Acoustic Transport of Fuel Bubbles in BSFusion
The preferred method of fuel locomotion in BSF is acoustical transport. The concept is based on the observation that a bubble immersed in a fluid and exposed to a pressure gradient will rapidly accelerate until it reaches a terminal velocity V_T . This velocity arises from a balance between buoyant force F_B and drag force F_D , such that:
F_B = F_D
Buoyancy is the same principle that makes boats float: fluid pressure increases with depth, so the bottom of a submerged object feels more pressure than the top. This pressure difference pushes the object upward. However, buoyancy can also be engineered to point in any direction—not just “up”—by creating synthetic pressure gradients. The buoyant force on a spherical bubble is:
F_B = (\rho_B - \rho_L) \cdot g \cdot \frac{4}{3} \pi r^3
where:
- ρ_B is the density of the bubble (kg/m³)
- ρ_L is the density of the surrounding liquid (e.g., molten FLiBe)
- g is gravitational acceleration (m/s²)
- r is the bubble radius (m)
Drag force opposes motion and depends on the viscosity μ, bubble size r, and velocity v. For small Reynolds numbers, Stokes’ Law gives:
F_D = 6\pi\mu r v
At terminal velocity, where forces balance, the bubble’s velocity is:
V_T = \frac{2}{9} \cdot \frac{(\rho_B - \rho_L)}{\mu} \cdot g r^2
This explains why larger bubbles rise faster than smaller ones: buoyant force scales with r³, while drag only scales with r. (More precisely, F_D∝r and F_B∝r³, so V_T∝r².
If the bubble starts from rest, its velocity over time is:
v(t) = V_T\left(1 - e^{- \frac{g t}{V_T}} \right)
Integrating this gives the total distance traveled:
d(t) = V_T t - \frac{V_T^2}{g} \left(1 - e^{- \frac{g t}{V_T}} \right)
This same principle can be used even without gravity. A fluid in a gravitational field develops a pressure gradient ∇P = ΔP/Δs = ρg, but other mechanisms—such as centrifugal force or acoustic pressure waves—can replicate this gradient. In BSF, acoustic fields are used to create controllable pressure gradients that steer fuel bubbles where they need to go.