Viscous characteristic length (JCA / JCAL)

A length that characterises the narrow parts of the pores, where the viscous losses occur. It sets where the equivalent density changes from its viscous (low-frequency) to its inertial (high-frequency) behaviour. It is an input of the JCA and JCAL models only; when blank, the program uses an estimate.

Last updated 2026-11-11

Theory

Johnson et al. (Johnson et al., 1987) defined $\Lambda$ as twice the pore volume to pore surface ratio weighted by the squared velocity of the inviscid flow; it fixes the high-frequency limit of the viscous loss. In the equivalent density, equation (1), it appears in the square root that blends the low-frequency Darcy behaviour (controlled by $R$ ) into the high-frequency one.

When the field is blank the program uses the estimate of equation (2), which corresponds to a pore-shape factor of 1 (cylindrical pores), evaluated with the local gas viscosity and the temperature-scaled flow resistivity. The value used is listed in the acoustic QA table.

Equations

\rho_{eq} = \frac{\alpha_\infty\rho_0}{\phi}\left[1 + \frac{R\,\phi}{i\omega\rho_0\alpha_\infty}\sqrt{1 + i\,\frac{4\alpha_\infty^2\eta\rho_0\omega}{R^2\Lambda^2\phi^2}}\right]

(1)

\Lambda = \sqrt{\frac{8\,\eta\,\alpha_\infty}{R\,\phi}} \quad \text{(estimate when blank)}

(2)

where	meaning	unit
$\Lambda$	Viscous characteristic length (this setting)	m
$\eta$	Viscosity of the local gas	Pa·s
$R$	Flow resistivity at the local temperature	Pa·s/m²
$\alpha_\infty, \phi$	Tortuosity, porosity	-

Default and rule

Default: blank = estimated from the flow resistivityComputed by the program
Rule: Blank: the estimate of equation (2). Because the scaled resistivity is proportional to $\eta$ , the estimate does not change with temperature. Example: air at 20 °C ( $\eta = 1.8\times10^{-5}$ Pa·s), $R = 20\,000$ Pa·s/m², $\phi = 0.95$ , $\alpha_\infty = 1$ gives $\Lambda \approx 87$ µm.
Source: The equations and the estimate follow Johnson et al. Johnson et al. (1987) in the form given by Atalla and Panneton Atalla and Panneton (2000).

Valid range > 0; should not exceed the thermal length

Values

Above 0; entered in µm.

Consistency

The QA gate warns when Thermal characteristic length (JCA / JCAL) is shorter than $\Lambda$ (real materials have $\Lambda' \ge \Lambda$ ).

Verified

Checked in a full acoustic run of a packed resonator (2026-11-11): every quality check passes; with estimated parameters the TL agrees with Miki within about 1 dB below 1 kHz and falls 7-9 dB below it at 2 kHz.

Theory

Equations

Default and rule

Valid range > 0; should not exceed the thermal length

Related 5

References 2