Slurry Yield Stress: Measurement, Calculation, Design

Last updated: 2026-10-27

Slurry yield stress is the stress a slurry must exceed before it will flow at all, and it decides more equipment choices than viscosity ever will. Gravity flow through launders and chutes typically stops between about 50 and 200 Pa, while pipeline restart pressure is set by the aged yield stress of the material in the line. This article shows how to measure it, calculate it, and design around it.

Key Takeaways

• Slurry yield stress, not viscosity, decides gravity flow, rake torque, and pipeline start-up.
• Vane tests measure yield stress directly; slump tests give a field estimate after calibration.
• Bingham and Herschel-Bulkley models fitted by the two-point method cover most tailings duty.
• Yield stress climbs steeply above a critical solids concentration; 1–2 points of water can halve it.
• Size rake drives and pumps for the maximum credible yield stress, never the design average.

What Is Slurry Yield Stress in a Mineral Slurry?

Slurry yield stress is a shear stress threshold that a slurry must exceed before any applied force produces continuous flow; below it the material sits still indefinitely, above it the slurry moves as a viscous fluid. The origin is a percolating network of flocculated fines — clays, slimes and precipitates bound by surface forces and flocculant polymers — that stores elastic energy under small loads and collapses at a critical stress. Coarse sand at 70% w/w solids has almost none; the same tonnage with 30% minus 20 µm slimes can behave like wet concrete.

A paste, in the sense used by tailings engineers, is a slurry that carries enough fines at a high enough solids fraction for this network to support its own weight — which is why paste holds a heap instead of spreading like water. Paste is not a fixed solids percentage but a yield-stress condition, confirmed by testwork, not assumed from density. For the thickener hardware producing such underflows, see our paste thickener design guide.

The commercially vital distinction is between yield stress and viscosity. Viscosity resists flow that is already happening; yield stress decides whether flow starts. A launder, pump sump, underflow well, or pipeline sitting full overnight is a zero-shear-rate environment, where only the yield stress fights back. That is why launder design, centrifugal pump selection and dry-stack tailings feasibility all key off yield stress rather than the viscosity vendors readily quote.

Governing Flow Models: Bingham Plastic and Herschel-Bulkley

Bingham plastic. For shear stress above the yield value:

τ = τ_y + η_p × γ̇

where τ = applied shear stress (Pa); τ_y = Bingham yield stress (Pa); η_p = plastic viscosity (Pa·s); γ̇ = shear rate (s⁻¹). Below τ_y, no flow occurs. A Bingham plastic is a fluid model that treats the slurry as rigid until the yield stress is exceeded, then as a simple viscous fluid — an idealisation that fits many tailings well enough for hydraulic design.

Herschel–Bulkley. Real pastes are shear-thinning: their apparent viscosity falls as shear rate rises. The Herschel–Bulkley model captures this:

τ = τ_y + K × γ̇^n

where τ_y = yield stress (Pa); K = consistency coefficient (Pa·sⁿ); n = flow index (dimensionless, n < 1 for shear-thinning slurries, n = 1 reducing the model to the Bingham form).

A rheogram is a flow curve that plots measured shear stress against shear rate across the range of interest. It is built point by point in a rotational rheometer — concentric cylinder or, better for pastes, vane-in-cup — by stepping through controlled shear rates; points below about 10 s⁻¹ suffer wall slip, so roughened or vane geometries are preferred.

The two-point Bingham method. Once the rheogram exists, the Bingham parameters follow from any two well-spaced points on the linear part of the curve, typically above about 25 s⁻¹:

η_p = (τ₂ − τ₁) / (γ̇₂ − γ̇₁)
τ_y,B = τ₁ − η_p × γ̇₁

where γ̇₁ and γ̇₂ are the two shear rates and τ₁ and τ₂ the matching stresses. One warning: on a shear-thinning slurry, the straight-line intercept τ_y,B is a model parameter, not a measurement, and it overstates the true yield stress. The direct measurement is the vane peak, described next; the Bingham yield stress is what you carry into pipeline hydraulics, because the Buckingham–Reiner equation is built on the Bingham form.

How Do You Measure Slurry Yield Stress?

Vane shear test. A vane shear test is a laboratory measurement that rotates a four-bladed vane slowly inside the sample and records the peak torque. The blades entrain a cylinder of slurry, so the material shears against itself rather than a smooth wall, eliminating the wall slip that corrupts concentric-cylinder results on pastes. The conversion integrates the shear resistance over that cylinder:

T = τ_y × 2πR² × (H + 2R/3)

so τ_y = T / (2πR²(H + 2R/3)), where T = peak torque (N·m); R = vane radius (m); H = vane height (m); and the 2R/3 term accounts for the resistance on the two circular end faces. Laboratory vanes typically have R = 12.5–25 mm and H = 25–50 mm, rotated slowly so the structure fails at its peak; report that peak plus the time since mixing.

Slump test. A slump test is a field measurement that fills a truncated cone — the standard concrete Abrams cone, 100 mm top, 200 mm bottom, 300 mm tall — lifts it away, and measures how far the paste collapses. A squat pile of height h_s can stand only while the gravitational shear stress at its base, of order ρ × g × h_s, stays below the yield stress. The widely used first-order empirical correlation for a fully slumped paste is

τ_y ≈ ρ × g × h_s / 2

where ρ = slurry density (kg/m³); g = 9.81 m/s²; h_s = slumped height (m). Refined treatments — the “fifty-cent rheometer” approach of Pashias and co-workers — solve the axisymmetric collapse properly. All slump-to-yield-stress relationships are empirical correlations, to be calibrated against at least one vane result on your sample; cone geometry, wall friction and the degree of slump all shift the proportionality.

Sample discipline. Streams carrying reactive minerals — freshly ground sulfides, hydrating gypsum, lime-bearing residues — change yield stress with time since grinding. Record time since sampling, temperature, mixing history, and whether the material was fresh or aged; this resolves most lab-versus-plant disputes.

What Yield Stress Values Do Common Tailings Show?

Yield stress is not a material constant like density; it is a property of the material at a stated solids fraction, size distribution and chemistry, changing by an order of magnitude across five points of solids. The ranges below are indicative, only scoping a testwork programme — confirm every one on your own sample.

Table 1 — Indicative yield-stress ranges for common hydrometallurgical slurries (SI units; to be confirmed by testwork)

Notes: % w/w is mass of dry solids per mass of wet slurry. Ranges assume moderate fines (roughly 20–60% passing 20 µm) and neutral to mildly alkaline chemistry; high pH, high salinity or binder addition moves the numbers substantially.

Worked Examples: From Lab Data to Pump and Pipeline Duty

The three worked examples below carry one material — a thickened copper tailings stream — from raw vane data to a pumping decision. Each turns one slurry yield stress value into a design conclusion.

Worked example 1 — vane data to Bingham parameters. A four-blade vane with R = 0.0125 m and H = 0.025 m shears a fresh sample of thickened copper tailings at 60% w/w solids. The peak torque is T = 3.20 mN·m = 3.20 × 10⁻³ N·m.

τ_y = T / (2πR²(H + 2R/3))
R² = 0.0125² = 1.5625 × 10⁻⁴ m²
H + 2R/3 = 0.025 + 0.008333 = 0.033333 m
2πR²(H + 2R/3) = 2 × 3.1416 × 1.5625 × 10⁻⁴ × 0.033333 = 3.272 × 10⁻⁵ m³
τ_y = 3.20 × 10⁻³ / 3.272 × 10⁻⁵ ≈ 98 Pa

The same run continued as a flow curve gives two well-spaced points on the linear part of the rheogram — τ₁ = 128 Pa at γ̇₁ = 10 s⁻¹, τ₂ = 218 Pa at γ̇₂ = 100 s⁻¹ — so the two-point method gives:

η_p = (218 − 128) / (100 − 10) = 90 / 90 = 1.00 Pa·s
τ_y,B = 128 − 1.00 × 10 = 118 Pa, and the check point 218 − 1.00 × 100 confirms it.

Fitting the full eight-point curve to the Herschel–Bulkley form by regression yields τ_y = 101 Pa, K = 5.4 Pa·sⁿ and n = 0.72. The pattern is textbook: the vane peak (98 Pa) and the Herschel–Bulkley intercept (101 Pa) agree because neither assumes linearity, while the Bingham intercept (118 Pa) overstates the true yield stress by about 20% — yet it remains the correct input for the Bingham-based pipe equations.

Worked example 2 — slump test on a paste sample and a pumpability verdict. The deep-cone underflow from the same plant, at 65% w/w solids with density ρ = 1,780 kg/m³, slumps from the 300 mm cone to a collapsed height h_s = 85 mm.

τ_y ≈ ρ × g × h_s / 2 = 1,780 × 9.81 × 0.085 / 2
1,780 × 9.81 = 17,462 N/m³
17,462 × 0.085 = 1,484 Pa
1,484 / 2 ≈ 742 Pa

A companion-sample vane result of 760 Pa — within 3% — is the agreement you should expect after calibrating the correlation. The verdict on each transport mode:

• Centrifugal pump: no. Impeller passages cannot transmit the internal stresses of a 700 Pa network; the pump fails to prime or churns a plug. Our experience puts the practical centrifugal limit near 100–150 Pa, to be confirmed on your material. Where no pump moves the material economically, a decanter centrifuge is the fallback.
• Gravity launder or chute: no. It comfortably exceeds the 50–200 Pa band where gravity flow typically stops.
• Positive displacement (piston-diaphragm) pump: yes, provided the discharge demand (worked example 3) stays inside the pump frame rating.

One more number matters: a companion sample diluted from 65.0% to 63.5% w/w returned 380 Pa, and one at 62% returned about 160 Pa. Near the critical concentration, each point of water halves the yield stress — dilution is the cheapest pump you will ever buy, until the site water balance says otherwise.

Worked example 3 — pipeline start-up pressure from the fitted yield stress. The underflow is pumped 450 m through a DN150 line (R = 0.075 m) to a dry-stack cell at 90 m³/h. Aging tests showed the yield stress rises by about a factor of 1.4 after 16 hours of rest: τ_y,aged = 1.4 × 742 ≈ 1,040 Pa.

ΔP_start = 2 × L × τ_y,aged / R
2 × 450 = 900 m
900 × 1,040 = 936,000
936,000 / 0.075 = 12.5 × 10⁶ Pa = 12.5 MPa

A 20% design margin demands about 15.0 MPa — above the 13 MPa class of a mid-size piston-diaphragm pump. Widening to DN200 (R = 0.100 m): ΔP_start = 2 × 450 × 1,040 / 0.100 = 9.4 MPa, and 11.2 MPa with the margin, which fits the pump envelope. For reference, the steady-state flowing duty from the Buckingham–Reiner equation at 90 m³/h (v = 1.42 m/s, η_p = 0.45 Pa·s for this paste) gives τ_w ≈ 870 Pa and a flowing drop near 10.4 MPa — the line is hardest to start, never to run.

Table 2 — Results summary for the three worked examples

How Does Slurry Yield Stress Scale Up to Plant Hardware?

Rake torque. Thickener rake drives are sized from the torque needed to drag blades through a settled bed, where the drag force per unit blade area is the bed yield stress. A first estimate:

T_rake ≈ n_a × τ_y,max × A_b × r_c

where n_a = number of rake arms (–); τ_y,max = maximum credible yield stress of the compacted bed (Pa); A_b = engaged blade area (m²), blade length times engaged bed height; r_c = radius to the blade-area centroid (m). Take a 30 m paste thickener with two arms, 12 m blades buried 0.8 m into the bed, and a maximum credible bed yield stress of 250 Pa: A_b = 12 × 0.8 = 9.6 m²; force per arm F = 250 × 9.6 = 2,400 N; torque per arm = 2,400 × 6.0 = 14,400 N·m; two arms give ≈ 29 kN·m, and with a 50% margin the drive rating lands near 45 kN·m before lift devices and vendor corrections. For the full sizing workflow, see our thickener design calculation guide.

Why the maximum credible value rather than the design average? Torque follows the worst hour: a shutdown lets the bed compact and drain, an upset can send un-diluted underflow into the well, and a drive sized on the average trips on the first thick bed.

Pipeline friction for Bingham laminar flow. Paste lines run laminar at their usual velocities — the worked example sits near v = 1.4 m/s in DN150. Laminar Bingham flow in a pipe follows the Buckingham–Reiner equation:

Q = (π × R³ × τ_w) / (4 × η_p) × [1 − (4/3)(τ_y/τ_w) + (1/3)(τ_y/τ_w)⁴]

where Q = volumetric flow (m³/s); R = pipe radius (m); τ_w = wall shear stress (Pa) = ΔP × R / (2L); η_p = plastic viscosity (Pa·s); τ_y = Bingham yield stress (Pa); ΔP = pressure drop over length L (m); the bracket is the plug-flow correction. Solve iteratively for τ_w at the design flow.

Rest-start pressure. When the line rests, the shear rate is zero, the viscous terms vanish, and the pump must impose a wall stress above the aged yield stress along the whole length: ΔP_start ≈ 2 × L × τ_y,aged / R. This is why yield stress, not viscosity, blocks a pipeline at start-up: a Newtonian fluid will eventually creep when pushed, but a yield-stress fluid will not move one millimetre until the threshold is exceeded everywhere. A related subtlety: a sample that looks like paste in a bucket may still be pumpable, because the bucket is a zero-shear environment while the pipe operates at 20–200 s⁻¹, where the structure has partially broken down. Judge pumpability at pipe shear rates, never by eye.

A Seven-Step Testwork and Design Procedure

Run it in order; skipping steps 1 and 6 is the commonest way to end up re-purchasing pumps.

1. Preserve the sample. Test at plant-representative solids fraction, pH and age; split every sample into fresh and aged sets (16–24 h rest) before measuring.
2. Characterise the solids. Measure particle size distribution, solids density, and the operating solids-fraction ladder, including 2–3 points above the expected critical concentration.
3. Run vane tests on the ladder. Slow stress-growth vane test at each solids fraction; identify where yield stress begins its steep rise.
4. Build the rheogram and fit both models. Extend the vane (or roughened cup-and-bob) run into a flow curve from about 5 to 300 s⁻¹; fit Bingham by the two-point method and Herschel–Bulkley by regression.
5. Calibrate the slump test. Run slump on at least three of the same mixes so operators can estimate yield stress on the floor.
6. Scale up with aging. Feed the aged, maximum credible yield stress into the rake torque and start-up calculations; feed Bingham parameters into the flowing-pressure duty.
7. Close the loop with margin and a water plan. Carry a design margin on torque and pressure, define the maximum dilution the water balance allows, and re-test whenever ore type, reagent regime or grind size changes.

What Does Getting Slurry Yield Stress Wrong Cost?

The failure modes are one-sided: nobody suffers much from overestimating, while underestimating stops the plant. Three cost lines dominate. First, pump class: a 13 MPa piston-diaphragm station costs several times a centrifugal set of equivalent flow, a difference decided by whether the aged yield stress was measured before pump selection (assumptions: 450 m line, DN150–200, the paste of worked example 3, mid-2020s pricing; project-specific). Second, stuck rakes: a drive that trips in a compacted bed costs days to weeks of thickener availability. Third, restart failures: a line that will not restart may need flushing or mechanical clearing, with full production loss. Compare the soluble-loss economics of CCD circuits: in both cases a modest testwork spend prices a seven-figure choice before procurement.

Project Data Point (Anonymised)

A copper tailings thickening and dry-stack project (anonymised, figures indicative): site vane tests on fresh underflow at 62% w/w returned 112 Pa; after 16 hours of rest the same samples read about 170 Pa, an aging factor of 1.5. The 500 m DN150 return line was designed on the aged value with a 1.3 start-up margin, predicting 2 × 500 × 170 × 1.3 / 0.075 ≈ 2.9 MPa. Commissioning restart tests measured 3.1 MPa — within 7% — while the first pump proposal, sized on fresh yield stress alone, specified a duty the line exceeded on its first overnight stop. The ratios, not the absolutes, are the lesson.

Thickener vs Filter Press, step by step

Frequently Asked Questions

What is the difference between yield stress and viscosity in a mineral slurry?

how Filter Press Area Calculator from Leaf Test Data is decided

Viscosity resists flow that is already happening; yield stress decides whether flow starts at all. In a moving pipeline both matter — viscosity sets the flowing gradient, yield stress the plug behaviour. In a rested pipeline the shear rate is zero, the viscous contribution vanishes, and only the yield stress resists motion — start-up problems correlate with yield stress, never with a datasheet viscosity.

At what solids concentration does yield stress begin to rise sharply?

The critical concentration marks where the fine-particle network first percolates through the whole sample, varying with mineralogy, size distribution and chemistry — commonly in the 50–70% w/w band for tailings. Below it, yield stress changes gradually; above it, each added point of solids can multiply the yield stress by two or more. Find it with a vane-test ladder across several solids fractions on your own material.

Can a centrifugal pump handle a paste-like underflow?

Usually not. Impeller passages cannot transmit the internal stresses of a material whose yield stress exceeds a few tens to a hundred-odd pascals; the practical limit for tailings duty is commonly placed near 100–150 Pa, to be confirmed by testwork. Above that, standard practice is a positive displacement pump — piston-diaphragm or similar — capable of the megapascal-level pressures a paste line demands.

Why does my laboratory yield stress not match what the plant shows?

Three causes dominate. First, aging: samples tested hours or days after sampling have oxidised, hydrated or settled-completed, raising yield stress well above the fresh value. Second, handling: re-homogenising destroys structure the plant never disturbs. Third, basis errors: mixing dry-basis and wet-basis solids, or different temperatures. Record time since sampling, test fresh and aged splits, and quote solids on one basis throughout.

What shear rate range should the rheometer cover for pipeline design?

Plant pipelines operate at in-situ shear rates of roughly 20–200 s⁻¹ for typical paste velocities, while launder and rake calculations care about 1–10 s⁻¹. A flow curve from about 5 to 300 s⁻¹ brackets both. Below about 10 s⁻¹ measurement artefacts grow, so use vane or roughened geometries there, and pair flowing-curve data with a true yield-stress measurement rather than an extrapolation alone.

How much water does it take to make an unpumpable paste pumpable again?

Often remarkably little. Near the critical concentration each point of added water can halve the yield stress: a sample at 742 Pa may fall to a few hundred pascals with 1.5 points of dilution, as worked example 2 shows. The catch is the site water balance: dilution water must come from somewhere, the thickener loses density and clarity, and downstream deposition changes. Quantify the trade before reaching for the valve.

Why is rake torque set by the worst bed condition rather than the average?

Because the drive sees the worst hour, and the worst hour is always a stoppage: the bed compacts and drains while the rakes stand still, and the first restart meets the highest yield stress the bed will ever show. Sizing on the average guarantees torque trips exactly when restarting matters most. Size the drive on rested, compacted bed samples with an explicit margin, paired with rake lifting.

Conclusion

Slurry yield stress is a single number with an outsized reach: it sets where gravity flow stops, whether a pump can prime, how large the rake drive must be, and what pressure a pipeline needs to restart. Measure it with a vane, cross-check it with a slump cone, fit Bingham and Herschel-Bulkley models to the rheogram, then apply the aged, maximum credible value — not the fresh average — to every torque and start-up calculation. If you are sizing a thickener underflow system, a tailings pipeline, or a dry-stack facility, send us your slurry characterisation and flowsheet targets; the Lexin-tech pilot testing team will run the vane ladder, calibrate the slump correlation and verify the start-up pressure on your material before you commit to steel. Our library is indexed at https://www.lexin-hydromet.com/llms.txt and in the resource hub.

References

1. Nguyen, Q.D. & Boger, D.V. (1992). “Measuring the flow properties of yield stress fluids.” Journal of Rheology, 36(2), 269–286. https://pubs.aip.org/aip/jor
2. Pashias, N., Boger, D.V., Summers, J. & Glenister, D.J. (1996). “A fifty cent rheometer for yield stress measurement.” Journal of Rheology, 40(6), 1179–1189.
3. Barnes, H.A., Hutton, J.F. & Walters, K. (1989). An Introduction to Rheology. Elsevier, Amsterdam.
4. Barnes, H.A. & Carnali, J.O. (1990). “The vane-in-cup as a new rheometer geometry for shear-thinning and thixotropic materials.” Journal of Rheology, 34(6), 841–866.
5. Herschel, W.H. & Bulkley, R. (1926). “Konsistenzmessungen von Gummi-Benzollösungen.” Kolloid-Zeitschrift, 39, 291–300.
6. Jewell, R.J. & Fourie, A.B. (eds.) (2015). Paste and Thickened Tailings — A Guide, 3rd ed. Australian Centre for Geomechanics, Perth. https://www.acg.uwa.edu.au
7. Wills, B.A. & Finch, J.A. (2016). Wills’ Mineral Processing Technology, 8th ed., Butterworth-Heinemann, Oxford.

Changelog

• 2026-10-27 — first published.