Dynamics of a “collective” bubble in a magma melt flow behind the decompression wave front

Kinetics of gas bubble nucleation and growth in magmatic melt at its rapid decompression

“…It is obvious that dependencē D e f f (ε) changes its character gradually from the linear to quadratic; at that, it stays linear (as it was expected) only at very low supersaturation. At high supersaturation the numerical value ofD e f f coincides with the analytical one, determined by formula (26).…”

“…In Fig. 2 there is dependence of coefficient of "effective diffusion" on initial supersaturation of the melt:D e f f (ε), calculated numerically and by formulas (25) and (26). It is obvious that dependencē D e f f (ε) changes its character gradually from the linear to quadratic; at that, it stays linear (as it was expected) only at very low supersaturation.…”

“…(21) and depends only on the degree of initial supersaturation ε. From the moment, when parameterRṘ becomes constant, concentration of gas, dissolved in the melt, becomes the function of only one variable χ , i.e., the solution to the ; dotted line -approximate solution at low supersaturation (25), it is also steady-state solution 14; dashed line -approximate solution at high supersaturation (26).…”

“…It can be concluded from the above said that the use of steady-state solution (14) in the entire range of initial supersaturation and for all times is inappropriate. Moreover, to describe the law of gas bubble growth in the melt for real volcano eruptions, when supersaturation is usually high, we should use solution (26) instead of solution (14).…”

“…Diffusion bubble growth is described in Refs. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. It is just a small number out of multitude of works that are mostly concerned about growth of bubbles in magma.…”