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Potential Error in the Electrostatic Force Expressions – Taylor Cone Model

Posted 11.10.2026, 03:00 GMT-4 Electromagnetics, Computational Fluid Dynamics (CFD), Studies & Solvers Version 6.4 0 Replies

Guy Schlatter

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Dear COMSOL Support Team, dear Forum,

I identified a potential error in the “Taylor Cone” application model (Application ID: 3828), which couples Electrostatics, Laminar Flow, and Level Set.

In this model, the volumetric electrostatic force components are defined as follows:

Radial component:

Fes_r = 0.5(es.Er^2+es.Ez^2)epsilon0_const(1+(er_liq-1)philsr)

Axial component:

Fes_z = 0.5(es.Er^2+es.Ez^2)epsilon0_const(1+(er_liq-1)philsz)

However, phils represents the dimensionless Level Set function, while philsr and philsz correspond to its spatial derivatives with respect to r and z, respectively. These derivatives therefore have units of m⁻¹.

Consequently, the terms (1+(er_liq-1)philsr) and (1+(er_liq-1)philsz) are dimensionally inconsistent, since they involve the addition of a dimensionless constant and a quantity expressed in m⁻¹.

Furthermore, assuming a perfect dielectric system without free electric charges, the volumetric electrostatic force derived from the divergence of the Maxwell stress tensor should be:

Fes = −0.5 E² ∇ε

With the relative permittivity interpolated using the Level Set function as:

εr = er_liq + (1-er_liq) phils

With phils = 0 in the liquid and phils = 1 in air (as proposed in the Taylor Cone Model). Thus, the corresponding force components should therefore be:

Fes_r = 0.5(es.Er^2+es.Ez^2)epsilon0_const(er_liq-1)philsr

Fes_z = 0.5(es.Er^2+es.Ez^2)epsilon0_const(er_liq-1)philsz

These expressions are dimensionally consistent and correspond to volumetric forces expressed in N/m³.

Could you please confirm whether the original expressions contain an error or whether a specific formulation or assumption justifies their use?

Since these forces directly influence the deformation of the liquid–air interface and the resulting Taylor cone geometry, such an error could potentially affect the simulation results.

Thank you in advance for your clarification.

Best regards,

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