Cross Model Non-Newtonian Viscosity Calculator

Polymer Rheology & Non-Newtonian Fluids: Calculate apparent viscosity ($\eta$), wall shear stress ($\tau$), and shear-thinning rate transitions using the Cross model.

Cross Model Parameters

Zero-Shear Viscosity $\eta_0$ (Pa·s):

Infinite-Shear Viscosity $\eta_\infty$ (Pa·s):

Cross Time Constant $K$ (s):

Cross Rate Exponent $m$:

Operating Shear Flow

Applied Shear Rate $\dot{\gamma}$ (s⁻¹):

Rheological State & Shear Stress

Apparent Viscosity ($\eta$)

-- Pa·s

In centipoise: -- cP

Shear Stress ($\tau$)

-- Pa

In kPa: -- kPa

Viscosity Ratio ($\eta / \eta_0$)

-- %

Thinning drop factor

Power Law Index ($n$)

Dissipation: -- kW/m³

Cross Model Formulation:

• $\eta(\dot{\gamma}) = \eta_\infty + \frac{\eta_0 - \eta_\infty}{1 + (K \dot{\gamma})^m}$. As $\dot{\gamma} \to 0$, $\eta \to \eta_0$; as $\dot{\gamma} \to \infty$, $\eta \to \eta_\infty$.

• At intermediate shear rates, the Cross model naturally recovers the Ostwald-de Waele power law with $n = 1 - m$.

Recommended Tools & Equipment

Tested hardware and components for high reliability

100% Free Tool Zero Sign-Up

Cross Model Non-Newtonian Viscosity Calculator

Cross Model Parameters

Operating Shear Flow

Rheological State & Shear Stress

Frequently Asked Questions