Liquid-Jet Capillary Instability: Wavelength and Growth Time Are Separate Questions

Define the Material or Thermodynamic Model

The MIT liquid-jet lecture gives an ideal cylindrical-jet instability condition kR < 1, where k = 2π/λ. The wavelength criterion says which small disturbances can grow in that model; it does not say that they have already reached breakup amplitude.

Review a Hypothetical Comparison

For an assigned jet radius R = 0.5 mm, wavelength λ = 5 mm gives kR = 0.628 and belongs to the unstable range. A 2 mm disturbance gives 1.571 and is outside it. Separately, if a mode has an assigned growth rate of 100 s−1, increasing its amplitude by a factor of 100 takes ln(100)/100 = 0.0461 s in the linear exponential model.

Keep the Evidence with the Decision

Keep jet radius, wavelength, disturbance amplitude and available travel time separate. State whether the ideal cylindrical, small-disturbance assumptions describe the comparison being made.

Real nozzles, viscosity, external gas and nonlinear breakup can change the result. The hypothetical growth rate is not a measured value or a universal atomization time, and the calculation supplies no final droplet distribution.

Does a proposed breakup disturbance belong to the unstable geometric range and have time to develop?

This blank worksheet is for your own project. It contains no H M machine trial result.

Customer Questions

Primary References

These references support the technical principles discussed in this guide. The worked examples and review questions are educational.

• MIT liquid-jet lecture
• Reference from hmpharmamachines.com