Injection Force Calculator - QATCH Technologies

This tool is an open injection-force screening model that fits a viscosity-shear-rate profile to the Carreau-Yasuda model and estimates plunger force using a hydrodynamic framework.

Allmendinger et al., Rheological characterization and injection forces of concentrated protein formulations: An alternative predictive model for non-Newtonian solutions, Eur. J. Pharm. Biopharm. (2014). doi:10.1016/j.ejpb.2014.01.009

It should be considered an approximate educational / early-screening implementation, not the original published model.

Two-step workflow

Step 1 - Viscosity profile. Pick Newtonian (one viscosity, n = 1) or Custom fit (≥ 4 shear-rate / viscosity points, or a CSV). Click Fit to get η₀, η_∞, n and γ_c plus the curve.
Step 2 - Syringe & injection. Enter barrel radius, needle dimensions and an injection rate. The force calculation needs the viscosity profile, so running it fits the profile if you have not yet.

Uncertainty bands

When shear-rate coverage is limited, an ensemble of plausible fits that still agree with the data is generated, so the confidence band widens naturally in unmeasured (e.g. high-shear needle) regions.

How force is estimated

Effective needle shear rate γ_eff= (2Q / πR_n³) · (3n+1)/(2n+1)
Viscosity at γ_eff read from the fitted profile (with its band)
Hydrodynamic force from Hagen-Poiseuille: F = 8 η L Q R_b² / R_n⁴
Stopper / barrel friction added as an offset term

Empirical correction φ

Real prefilled syringes and staked needles are not ideal flow channels. An optional shape / needle-tip factor φ (Chen-Wei / WuXi approach) scales the hydrodynamic term to improve agreement with measured force.

Wu et al. (2024) - injection force modeling for PFS

This software is provided "as is" without warranty of accuracy, fitness for a particular purpose, or regulatory suitability.

Users are responsible for validating results experimentally before use in research, development, manufacturing, or process decisions.

Comfort thresholds on the force scale are heuristic screening guides only and do not constitute regulatory, clinical, or engineering advice.

Questions, feedback, or want to learn more about QATCH's viscosity and injectability solutions? We'd love to hear from you.

Or email us directly: info@qatchtech.com

Viscosity Profile STEP 1

Shear rate / viscosity measurements ≥ 2 rows

Shear rate (s⁻¹) Viscosity (cP)

One measurement per row; empty rows are ignored. With only 2-3 points the data is duplicated to produce a rough, low-confidence fit.

Syringe & Injection STEP 2

Geometry

Barrel Radius mm

Needle gauge

Needle Length mm

Injection Rate

Injection volume mL

Injection time s

Flow rate Q

Plunger velocity

Injection time

Corrections

Correction factor φ - i

The hydrodynamic equation is derived for an ideal syringe/needle channel. Real prefilled syringes and staked needles deviate, and an empirical shape / needle-tip factor is commonly needed - values such as φ ≈ 0.75 are reported. Wu et al. (2024). Leave at 1 for the uncorrected ideal model.

Stopper / barrel friction N i

The sliding-friction offset between stopper and barrel (silicone-oil layer), added on top of the hydrodynamic force. Defaults to 1.5 N; measure it from an empty / water-filled barrel for your specific syringe.

Predicted Injectability

Ready to calculate

Fit a viscosity profile in Step 1 to see the rheology curve and confidence band, then add a syringe & injection rate in Step 2 to estimate the plunger force.

Model: Allmendinger et al. (2014) Eur. J. Pharm. Biopharm. - Carreau-Yasuda rheology with effective-needle-shear Hagen-Poiseuille force and an optional Chen-Wei / WuXi shape factor φ. doi:10.1016/j.ejpb.2014.01.009