SpringerImages - Evolution of bubble number density with decreasing pressure PL for an equivalent surface tension $$ \sigma _{\rm LB}^{\rm E} $$ = 0.078 N/m; the thick line corresponds to $$ \left| {\left. {{\text{d}}P/{\text{d}}t} \right|} \right. $$ = 1,000 kPa/s, the thin line decorated with empty circles to $$ \left| {\left. {{\text{d}}P/{\text{d}}t} \right|} \right. $$ = 27.8 kPa/s. With $$ \sigma _{\rm LB}^{\rm E} $$ = 0.078 N/m and a detectability threshold equal to 5 mm−3, the nucleation pressures (65.1 MPa at 1,000 kPa/s; 69.0 MPa at 27.8 kPa/s) match those measured in the system rhyolite-hematite-water

$Evolution of bubble number density with decreasing pressure PL for an equivalent surface tension $$ \\sigma _{\\rm LB}^{\\rm E} $$ = 0.078 N/m; the thick line corresponds to $$ \\left| {\\left. {{\\text{d}}P/{\\text{d}}t} \\right|} \\right. $$ = 1,000 kPa/s, the thin line decorated with empty circles to $$ \\left| {\\left. {{\\text{d}}P/{\\text{d}}t} \\right|} \\right. $$ = 27.8 kPa/s. With $$ \\sigma _{\\rm LB}^{\\rm E} $$ = 0.078 N/m and a detectability threshold equal to 5 mm−3, the nucleation pressures (65.1 MPa at 1,000 kPa/s; 69.0 MPa at 27.8 kPa/s) match those measured in the system rhyolite-hematite-water$

Caption

Fig 8

Evolution of bubble number density with decreasing pressure P_L for an equivalent surface tension $$ \sigma _{\rm LB}^{\rm E} $$ = 0.078 N/m; the thick line corresponds to $$ \left| {\left. {{\text{d}}P/{\text{d}}t} \right|} \right. $$ = 1,000 kPa/s, the thin line decorated with empty circles to $$ \left| {\left. {{\text{d}}P/{\text{d}}t} \right|} \right. $$ = 27.8 kPa/s. With $$ \sigma _{\rm LB}^{\rm E} $$ = 0.078 N/m and a detectability threshold equal to 5 mm⁻³, the nucleation pressures (65.1 MPa at 1,000 kPa/s; 69.0 MPa at 27.8 kPa/s) match those measured in the system rhyolite-hematite-water

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the value of σ_LB such that homogeneous bubble nucleation would occur at a pressure equal to the pressure of heterogeneous nucleation measured in the experiments, P_N ; $$ P_{\text{\rm N}}^{\text{\rm E}} $$ is the pressure of homogeneous bubble nucleation for a bubble–liquid surface tension equal to $$ \sigma _{\rm LB}^{\rm E} $$ (Figure 8 ).

Pressures of homogeneous nucleation equal within error to the pressures of heterogeneous nucleation in the experiments (63 ± 3 MPa in the 1,000 kPa/s series; 69 ± 1 MPa in the 27.8 kPa/s series) are predicted for $$ \sigma _{\rm LB}^{\rm E} $$ = 0.078 N/m (Fig. 8 ; Table 2 ): 65.1 MPa at 1,000 kPa/s and 69.0 MPa at 27.8 kPa/s.

Note that the effect of decompression rate on nucleation pressure is small: according to the classical theory, the nucleation pressure decreases by only 4 MPa when decompression rate increases from 27.8 to 1,000 kPa/s (Fig. 8 ), in perfect agreement with our experimental results. .

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