Viscous modulus (G double prime) and tan delta in fillers
Quick facts
- G'' (G double prime)
- Viscous modulus: measures the share of energy the gel dissipates when deformed, its liquid side.
- Tan delta
- Ratio of G'' to G'. Below 1, elastic behavior dominates; above 1, viscous behavior does.
- Unit
- G'' in pascals (Pa), like G'; tan delta has no unit.
- Depends on
- Test frequency and amplitude, temperature and method; values from different sources are not directly comparable.
- Relevance in facial harmonization
- Completes the reading of G': shows whether the gel tends to hold its shape or spread in the tissue.
The viscous modulus, written G'' and read "G double prime", measures the liquid side of a gel: the share of energy it dissipates when it is deformed and flows. Tan delta is the ratio between that viscous modulus and the elastic modulus, G prime (G'), and sums up in one number whether the gel behaves more like a solid or more like a liquid. Both appear on data sheets and in articles about hyaluronic acid fillers, and they complete the picture that G' gives on its own.
How do G'' and G' relate?
Every filler gel is viscoelastic. In a rheology test, the gel is placed between two plates and subjected to small oscillations. Part of the applied energy is stored and returned, like a spring: that is G'. Another part is lost to flow, like a thick liquid: that is G''.
| Measure | What it represents | Practical reading |
|---|---|---|
| G' (elastic modulus) | Energy stored and returned | Firmness, resistance to deformation |
| G'' (viscous modulus) | Energy dissipated by flow | Fluidity, tendency to spread |
| Tan delta (G''/G') | Balance between the two | Below 1: solid dominates; above 1: liquid dominates |
| Phase angle (delta) | The same balance, in degrees | Near 0°: elastic; near 90°: viscous |
| G* (complex modulus) | Total resistance to deformation | Combines G' and G'' in a single value |
A simple way to think about it: G' tells you how firm the gel is, and tan delta tells you what kind of firmness it is.
How do you read tan delta in practice?
Most cross-linked fillers have a tan delta well below 1, meaning predominantly elastic behavior. Within that range, gels with a lower tan delta tend to hold their shape better and resist tissue pressure, which contributes to projection capacity. Gels with a higher tan delta tend to spread and blend into the tissue more, behavior associated with thin skin and areas of high movement.
Products with little or no cross-linking, such as many used for skin boosters, may have a tan delta close to or above 1, because they behave more like a viscous liquid.
What does tan delta not tell you?
No single rheological parameter sums up a product. Cohesivity, concentration, hydrophilicity, particle size and how the gel is prepared, as with monophasic and biphasic gels, also change behavior in the tissue. Viscosity, which relates to the force needed to inject, is another measure. In addition, real-world behavior depends on the plane, the volume, the tissue type and the movement of the area. The area-by-area view is in hyaluronic acid by area.
Also called: G'' (G double prime), loss modulus, loss factor, tangent delta.
Frequently asked questions
What is tan delta in hyaluronic acid?
It is the ratio between the gel's viscous modulus (G'') and its elastic modulus (G'). When it is below 1, the gel behaves more like a solid and tends to hold its shape; when it approaches or exceeds 1, it behaves more like a liquid and tends to spread.
What does G double prime mean in a filler?
G double prime, written G'', is the viscous modulus: the part of the gel's behavior that is liquid-like, meaning the energy it dissipates as it flows. Read together with G prime, it helps show whether the gel is firmer and more structured or more fluid.