On-line, non-Newtonian capillary rheometry for continuous and in-line coatings production


Moving from traditional batch production into in-line or continuous coatings production requires accurate on-line quality control instruments. The aim of the present work was to investigate the principle of non-Newtonian capillary rheometry for quality control purposes. In the investigation, three series of acrylic-based viscoelastic coating samples with different types and concentrations of pigments and thickening agents were used, and the rheological measurements were compared to results obtained with the so-called Stormer viscometer and an advanced off-line rheometer. A detailed analysis of the potential measurement implications was also conducted. For shear stresses from 15.0 to 350.0 Pa (the upper boundary), the novel capillary rheometer was found to provide results in good quantitative agreement with the advanced rheometer when sample holding time, and thereby shear history, was properly controlled. At a shear stress between 1.0 Pa (lower boundary) and 15.0 Pa, the agreement was not as good, with a difference in results of the non-Newtonian capillary rheometer and the advanced rheometer between 15% and 74%. The resolution of the capillary rheometer was sufficiently high to allow detection of the rheology changes associated with variations in coating formulations of pigment volume and rheology modifier concentrations. In summary, for fast on-line evaluation of coating rheology, the principle of capillarity has been demonstrated to be a varied and robust technique.

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D :

Diameter of the capillary tube (m)

f s :

Moody friction factor of the fluid in a straight pipe

k b :

Bend loss coefficient

L :

Length of the capillary tube (m)

Q :

Flow rate of the sample (m3/s)

R :

Radius of the capillary tube (m)

R b :

Radius of the bend (m)

u :

Velocity of the fluid (m/s)

ΔP :

Total pressure drop caused by the friction in the capillary tube (Pa)

ΔP f,y :

Pressure drop to overcome the yield stress (Pa)

ΔP bend :

Total pressure drop inside a bend (Pa)

ΔP f,bend :

Pressure drop caused by the friction inside a bend (Pa)

ΔP add :

Additional pressure drop generated by the change of direction of the fluid inside a bend (Pa)

α :

Calculated ratio between the viscosity results measured by the non-Newtonian capillary or the advanced rheometer and the Stormer viscometer

β :

Calculated ratio value between the results of the non-Newtonian capillary rheometer with and without a holding time and the advanced rheometer

η :

Viscosity of the fluid (Pa·s)

θ :

Angle of the bend (°)

\(\mathop {\gamma_{\text{a}} }\limits^{ \cdot }\) :

Apparent shear rate applied to the measured sample (s−1)

\(\mathop {\gamma_{\text{w}} }\limits^{ \cdot }\) :

Shear rate at the tube wall (s−1)

λ :

Reduced PVC value (PVC/CPVC)

ρ :

Density of the fluid (kg/m3)

τ w :

Shear stress at the tube wall (Pa)


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Financial support from The Hempel Foundation to CoaST (The Hempel Foundation Coating Science and Technology Centre) is gratefully acknowledged.

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Correspondence to Søren Kiil.

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Luo, S., Weinell, C.E., Okkels, F. et al. On-line, non-Newtonian capillary rheometry for continuous and in-line coatings production. J Coat Technol Res (2021). https://doi.org/10.1007/s11998-020-00447-9

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  • On-line measurement
  • Quality control
  • Viscosity
  • Capillary rheometer