Coherent Capillary Wave Structure Revealed by ISS Experiments for Spontaneous Nozzle Jet Disintegration


A series of International Space Station (ISS) experiments were conducted to observe the disintegration feature of a water jet issued from an orifice/nozzle into atmospheric air. The purpose was to validate our proposal that any laminar liquid jet can spontaneously disintegrate by its own self-destabilizing loop formed along the jet. This paper reports the experiment results focusing on a water jet issued from a nozzle with a radius 0.4 mm and length 120 mm, in which the parabolic velocity profile relaxes toward that of a plug flow along the jet. As predicted in our proposal, the nozzle jet had a two-valued breakup distance in a certain jet issue speed range and exhibited hysteresis behaviors, indicating that the jet disintegration state is determined by past jet disintegration history. Analyses of video images suggest the establishment of a coherent capillary wave structure in the steady jet disintegration state. New fundamental theories were developed to examine the underlying physics involved. The short-length breakup mode was confirmed to essentially follow the same self-destabilizing mechanism as that of the plug flow jet, in which the upstream propagating capillary wave produced by the release of surface energy due to jet tip contraction or nonlinear unstable wave growth is reflected at the orifice, and becomes the unstable wave responsible for jet disintegration. In the long-length breakup mode, the velocity profile relaxation plays a role equivalent to an orifice and the average nozzle jet length is expressed as the sum of the velocity profile relaxation length and average orifice jet length at large jet issue speeds. This paper focuses on the coherent capillary wave structure of long-length breakup mode.

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a :

inner radius of injector

c :

complex phase velocity(=cr + ici)

D :

diffusivity(\( = Va/\sqrt{2} \))

f :

complex function defined in Eq. (16)

G :

Green function

k :


\( \overline{L} \) :

average jet length

L B :

breakup distance

L e :

Boussinesq inlet length


nozzle length

m :


n :


R :

inner radius of syringe barrel

Red :

Reynolds numer of nozzle flow

r s :

local jet surface radius


surface displacement(= rs-a)

T :

breakup period

t :


U :

jet discharge speed, jet speed

u max :

centerline velocity of nozzle jet

u s :

surface velocity of nozzle jet

V :

jet tip contraction speed (=\( \sqrt{\sigma /\rho a} \))

v :

piston rot speed


Weber number(=(U/V)2)

x :

axial coordinate

Δu :

excess velocity from surface velocity (=umax-us)


Diracs delta function


surface deformation amplitude



λs :

wavelength of standing wave


density of water


surface tension coefficient of water


instant when an impulsive force is applied




frequency of most unstable wave



ωS :

resonant frequency(=kcr)


long-length breakup mode


maximum point trajectory


short-length breakup mode


tip contraction wave


velocity profile relaxation


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Umemura, A., Osaka, J., Shinjo, J. et al. Coherent Capillary Wave Structure Revealed by ISS Experiments for Spontaneous Nozzle Jet Disintegration. Microgravity Sci. Technol. 32, 369–397 (2020).

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  • Microgravity
  • Spontaneous nozzle jet disintegration
  • Velocity profile relaxation
  • Capillary wave
  • Linear stability analysis
  • Self-destabilizing loop