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0053997039795, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 1.77150893211365 + }, + { + "Displacement_rad": 18.260799407959, + "Axial force_N": 0.080164946615696, + "Gap_\u00b5m": 30.0227002298925, + "Torque_\u00b5N.m": 1942.1725301072, + "Step time_s": 158.070526123047, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0132007598877, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 1.40716218948364 + }, + { + "Displacement_rad": 14.6035003662109, + "Axial force_N": 0.0567191988229752, + "Gap_\u00b5m": 30.0376996165141, + "Torque_\u00b5N.m": 1763.96360620856, + "Step time_s": 171.195846557617, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9981002807617, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 1.11774456501007 + }, + { + "Displacement_rad": 11.3543996810913, + "Axial force_N": 0.0469932705163956, + "Gap_\u00b5m": 30.0102001347113, + "Torque_\u00b5N.m": 1595.12087702751, + "Step time_s": 184.30126953125, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0084991455078, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.887857615947723 + }, + { + "Displacement_rad": 9.09974002838135, + "Axial force_N": 0.0342493280768394, + "Gap_\u00b5m": 30.0461997539969, + "Torque_\u00b5N.m": 1435.71547232568, + "Step time_s": 197.421676635742, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9976005554199, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.705249965190887 + }, + { + "Displacement_rad": 7.13551998138428, + "Axial force_N": 0.0230163000524044, + "Gap_\u00b5m": 29.9926996376598, + "Torque_\u00b5N.m": 1283.71722530574, + "Step time_s": 210.531692504883, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9981994628906, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.560200989246368 + }, + { + "Displacement_rad": 5.72175979614258, + "Axial force_N": 0.0133975129574537, + "Gap_\u00b5m": 29.9968996841926, + "Torque_\u00b5N.m": 1141.30228757858, + "Step time_s": 223.605407714844, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9923992156982, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.444982588291168 + }, + { + "Displacement_rad": 4.49318981170654, + "Axial force_N": 0.00192471651826054, + "Gap_\u00b5m": 29.9958992400207, + "Torque_\u00b5N.m": 1008.43980908394, + "Step time_s": 236.717163085938, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0049991607666, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.35346195101738 + }, + { + "Displacement_rad": 3.61329007148743, + "Axial force_N": -0.0079538943246007, + "Gap_\u00b5m": 30.028999390197, + "Torque_\u00b5N.m": 884.570821654052, + "Step time_s": 249.806625366211, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0011005401611, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.280766516923904 + }, + { + "Displacement_rad": 2.89287996292114, + "Axial force_N": -0.0121585056185722, + "Gap_\u00b5m": 30.0189003610285, + "Torque_\u00b5N.m": 771.244755014777, + "Step time_s": 262.902709960938, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.99880027771, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.223020136356354 + }, + { + "Displacement_rad": 2.26117992401123, + "Axial force_N": -0.0111965779215097, + "Gap_\u00b5m": 30.0432002404705, + "Torque_\u00b5N.m": 667.104905005544, + "Step time_s": 275.976837158203, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0051002502441, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.177149832248688 + }, + { + "Displacement_rad": 1.78568005561829, + "Axial force_N": -0.0228670630604029, + "Gap_\u00b5m": 30.0099000014598, + "Torque_\u00b5N.m": 573.575845919549, + "Step time_s": 289.135894775391, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0034999847412, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.1407151222229 + }, + { + "Displacement_rad": 1.42114996910095, + "Axial force_N": -0.0238969717174768, + "Gap_\u00b5m": 30.0267001875909, + "Torque_\u00b5N.m": 489.507569000125, + "Step time_s": 302.27978515625, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9930000305176, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.111772440373898 + }, + { + "Displacement_rad": 1.14371001720428, + "Axial force_N": -0.0182793159037828, + "Gap_\u00b5m": 30.0307001452893, + "Torque_\u00b5N.m": 414.720736443996, + "Step time_s": 315.423767089844, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9985008239746, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.0887838006019592 + }, + { + "Displacement_rad": 0.900202989578247, + "Axial force_N": -0.0292439926415682, + "Gap_\u00b5m": 30.0292995234486, + "Torque_\u00b5N.m": 348.898873198777, + "Step time_s": 328.567474365234, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0081005096436, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.0705227628350258 + }, + { + "Displacement_rad": 0.717070996761322, + "Axial force_N": -0.0231057964265347, + "Gap_\u00b5m": 30.0097999570426, + "Torque_\u00b5N.m": 291.7273377534, + "Step time_s": 341.742584228516, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9983997344971, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.0560184866189957 + }, + { + "Displacement_rad": 0.578025996685028, + "Axial force_N": -0.0332741402089596, + "Gap_\u00b5m": 30.0291994790314, + "Torque_\u00b5N.m": 242.225680267438, + "Step time_s": 354.871185302734, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0004005432129, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.0444989614188671 + }, + { + "Displacement_rad": 0.451389014720917, + "Axial force_N": -0.0382713861763477, + "Gap_\u00b5m": 30.0455994874937, + "Torque_\u00b5N.m": 199.947215151042, + "Step time_s": 367.9990234375, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9906997680664, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.0353472419083118 + }, + { + "Displacement_rad": 0.36031100153923, + "Axial force_N": -0.0333370380103588, + "Gap_\u00b5m": 30.0055999105098, + "Torque_\u00b5N.m": 163.991047884338, + "Step time_s": 381.126556396484, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0021991729736, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.0280745662748814 + }, + { + "Displacement_rad": 0.28583300113678, + "Axial force_N": -0.0310314986854792, + "Gap_\u00b5m": 30.0350002362393, + "Torque_\u00b5N.m": 133.842942886986, + "Step time_s": 394.215179443359, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9902000427246, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.0223012994974852 + }, + { + "Displacement_rad": 0.274789988994598, + "Axial force_N": -0.0344673730432987, + "Gap_\u00b5m": 30.0005995086394, + "Torque_\u00b5N.m": 108.696913230233, + "Step time_s": 410.299652099609, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9888000488281, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.0177152305841446 + }, + { + "Displacement_rad": 0.179460003972054, + "Axial force_N": -0.0320811606943607, + "Gap_\u00b5m": 30.0200008496176, + "Torque_\u00b5N.m": 87.8441278473474, + "Step time_s": 423.396270751953, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9969997406006, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.014070906676352 + }, + { + "Displacement_rad": 0.141882002353668, + "Axial force_N": -0.0315823815762997, + "Gap_\u00b5m": 30.0066003546817, + "Torque_\u00b5N.m": 70.7272629369982, + "Step time_s": 436.470672607422, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9969005584717, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.0111782550811768 + }, + { + "Displacement_rad": 0.142499998211861, + "Axial force_N": -0.0322861708700657, + "Gap_\u00b5m": 30.0485007755924, + "Torque_\u00b5N.m": 56.7864262848161, + "Step time_s": 452.593383789063, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0004997253418, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00887863989919424 + }, + { + "Displacement_rad": 0.0916453972458839, + "Axial force_N": -0.0308327674865723, + "Gap_\u00b5m": 30.0298997899517, + "Torque_\u00b5N.m": 45.4531837021932, + "Step time_s": 465.772491455078, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9902992248535, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00705336732789874 + }, + { + "Displacement_rad": 0.0728126019239426, + "Axial force_N": -0.0304964017122984, + "Gap_\u00b5m": 30.0288993457798, + "Torque_\u00b5N.m": 36.3033286703285, + "Step time_s": 478.893188476563, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0023002624512, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00560402637347579 + }, + { + "Displacement_rad": 0.0582447983324528, + "Axial force_N": -0.0293821096420288, + "Gap_\u00b5m": 30.0224000966409, + "Torque_\u00b5N.m": 28.9152085315436, + "Step time_s": 492.035919189453, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0065994262695, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00444753747433424 + }, + { + "Displacement_rad": 0.0450566001236439, + "Axial force_N": -0.0303391069173813, + "Gap_\u00b5m": 30.0415995297953, + "Torque_\u00b5N.m": 23.0011901294347, + "Step time_s": 505.147766113281, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.994499206543, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00353242922574282 + }, + { + "Displacement_rad": 0.0360018983483315, + "Axial force_N": -0.0313079990446568, + "Gap_\u00b5m": 30.0272004096769, + "Torque_\u00b5N.m": 18.2564126589568, + "Step time_s": 518.321899414063, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.00830078125, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00280607934109867 + }, + { + "Displacement_rad": 0.0286746006458998, + "Axial force_N": -0.0299239251762629, + "Gap_\u00b5m": 30.0149004033301, + "Torque_\u00b5N.m": 14.5103795148316, + "Step time_s": 531.486755371094, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0049991607666, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00223009032197297 + }, + { + "Displacement_rad": 0.0228288993239403, + "Axial force_N": -0.0277185626327991, + "Gap_\u00b5m": 30.0057999993442, + "Torque_\u00b5N.m": 11.5366456157062, + "Step time_s": 544.623596191406, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.00119972229, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00176955398637801 + }, + { + "Displacement_rad": 0.018240200355649, + "Axial force_N": -0.0321212969720364, + "Gap_\u00b5m": 30.0021001748974, + "Torque_\u00b5N.m": 9.16477711143671, + "Step time_s": 557.704284667969, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9986000061035, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00140580977313221 + }, + { + "Displacement_rad": 0.0142026003450155, + "Axial force_N": -0.030185628682375, + "Gap_\u00b5m": 29.9956991511863, + "Torque_\u00b5N.m": 7.297207503143, + "Step time_s": 570.7783203125, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0039005279541, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00111949048005044 + }, + { + "Displacement_rad": 0.0113952998071909, + "Axial force_N": -0.0294911898672581, + "Gap_\u00b5m": 30.0243991659954, + "Torque_\u00b5N.m": 5.80940513827954, + "Step time_s": 583.836975097656, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0056991577148, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.000887060887180269 + }, + { + "Displacement_rad": 0.00915286038070917, + "Axial force_N": -0.0296526197344065, + "Gap_\u00b5m": 30.0268002320081, + "Torque_\u00b5N.m": 4.62752723251469, + "Step time_s": 596.917541503906, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9974994659424, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.000703621015418321 + }, + { + "Displacement_rad": 0.00711575010791421, + "Axial force_N": -0.0308739617466927, + "Gap_\u00b5m": 30.0231004075613, + "Torque_\u00b5N.m": 3.69228223462414, + "Step time_s": 610.006896972656, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9960994720459, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.000559444073587656 + }, + { + "Displacement_rad": 0.00570436986163259, + "Axial force_N": -0.0308786351233721, + "Gap_\u00b5m": 30.0298997899517, + "Torque_\u00b5N.m": 2.95531481242506, + "Step time_s": 623.103271484375, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9999008178711, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.000446106831077486 + }, + { + "Displacement_rad": 0.00456504989415407, + "Axial force_N": -0.0317648351192474, + "Gap_\u00b5m": 30.0399005936924, + "Torque_\u00b5N.m": 2.36242362916528, + "Step time_s": 636.189453125, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9972991943359, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00035156004014425 + }, + { + "Displacement_rad": 0.00365780992433429, + "Axial force_N": -0.0309158768504858, + "Gap_\u00b5m": 30.0366991723422, + "Torque_\u00b5N.m": 1.90112552900246, + "Step time_s": 649.333190917969, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 25.0041999816895, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.00028039058088325 + }, + { + "Displacement_rad": 0.00291468994691968, + "Axial force_N": -0.0301929302513599, + "Gap_\u00b5m": 30.0352003250737, + "Torque_\u00b5N.m": 1.52529833030712, + "Step time_s": 662.514526367188, + "Results Step Id": "e92a97e5-325c-420d-8332-150c9d185a93", + "Termination reason": "Steady state", + "Temperature_\u00b0C": 24.9997997283936, + "Procedure Step Id": "238f4405-bbb8-4ad8-9d70-f99f8e524071", + "Velocity_rad/s": 0.000223643219214864 + }, + { + "Axial force_N": -0.0343667007982731, + "Gap_\u00b5m": 30.010000045877, + "Angular frequency_rad/s": 100.000038146973, + "Raw phase_\u00b0": 168.032994488717, + "Torque_\u00b5N.m": 0.073158197722023, + "Step time_s": 6.03685522079468, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 25.0049991607666, + "Oscillation torque_\u00b5N.m": 34.9569017998874, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": 5.45210014024633E-07, + "Oscillation displacement_rad": 8.86194538907148E-05 + }, + { + "Axial force_N": -0.0323068015277386, + "Gap_\u00b5m": 30.0376996165141, + "Angular frequency_rad/s": 79.4326553344727, + "Raw phase_\u00b0": 160.811312535858, + "Torque_\u00b5N.m": 0.0724552009501167, + "Step time_s": 12.7601747512817, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 24.99880027771, + "Oscillation torque_\u00b5N.m": 20.2609007828869, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": 1.84554005500104E-06, + "Oscillation displacement_rad": 8.75191472005099E-05 + }, + { + "Axial force_N": -0.0323176011443138, + "Gap_\u00b5m": 30.0227002298925, + "Angular frequency_rad/s": 63.0957450866699, + "Raw phase_\u00b0": 148.878739829413, + "Torque_\u00b5N.m": 0.0867813980676146, + "Step time_s": 19.4833889007568, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 24.9925003051758, + "Oscillation torque_\u00b5N.m": 12.0082004286814, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": -1.62576000661829E-07, + "Oscillation 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5.61307979296544, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": 2.27726991397503E-06, + "Oscillation displacement_rad": 8.88229187694378E-05 + }, + { + "Axial force_N": -0.0358088985085487, + "Gap_\u00b5m": 30.0102001347113, + "Angular frequency_rad/s": 31.6230201721191, + "Raw phase_\u00b0": 89.8442946819694, + "Torque_\u00b5N.m": 0.0782179014890971, + "Step time_s": 39.5842018127441, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 24.9967002868652, + "Oscillation torque_\u00b5N.m": 4.89651984025841, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": 2.20097990677459E-06, + "Oscillation displacement_rad": 8.91631279955618E-05 + }, + { + "Axial force_N": -0.0233047995716333, + "Gap_\u00b5m": 30.0423998851329, + "Angular frequency_rad/s": 25.1187934875488, + "Raw phase_\u00b0": 77.9737674139457, + "Torque_\u00b5N.m": 0.0735189971123873, + "Step time_s": 46.2285461425781, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 25.0161991119385, + "Oscillation torque_\u00b5N.m": 4.57841997558717, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": 7.60295009172296E-08, + "Oscillation displacement_rad": 8.93681281013414E-05 + }, + { + "Axial force_N": -0.0372561998665333, + "Gap_\u00b5m": 30.024699299247, + "Angular frequency_rad/s": 19.9525699615479, + "Raw phase_\u00b0": 71.479719173746, + "Torque_\u00b5N.m": 0.074051399678865, + "Step time_s": 53.190185546875, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 24.9974002838135, + "Oscillation torque_\u00b5N.m": 4.27699978899909, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": 1.38437997065921E-06, + "Oscillation displacement_rad": 8.97307400009595E-05 + }, + { + "Axial force_N": -0.0316241011023521, + "Gap_\u00b5m": 30.020399208297, + "Angular frequency_rad/s": 15.8490209579468, + "Raw phase_\u00b0": 67.7485507547081, + "Torque_\u00b5N.m": 0.0781830991058996, + "Step time_s": 60.161018371582, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 24.9930992126465, + "Oscillation torque_\u00b5N.m": 3.92785977965104, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": -1.16054002319288E-06, + "Oscillation displacement_rad": 8.99897495401092E-05 + }, + { + "Axial force_N": -0.0298216007649899, + "Gap_\u00b5m": 30.0403007713612, + "Angular frequency_rad/s": 12.5891790390015, + "Raw phase_\u00b0": 66.3100924249359, + "Torque_\u00b5N.m": 0.078196698893862, + "Step time_s": 66.9845199584961, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 24.9948997497559, + "Oscillation torque_\u00b5N.m": 3.54532994606416, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": 1.14314002530591E-06, + "Oscillation displacement_rad": 8.99532533367164E-05 + }, + { + "Axial force_N": -0.0457380004227161, + "Gap_\u00b5m": 30.0347001029877, + "Angular frequency_rad/s": 10.0000667572021, + "Raw phase_\u00b0": 65.8652353741038, + "Torque_\u00b5N.m": 0.0787456002626641, + "Step time_s": 73.7614135742188, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 25.0023002624512, + "Oscillation torque_\u00b5N.m": 3.14884005092608, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": -9.68583009353097E-08, + "Oscillation displacement_rad": 9.02614920050837E-05 + }, + { + "Axial force_N": -0.0299235992133617, + "Gap_\u00b5m": 30.024000807316, + "Angular frequency_rad/s": 7.94326591491699, + "Raw phase_\u00b0": 66.577337236591, + "Torque_\u00b5N.m": 0.0794941996673515, + "Step time_s": 80.7322845458984, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 24.9958000183105, + "Oscillation torque_\u00b5N.m": 2.75901993518346, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": -1.39076996674703E-06, + "Oscillation displacement_rad": 9.06256900634617E-05 + }, + { + "Axial force_N": -0.0330784991383553, + "Gap_\u00b5m": 30.0379997497657, + "Angular frequency_rad/s": 6.30957460403442, + "Raw phase_\u00b0": 67.3426531029017, + "Torque_\u00b5N.m": 0.0754349969156465, + "Step time_s": 87.5935211181641, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 24.9934005737305, + "Oscillation torque_\u00b5N.m": 2.37796007240831, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": -9.32362979710888E-07, + "Oscillation displacement_rad": 9.04277476365678E-05 + }, + { + "Axial force_N": -0.0324029996991158, + "Gap_\u00b5m": 30.0291994790314, + "Angular frequency_rad/s": 5.0118579864502, + "Raw phase_\u00b0": 68.5518288124258, + "Torque_\u00b5N.m": 0.0768445005405738, + "Step time_s": 93.8307342529297, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 24.9969005584717, + "Oscillation torque_\u00b5N.m": 2.03445006263792, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": 6.06794969826296E-08, + "Oscillation displacement_rad": 9.05471024452709E-05 + }, + { + "Axial force_N": -0.0201383996754885, + "Gap_\u00b5m": 30.020899430383, + "Angular frequency_rad/s": 3.98105144500732, + "Raw phase_\u00b0": 69.7881272031439, + "Torque_\u00b5N.m": 0.0775723023593855, + "Step time_s": 100.701042175293, + "Results Step Id": "fb83b26a-70c6-4a59-8309-96448b17fdb7", + "Temperature_\u00b0C": 24.9983997344971, + "Oscillation torque_\u00b5N.m": 1.72446004853555, + "Procedure Step Id": "a7011543-b185-41a6-973a-bc33e519edab", + "Velocity_rad/s": -1.90943001143751E-06, + "Oscillation displacement_rad": 9.12494069780223E-05 + }, + { + "Axial force_N": -0.0294032990932465, + "Gap_\u00b5m": 30.0306001008721, + "Angular frequency_rad/s": 3.16228938102722, + "Raw 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a_remake_dhr2.json
high-MW linear polymer, 25 °C

Amplitude sweep
γ₀ = 0.1–1000 % @ ω = 1 rad/s

Flow sweep
γ̇ = 0.01–1000 s⁻¹

Frequency sweep
ω = 0.1–100 rad/s @ γ = 0.5 %

Delaware–Rutgers check
η′(γ₀ω) vs η(γ̇)

Carreau fit
η₀, λ, n

Cox–Merz check
|η*(ω)| vs η(γ̇)

✅ steady & oscillatory agree

 \ No newline at end of file