Meaning
Mathematical rheology models describe fluid behavior by incorporating yield stress and consistency coefficients to characterize non-Newtonian flow properties under varied shear rates. Formulators apply the Herschel-Bulkley equation to model industrial fluids like pastes and slurries that require a minimum stress threshold before flow initiates. The model combines power-law shear rate dependence with a distinct initial yield stress parameter.
Accurately fitting viscometer data to this model enables engineers to predict pressure drops in piping, slot die flow distribution and coating layer stability.
Flow Characterization
Determining fluid parameters under this model requires rotational rheometer testing across multiple shear rate decades. The flow curve establishes the precise yield point alongside the flow behavior index that describes whether fluid thins or thickens under high shear. Using simple power-law or Bingham plastic models for a Herschel-Bulkley fluid leads to incorrect predictions of die pressure and velocity profiles.
Process engineers adjust coating formulations to maintain target parameters during high-speed fluid application.
Pumping Assessment
Scale-up audits evaluate whether pilot pumping systems generate sufficient shear to maintain continuous flow without fluid stagnation. A supplier forecast assuming simple Newtonian fluid behavior underestimates line pressure drops when pumping fluids described by the Herschel-Bulkley model through narrow delivery lines. Pilot line tests verify that slot dies distribute shear-thinning fluids evenly across full production web widths.
Validating fluid constants under actual shear rates prevents pump cavitation and uneven coating weights during commercial production runs.
Yield Miscalculation
Incorrect estimation of fluid yield stress causes pipe blockages and slot die starvation across high-speed coating heads. Capital investments in high-viscosity pumping infrastructure fail when shear-thinning assumptions ignore high initial yield requirements.