# Bubble velocity¶

As stated in the Kunii and Levenspiel book, the bubble rise velocity in a dense bed can be calculated as

$u_{br} = 0.711(g d_b)^{1/2} \quad \text{where} \quad d_b/d_t < 0.125$

Wall effects can slow the rise of bubbles when $$d_b/d_t > 0.125$$; as such, the rise velocity is calculated as

$u_{br} = \left[0.711(g d_b)^{1/2}\right]1.2\,exp\left(-1.49 \frac{d_b}{d_t}\right) \quad \text{where} \quad 0.125 < d_b/d_t < 0.6$

For conditions where $$d_b/d_t > 0.6$$, the fluidized bed is considered to be slugging.

## Nomenclature¶

$$d_b$$ - Diameter of sphere having same volume as spherical cap bubble, effective bubble diameter (m)
$$d_t$$ - Bed or tube diameter (m)
$$g$$ - Acceleration due to gravity, 9.81 m/s²
$$u_{br}$$ - Rise velocity of single bubbles in a fluidized bed (m/s)

## Source code¶

chemics.bubble_velocity.ubr(db, dt)[source]

Rise velocity of single bubbles in a fluidized bed from Equations 5.3 and 5.4 in Kunii and Levenspiel book 1.

Parameters
• db (float) – Diameter of sphere having same volume as spherical cap bubble, referred to as the effective bubble diameter [m]

• dt (float) – Bed or tube diameter [m]

Returns

ubr (float) – Rise velocity of single bubbles in fluidized bed [m/s]

Example

>>> ubr(0.05, 0.6)
0.4979


References

1

Daizo Kunii and Octave Levenspiel. Fluidization Engineering. Butterworth-Heinemann, 2nd edition, 1991.