Water–Glycerol Mixture Viscosity and Density Calculator

Estimate water–glycerol mixture viscosity, formulation composition, and additive-volume density from temperature and concentration.

Mixture inputs

Dynamic viscosity

—mPa·s

Enter valid inputs to calculate.

Estimated density— kg/m³

Kinematic viscosity—

Composition by mass—

Composition by volume—

Viscosity across composition

How to use

Select Mass fraction, Component volumes, or Target viscosity.
Enter temperature from 0 to 100 °C and the required composition or target value in the displayed units.
Select Calculate; results also update as inputs change. Select Reset to restore the 25 °C, 90 wt% example.
Read dynamic viscosity as the primary result. Density, kinematic viscosity, mass fraction, volume fraction, and the composition plot are supporting estimates.
Correct any warning before using the result. A target outside pure-water and pure-glycerol limits cannot be solved.
Do not use this model for other solutes, temperatures outside 0–100 °C, pressure-sensitive work, or precise volumetric formulation where contraction must be measured.

Equations used

μ_w = 1.790 exp[((−1230 − T)T)/(36100 + 360T)] mPa·s
μ_g = 12100 exp[((−1233 + T)T)/(9900 + 70T)] mPa·s
a = 0.705 − 0.0012T; b = (4.9 + 0.036T)a^2.5
α = 1 − C_m + abC_m(1 − C_m)/[aC_m + b(1 − C_m)]
μ = μ_w^α μ_g^{(1 − α)}
ρ_w = 1000{1 − |(T − 4)/622|^1.7}; ρ_g = 1277 − 0.654T, in kg/m³
ρ = 1/[C_m/ρ_g + (1 − C_m)/ρ_w]; C_m = ρ_gV_g/(ρ_gV_g + ρ_wV_w)
φ_g = (C_m/ρ_g)/[C_m/ρ_g + (1 − C_m)/ρ_w]
ν = 1000μ/ρ in mm²/s.

T is temperature in °C; C_m is glycerol mass fraction; V_w and V_g are water and glycerol volumes; μ_w, μ_g, and μ are dynamic viscosities; ρ_w, ρ_g, and ρ are densities; and ν is kinematic viscosity. a and b are empirical intermediate quantities; α is the Cheng mixture exponent; and φ_g is glycerol volume fraction. The target μ_target is inverted for C_m by bounded bisection of the same Cheng equation.

Sign conventions and limits: T is 0–100 °C; C_m and φ_g are fractions from 0 to 1; V_w and V_g are nonnegative with a positive total; and μ, μ_target, ρ, and ν are positive.

Assumption: density and mass/volume conversion assume additive volumes and neglect mixture contraction. The viscosity correlation applies from 0–100 °C and 0–100 wt% glycerol.

Reference: N.-S. Cheng (2008), “Formula for the Viscosity of a Glycerol–Water Mixture,” Industrial & Engineering Chemistry Research 47(9), 3285–3288. doi:10.1021/ie071349z.