graph LR
A[Cooling] --> B[Crystallisation]
B --> C[Second Boiling]
C --> D[Volatile Exsolution]
E[Decompression] --> F[Saturation]
F --> D
style D fill:#eb811b,stroke:#213737,stroke-width:2px,color:#fff
style A fill:#2F4647,stroke:#213737,stroke-width:2px,color:#fff
style E fill:#2F4647,stroke:#213737,stroke-width:2px,color:#fff
Melt properties at shallow levels
Class 4 - Conditions for magma reservoir emplacement
Sébastien Biass 
Group of physical volcanology and geological risk - 1st floor, office 103
March 9, 2026
Viscosity of silica melts
- Network formers: \(Si^{4+}\), \(Al^{3+}\)
- Occupy tetrahedral sites and link through bridging oxygens
- Full polymerisation = high viscosity
- Network modifiers: \(Na^+\), \(K^+\), \(Ca^{2+}\), \(Mg^{2+}\), \(Fe^{2+}\)
- Create non-bridging oxygens
| NBO/T | Structure | Viscosity |
|---|---|---|
| 0 | fully polymerized | very high |
| 0.5–1 | chains/sheets | intermediate |
| >1 | depolymerized | low |
Viscosity behaviour
Modes of deformation
Failure mode:
- Brittle → Fracture
- Ductile → Distributed deformation
Reversibility:
- Elastic → Reversible until rupture
- Plastic → Permanent (i.e., creep)
- Viscous → Permanent (liquid)
Rheology
- \(e\): Elongation
- \(t\): Time
- \(\sigma\): Stress
Reservoir importance
Today’s focus:
- Storage region fed from deep plumbing system
- Focus on max 10 km depth
- Staging post for magma from source → surface
- Sufficient cooling → differentiation
- Controlled by:
- Supply of magma from depth
- Eruption frequency
Examples:
- Hawaii: Constant supply → short residence time + frequent eruptions = constant chemistry
- Iceland: Intermittent supply → cooling between events = magma evolution
From sill to reservoir
Amalgamation of dike-fed sills
- What are the conditions required to:
- initiate a magma “chamber”?
- keep it stable to grow?
- Magma flux?
- Cooling?
- Space accommodation?
Geophysics and geochronology evidences
Magma reservoir
- Deep portion of the volcano which includes
- Crystal- and melt-dominated region(s)
- Pockets of exsolved magmatic fluids
- Can range from Moho to surface → transcrustal magma reservoir
Mush
- Dominant in space and time
- Crystal-dominated → non-eruptible
- 40-65% crystals framework
- Stops convection, allows melt segregation from crystals
- Melt remobilised through compaction and percolation
- Heated in short bursts → magma injection from deeper
Magma chambers
- Short lived
- Melt-dominated → eruptible
- Lower/middle crust → differentiation
- Upper crust → storage → eruptions
Transcrustal magma reservoir
Conceptual framework for stability
Injection time-scale → time to replenish the chamber mass
\[ \tau_{\text{in}} = \frac{\rho_0 V_0}{\dot{M}_{\text{in}}} = \frac{4\pi}{3} \frac{\rho_0 R_0^{3}}{\dot{M}_{\text{in}}} \]
Cooling time scale → time for heat to diffuse across the chamber
\[ \tau_{\text{cool}} = \frac{R_0^{2}}{\kappa} \]
Relaxation time scale → time for crust to relax stress by viscous deformation
\[ \tau_{\text{relax}} = \frac{\eta r_0}{(\Delta P)_c} \]
- x: supply of heat by injection / heat loss by conduction out to the crust
- y: viscous relaxation timescale / injection timescale
Crystallisation
Undercooling controls crystal formation
Low \(\Delta\ T\):
- Low nucleation, fast growth
- Few crystals, large phenocrysts
- Slow cooling → large, deep reservoirs
Moderate \(\Delta\ T\):
- Simultaneous nucleation and growth
- Many crystals, microlites
- Shallow reservoirs, thick lava flows
Large \(\Delta\ T\):
- Slow diffusion inhibits growth
- Slow nucleation → glass
How does a porphyritic texture form?
Importance of rate of magma transfer and staging
Volatiles
Why are volatiles important?
- Change the solidus/liquidus
- Modify viscosity/density
Volatiles: solubility
Volatile phases:
- H₂O: Most abundant → \(\eta\), \(\rho\), crystals
- CO₂: Exsolves at greater depth
- SO₂, H₂S, …
Solubility: → volatiles not always present as bubbles
- Formation of bubbles by diffusion once saturation
- Pure diffusion is difficult, especially in silica-rich melts
- Require large supersaturation
- Alternative: nucleii
Volatiles: viscosity
Do bubbles increase or decrease viscosity?
Capillary number: competition between
- Viscous forces deforming bubbles
- Surface tension to keep bubbles spherical
\(Ca = \frac{\eta \dot{\gamma} R}{\sigma}\)
- \(\eta\) = melt viscosity
- \(\dot{\gamma}\) = shear (strain) rate
- \(R\) = bubble radius
- \(\sigma\) = surface tension
- \(Ca<0.645\): Surface tension dominates
- Spherical bubbles behave as rigid inclusion
- \(Ca>0.645\): Viscous stress dominates
- Bubbles deform and align
- Lubrication
Volatiles: second boiling
Second boiling = volatile exsolution caused by crystallisation
- Cooling → crystallisation
- Volatile phases remain in the melt
- Saturation → exsolution
→ Especially important for evolved, water-rich magmas
Feedback
- Melt enriched in \(SiO_2\) → increase \(\eta\)
- Bubbles with high \(Ca\) → decrease \(\eta\)
CO₂ flushing
Compressibility
Open vs closed degassing
What parameters control open vs closed?
Conceptual framework for stability
Injection time-scale → time to replenish the chamber mass
\[ \tau_{\text{in}} = \frac{\rho_0 V_0}{\dot{M}_{\text{in}}} = \frac{4\pi}{3} \frac{\rho_0 R_0^{3}}{\dot{M}_{\text{in}}} \]
Cooling time scale → time for heat to diffuse across the chamber
\[ \tau_{\text{cool}} = \frac{R_0^{2}}{\kappa} \]
Relaxation time scale → time for crust to relax stress by viscous deformation
\[ \tau_{\text{relax}} = \frac{\eta r_0}{(\Delta P)_c} \]
- x: supply of heat by injection / heat loss by conduction out to the crust
- y: viscous relaxation timescale / injection timescale
Surface deformation
Surface deformation: cyclicity
Earthquakes
Gas monitoring
| Ratio | Interpretation |
|---|---|
| CO₂ / SO₂ | Depth of degassing |
| SO₂ / H₂S | Temperature and oxidation |
| H₂O / CO₂ | Magma dehydration |
| SO₂ / CO₂ | Magma ascent vs deep gas input |
Bubble regimes is not static
| Capillary number | Bubble behaviour | Rheological effect |
|---|---|---|
| \(Ca \ll 1\) | bubbles remain spherical | viscosity increases (rigid inclusions) |
| \(Ca \sim 1\) | bubbles deform | viscosity decreases |
| \(Ca \gg 1\) | strongly deformed / foam-like flow | strong shear thinning |
→ Everything is dynamic!
Cooling
If we inject a 5–10 km wide fully molten body into colder crust, what must happen?
Observation
- Magma temperature ≈ 1100–1200 °C
- Crustal host rock ≈ 300–600 °C
Consequence:
- Crystallisation
- Volatile exsolution
Characteristic cooling timescale due to conduction: \(\frac{R_0^{2}}{\kappa}\)
Thermal diffusivity
\(\kappa\) → thermal diffusivity → \(10^{-6}\ m^2\ s^{-1}\)