# [SVC43-P01] Estimating the parameter to determine bubble - crystal interaction styles

Keywords:analog experiment, bubble-crystal interaction

In the magma, the interaction between suspended crystals and the rising bubble made

by buoyancy is important because the interaction can be expected to control the chemical

evolution of magma chamber and their stratification through the rheological properties

and bulk densities. Beline et al (2010) showed that there are three interaction styles with

changing bubble diameter and viscosity of the liquid by laboratory experiments using an

analog material: a single plastic cube and a controlled single bubble in viscous liquid.

However, the crystal - bubble interaction is still poorly understood since the factors to

make a difference among the three interaction styles are not explained enough. In order

to solve this problem, we give some constraint on the controlling parameters to determine

three interaction styles by analogue experiments.

The experiments are performed in the tank filled with viscous liquid (analog material of

silicate melt)and prepared three different viscosity(0.29 Pa・s, 6.46 Pa・s, 19.1 Pa・s ).

The plastic cube (analog material of crystal) with 10 mm is suspended in liquid by a rod.

The bubble is injected into the liquid from 11cm below the plastic cube from a syringe

connected to a motor controlled by the PC program by which we can change the initial

bubble size. We examine the probability of occurrence of three styles of interaction:

"stuck", "pass", and "split"; "stuck" in which a bubble stays under the solid cube, "pass" in

which a bubble moves around the cube and "split" in which a bubble separated into two

bubbles. To determine the probabilities, we did the repetition of 10 times for the same

condition of initial bubble radii and viscosity.

In our experiments, we observed two styles of the interaction of "stuck" and "pass" and

not "split". It is found that the smaller bubble tends to “stuck”, on the other hand, the

probability of “pass” became higher as the bubble radii are larger. To reveal the boundary

of “stuck” and “pass”, we use Bound number which is a dimensionless number

representing the ratio of bubble relaxation time and the bubble rising time per their radius.

From the results of the examination using the size ratio between solid cube and the final

attached bubble, and Bond number, it is suggested that there are two regimes in the

mechanism of interaction styles. These two different regimes are caused by Reynolds

number which is the ratio of inertia force and viscous resistance. In low Reynolds number

regime is controlled by the final maximum bubble diameter which resulted from

mechanical interaction between bubble and cubes in the higher viscosity. For example, if

the deformed bubble diameter is larger in the horizontal length than the cube width, the

bubble path throws the cube. In high Reynolds number regime is controlled by inertia

force. The probability of occurrence of “pass” is higher as the bubble radius becomes

larger with inertia force.

Thus, we found that there are two regimes in the bubble-crystal interaction style; one

is a static regime (low Re) controlled by the geometrical relation in the horizontal sizes

including static deformation, another is a dynamic regime (high Re) controlled by the

inertia of a rising bubble by buoyancy.

by buoyancy is important because the interaction can be expected to control the chemical

evolution of magma chamber and their stratification through the rheological properties

and bulk densities. Beline et al (2010) showed that there are three interaction styles with

changing bubble diameter and viscosity of the liquid by laboratory experiments using an

analog material: a single plastic cube and a controlled single bubble in viscous liquid.

However, the crystal - bubble interaction is still poorly understood since the factors to

make a difference among the three interaction styles are not explained enough. In order

to solve this problem, we give some constraint on the controlling parameters to determine

three interaction styles by analogue experiments.

The experiments are performed in the tank filled with viscous liquid (analog material of

silicate melt)and prepared three different viscosity(0.29 Pa・s, 6.46 Pa・s, 19.1 Pa・s ).

The plastic cube (analog material of crystal) with 10 mm is suspended in liquid by a rod.

The bubble is injected into the liquid from 11cm below the plastic cube from a syringe

connected to a motor controlled by the PC program by which we can change the initial

bubble size. We examine the probability of occurrence of three styles of interaction:

"stuck", "pass", and "split"; "stuck" in which a bubble stays under the solid cube, "pass" in

which a bubble moves around the cube and "split" in which a bubble separated into two

bubbles. To determine the probabilities, we did the repetition of 10 times for the same

condition of initial bubble radii and viscosity.

In our experiments, we observed two styles of the interaction of "stuck" and "pass" and

not "split". It is found that the smaller bubble tends to “stuck”, on the other hand, the

probability of “pass” became higher as the bubble radii are larger. To reveal the boundary

of “stuck” and “pass”, we use Bound number which is a dimensionless number

representing the ratio of bubble relaxation time and the bubble rising time per their radius.

From the results of the examination using the size ratio between solid cube and the final

attached bubble, and Bond number, it is suggested that there are two regimes in the

mechanism of interaction styles. These two different regimes are caused by Reynolds

number which is the ratio of inertia force and viscous resistance. In low Reynolds number

regime is controlled by the final maximum bubble diameter which resulted from

mechanical interaction between bubble and cubes in the higher viscosity. For example, if

the deformed bubble diameter is larger in the horizontal length than the cube width, the

bubble path throws the cube. In high Reynolds number regime is controlled by inertia

force. The probability of occurrence of “pass” is higher as the bubble radius becomes

larger with inertia force.

Thus, we found that there are two regimes in the bubble-crystal interaction style; one

is a static regime (low Re) controlled by the geometrical relation in the horizontal sizes

including static deformation, another is a dynamic regime (high Re) controlled by the

inertia of a rising bubble by buoyancy.