TABLE III.
1-D Microbubble Acoustic Radiation Force (ARF) Translation Model Variables and Inputs With sources When Appropriate.
| Symbol | Variable | Value |
|---|---|---|
| A | Microbubble cross-sectional area | Varies |
| b | van der Waals constant | 0.1727 [48] |
| c | Speed of sound in liquid | 1540 m/s |
| ε | Lipid shell thickness | 1 nm [47] |
| g | Gravitational constant | 9.8 m/s2 |
| γ | Polytropic gas exponent | 1.07 [47] |
| P driv | Acoustic driving pressure | Varies |
| P l | Pressure in liquid | Varies |
| P 0 | Hydrostatic pressure | 101 × 103 Pa |
| ρ l | Liquid density | 1000 kg/m3 |
| ρ b | Microbubble shell density | 1150 kg/m3 [49] |
| R | Microbubble radius | Varies |
| Ṙ | Microbubble wall velocity | Varies |
| R̈ | Microbubble wall acceleration | Varies |
| R 0 | Initial microbubble radius | Varies |
| σ | Interfacial tension | 0.051 N/m [50] |
| T | Time | Varies |
| u r | Relative velocity of bubble to liquid | ub – ul |
| u l | Liquid velocity | Varies |
| u b | Bubble velocity | Varies |
| μ | Liquid viscosity | 1 × 10–3 Pa-s |
| μ sh | Microbubble shell viscosity | 1.9*R0 – 1.1 [47] |
| μ F | Coefficient of friction | 0.5 [43] |
| ν | Kinematic viscosity of the medium | μ/ρl |
| V b | Microbubble volume | Varies |
| V m | Universal molar volume | 22.4 L |
| χ | Elastic modulus of lipid shell | 0.5 [47] |