Appendix D
Bubbles
D.1 Biobubbles
The behavior of bubbles in biological systems is of some interest. Cases in point:
Cavitation within cells by strong ultrasonic waves, or the formation of nitrogen
bubbles in the blood as divers surface too rapidly from ocean depths, or pilots who
fly to high altitudes too quickly, producing ‘the bends’, also called decompression
sickness. 1
The vibrational frequencies of microsized gas bubbles in biological cells falls
in the ultrasonic region. Strong ultrasonic waves can cause cavitation bubbles.
Correspondingly, weaker ultrasonic waves can increase the rate nitrogen bubbles
in the blood dissolves.
Ultrasonic image contrast is facilitated by the prior injection of microbubbles,
but with added dangers (See Sect. 5.22.1.)
D.2 Minimum Area Surfaces
Consider the surface of a bubble. Such a surface might exist as a two-dimensional
liquid surface on a closed frame in three dimensions. Locally, surface tension in the
liquid draws the fluid into a surface with minimal area. If the surface has minimal
area, then small variations in that surface for the given frame boundary B must
vanish:
δ
B
dA =
B
dA
A 2
−
B
dA
A 1
= 0 ,
(D.1)
1 Pilots can breathe pure oxygen a half hour before rapid decompression to avoid the bends.
© Springer Nature Switzerland AG 2020
W. C. Parke, Biophysics, https://doi.org/10.1007/978-3-030-44146-3
641
Bubbles
D.1 Biobubbles
The behavior of bubbles in biological systems is of some interest. Cases in point:
Cavitation within cells by strong ultrasonic waves, or the formation of nitrogen
bubbles in the blood as divers surface too rapidly from ocean depths, or pilots who
fly to high altitudes too quickly, producing ‘the bends’, also called decompression
sickness. 1
The vibrational frequencies of microsized gas bubbles in biological cells falls
in the ultrasonic region. Strong ultrasonic waves can cause cavitation bubbles.
Correspondingly, weaker ultrasonic waves can increase the rate nitrogen bubbles
in the blood dissolves.
Ultrasonic image contrast is facilitated by the prior injection of microbubbles,
but with added dangers (See Sect. 5.22.1.)
D.2 Minimum Area Surfaces
Consider the surface of a bubble. Such a surface might exist as a two-dimensional
liquid surface on a closed frame in three dimensions. Locally, surface tension in the
liquid draws the fluid into a surface with minimal area. If the surface has minimal
area, then small variations in that surface for the given frame boundary B must
vanish:
δ
B
dA =
B
dA
A 2
−
B
dA
A 1
= 0 ,
(D.1)
1 Pilots can breathe pure oxygen a half hour before rapid decompression to avoid the bends.
© Springer Nature Switzerland AG 2020
W. C. Parke, Biophysics, https://doi.org/10.1007/978-3-030-44146-3
641