With milk poured from a newly opened carton, I have observed over the years that the flow of the liquid starts off flowing smoothly and continuously but after some time t becomes "sporadic" in such a way that the liquid flow out of the mouth of the carton becomes more periodic than smooth. This is in tandem with the contraction and expansion of the carton. Any liquid from time t, henceforth, hitting whatever liquid that has been in the cup before time t tends to splash.

I am unsure how to frame this question in a much better way but would be more than appreciative for anyone who could either reword the question or provide an explanation to the phenomenon (and can it be modelled with a PDE?)

  • $\begingroup$ Duplicate physics.stackexchange.com/questions/15950/… and physics.stackexchange.com/questions/103766/… $\endgroup$
    – Farcher
    Commented Jan 30, 2018 at 9:36
  • $\begingroup$ -1 Not clear what you are asking as your observation contradicts the usual observation that poured liquid starts glugging and gets smoother as the carton empties. The "contraction and expansion of the carton" is consistent with glugging. Please can you provide more details of how you are pouring? Are you adjusting the angle of the carton as you pour? Are you increasing the rate of flow? Are you squeezing the carton? Ideally a video would help so that we can see how your observation is different. $\endgroup$ Commented Jan 30, 2018 at 15:15
  • $\begingroup$ From your description I would guess that an oscillation is building up in the carton ("sloshing") as you tilt it. This problem occurs in automated control - eg waset.org/publications/9248/…. Splashing in the cup is a separate phenomenon. $\endgroup$ Commented Jan 30, 2018 at 16:06

1 Answer 1


This unsteady (jerky) liquid flow out of the opened carton has probably a very simple explanation. The necessary inflow of air to compensate for the outflow of the liquid of the carton. First the liiquid flows out smoothly creating a lower air pressure in the carton until the flow stops and air can flow in through the opening. Then the liquid flow starts again until the reduced air pressure i the carton reduces the liquid flow. In all of this, also the movable walls of the carton can play a role. PS: I would not try to describe this process with PDE. This is rather complicated phenomenon. Maybe you can find a simpler model description for it.

  • $\begingroup$ Is your explanation based on research? This description does not agree with my experience that the flow is jerky ("glug-glug-glug") when air cannot get into the carton/bottle and smooth when it can. $\endgroup$ Commented Jan 30, 2018 at 6:46
  • $\begingroup$ @sammy gerbil - There might be variations of the phenomenon that could also depend on the shape and material of the container. Air pressure difference and/or movements seem to play a significant role here. Once I even observed a pronounced "glug-glug-glug" phenomenon in a glass bottle with no liquid flowing out at all. Somebody lifted the filled bottle to the mouth which produced a loud "glug-glug-glug" as if he was already pouring down his throat the high percentage drink. But nothing had come out yet. Much to his embarrassment and amusement of the bystanders. $\endgroup$
    – freecharly
    Commented Jan 30, 2018 at 14:54
  • $\begingroup$ The glugging only occurs when the level of the liquid (and the pouring angle of the container) is sufficient to obstruct a balanced flow of air into the container to replace the liquid outflow. The flow then becomes fitful because the weight and inertia of the flowing liquid produces an overly low pressure inside the container, which first resists further outflow, then takes in a gulp of air (due to atmospheric pressure forcing into the low-pressure container), and the cycle repeats regularly producing a resonance (exacerbated in plastic containers with flexible sides). $\endgroup$
    – Steve
    Commented Jan 30, 2018 at 17:03
  • $\begingroup$ @Steve - I think that you are describing it correctly. An important factor is the "valve function" of the liquid level at the edge that separates the outlet tube space from an upper inner volume where an air space develops with lower pressure and thus a higher liquid level appears until air can flow in through the "valve" so that (some) of the liquid there can flow out which closes the valve, and so forth. $\endgroup$
    – freecharly
    Commented Jan 30, 2018 at 17:15

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