Investigation of the rise of an air bubble in a square-section water channel. Features of air bubble type washing machines Air bubble

Yu.B. Bazarov 1 , D.E. Meshkov 3 , E.E. Meshkov 1,2 , V.S. Sivolgin 3
1 RFNC - VNIIEF 2 SarFTI 3Lyceum №15 (Sarov)

Introduction

AT last years high school students of the Physics and Mathematics Lyceum No. 15 of Sarov take part in the work of the educational and research hydrodynamic laboratory at SarFTI. In 2003, on the basis of this collaboration, work was started to test the hypothesis about the influence of the scale factor on the nature of the development of the turbulent mixing zone at the gas-liquid interface during the development of the Rayleigh-Taylor instability.

A laboratory technique was developed for obtaining and studying air bubbles of a given volume, initially up to 2.5 cm3 and later up to 1 liter or more. This technique is a modification of the method for obtaining large approximately spherical air bubbles in water, which was used to model the rise of a cloud of a strong explosion in the atmosphere. The results of such experiments make it possible to obtain more detailed (compared to ) information about the initial stage of the rise of an air bubble, the mechanism of its transformation into a vortex ring, and some of the effects associated with this phenomenon.

Further development of experimental techniques and, in particular, the use of a high-speed video camera VS-FAST (now the camera is produced under the trademark - editor's note) to register the emerging flow made it possible to obtain new data on some effects associated with hydrodynamic instabilities accompanying the initial stage of bubble rise.

The installation is a channel of square section with walls made of window glass (Fig. 1).

fig 1. General form installations

The basis is a plate of textolite. At the base there is a device for obtaining bubbles (Fig. 2).

Fig 2. Bubble device

Its main part is the body of a medical syringe. The body of the syringe is fixed in the plate. A small piece of rubber is attached to the top of the syringe with tape. A plexiglass stopper is inserted into the lower part of the syringe, into which, in turn, a sealing gum made of an eraser is driven. On the side, a fitting is screwed into the body of the syringe, connected through a hose to a car pump. A needle of the desired length is inserted into the elastic band. The experimental technique is described in more detail in the article.

During the experiment, a rubber bubble of the required size was inflated. Next, the rubber sheath was pierced with a needle at the pole; in this case, the remains of the shell slide along the water-air interface, forming an air bubble.

The rise of the bubble and the resulting flow were recorded by a high-speed VS-FAST video camera with a frequency of ~500 frames per second.

Experimental results and discussion

Figure 3 shows frames of a videogram of the rise of a 0.15 L bubble, obtained using a high-speed camera. At the first moment, the stretched rubber shell of the bladder, after being punctured by a needle in the pole, contracts in ~1 ms, “exposing” the air bubble

Figure 3. High-speed (500 fps) filming of the rise and formation of a vortex ring
from an air bubble with a volume of 0.15 liters. The time on the frames is indicated from the moment of breakdown
rubber sheath. In the process of rising, the bottom jet (DS) breaks through the bubble
air, forming a vortex ring.

video of this shoot 3.0 MB

In this case, the surface of the bubble turns out to be perturbed - it becomes similar to the bumpy surface of an orange. This perturbation is a consequence of the sliding of the contracting rubber along the water-air interface on the bubble surface. After some time (~60 ms), the surface of the bubble becomes smooth, and the hillocks of the initial perturbation generate a layer of small air bubbles surrounding the main bubble, shown in Fig. 4.

Figure 4. Formation of a layer of small bubbles surrounding the main bubble
in the initial stage of the flow. (Fragments of frames in Fig. 3 are shown.)

The origin of these bubbles is connected, apparently, with the instability of the air-water interface on the surface of the bubble during its impulse acceleration due to a small expansion of the bubble. The air pressure in the bubble under water before the shell rupture has two components: a) the pressure of the water column above the bubble and the air atmosphere, and b) the pressure of the stretched rubber shell.

When the shell breaks, only the first component remains, and as a result, the bubble expands slightly. Figure 5 shows the results of measurements of the transverse size of the bubble (d) after the descent of the shell as a function of time.

Fig. 5. Dependences of the transverse dimension on time in the initial stage of the ascent

It can be seen from this plot that the value of d practically increases abruptly by ~3 mm. Correspondingly, the bubble boundary is displaced abruptly by ~1.5 mm in the radial direction. The consequence of such a double impulsive acceleration (first caused by a sharp expansion of the bubble from the state of rest and then stopping) is the growth of bumpy initial perturbations due to the development of instability and then their detachment from the main bubble.

During the subsequent rise of the main bubble, a layer of these small bubbles rolls down under the main bubble, and forms a cloud there, which rises relatively slowly after the main bubble.

The high-speed shooting frames presented in Fig. 3 also allow us to examine in detail the process of the bubble transformation into a vortex ring due to the formation and development of the bottom jet (t~ 40 ms ÷ 120 ms) and the breakthrough of its dome (t~ 120 ms ÷ 160 ms). The breakthrough is accompanied by the formation of a cloud of small bubbles above the main bubble. The bubble transforms into a vortex ring.

At the initial stage of ascent, the bubble floats up with an ascent velocity of 0.37 m/s, and after the formation of a vortex ring, the velocity decreases to 0.18 m/s.

If we observe this process in dynamics (like a movie), we can see that this ring rotates in the direction specified by the movement of the bottom jet.

The flow dynamics in this experiment is shown in the graph in Fig.6. Here, the dependence of the height of the rise of the upper part of the bubble H, the lower part of the bubble h, the top of the bottom jet Hs, and the transverse size of the bubble d on time t is given. Distances are measured from the bottom of the vessel.

Figure 6. Graph of the dependence of the height of the upper border of the bubble H,
the lower boundary h, the bottom jet Hs, and the transverse size of the bubble d on time t.

The graph shows that the velocity of the bottom jet significantly exceeds the velocity of the upper boundary of the bubble, as a result of which the bottom jet catches up with the upper boundary and breaks through it (t ~ 120 ms).

Let us dwell on the reasons for the formation of a bottom jet. In the initial stage of motion, the bubble has an almost spherical shape. As soon as it starts to move upwards, a flow around the bubble simultaneously appears (Fig. 7). The bubble rises, and the water flows around it and rushes under the bubble. The flow of water around the bubble is symmetrical with respect to the vertical axis of the bubble. And as a result, under the bubble, the flow has a convergent, converging character.

Figure 7. Scheme of flows around the bubble

As a result of this converging flow, a cumulative effect arises, which is expressed in a local increase in pressure under the bubble. It is this circumstance that determines the formation and subsequent development of the bottom jet, which is essentially a cumulative jet.

Fig. 8. High-speed (490 fps) filming of the process of rising an air bubble with a volume of 0.3 l.
In this case, the bottom jet does not reach the upper boundary and breaks through the bubble from the side,
tearing off the upper part in the form of a mushroom cap from the bubble

On fig. Figure 8 shows an experiment illustrating the process of lifting and changing the shape of a bubble with a volume of 0.3 liters. It can be seen that during the ascent the bottom jet expands and its upper boundary is unstable. As a result, the bottom jet breaks through the bubble non-symmetrically around the entire perimeter; the break begins laterally and spreads horizontally, separating the upper part of the bubble in the form of a mushroom cap.

Figure 9 shows the dependence of the height of the upper boundary of the bubble H, the lower boundary h, the bottom jet Hs, the lower boundary of the cap H1, the upper boundary of the detached cap h1 on time t.

Figure 9. Graph of the dependence of the height of the upper border of the bubble and then the “cap” H,
lower boundary h, bottom jet Hs, lower boundary of the “cap” H1,
upper boundary of the detached hat h1 on time t

It is also interesting to note the unusual nature of the development of the Rayleigh-Taylor instability on the upper part of the bubble, at the initial stage of its rise (Fig. 8). After the rubber shell comes off, small-scale perturbations are formed on the surface of the bubble (which we have already written about above). In the upper part of the bubble, the conditions for the development of the Rayleigh-Taylor instability (water over air) are realized. As a result of the development of this instability, the initial perturbations begin to develop: on the one hand, their amplitude increases, and on the other hand, their scale (the characteristic wavelength of the perturbation) also increases. At the same time, there is a predominant increase in the perturbation located in the region of the symmetry axis of the bubble at its upper boundary. As a result, the central perturbation in the form of a dome, as it were, displaces other perturbations to the periphery, and the growth of these perturbations stops; at the same time, they seem to roll down, forming a smooth dome.

Thus, with the help of high-speed video recording (500 frames per second), data were obtained that illustrate in detail the process of formation of a vortex ring when an air bubble with a volume of 0.15 to 0.3 liters rises in water. Data were obtained on the formation and development of the "bottom jet". Some unusual effects associated with hydrodynamic instabilities were observed in experiments; in particular, the processes of stabilization of the Rayleigh-Taylor instability in the upper part of the bubble, associated with shear flow and surface tension, were observed.

Literature

Sivolgin V.S., Meshkov D.E. Development of a methodology for conducting a large-scale underwater experiment on a small laboratory model. Bulletin of the Sarov PhysTech. No. 7, 2004, pp. 46-50.
E.E. Meshkov, N.V. Nevmerzhitsky, V.G. Rogachev, Yu.V. Yanilkin. On the possible role of the scale factor in the problem of turbulent mixing. Proceedings of the International Conference V Kharitonov thematic scientific readings, Sarov, March 17-21, 2003, edited by A.L. Mikhailov, pp. 415-418
D.E. Meshkov, E.E. Meshkov, V.S. Sivolgin. Investigation of the influence of the volume of a floating bubble on the nature of the flow. Bulletin of the Sarov PhysTech, No. 8, 2005, pp. 68-73.
Zhidov I.G., Meshkov E.E., Popov V.V., Rogachev V.G., Tolshmyakov A.I. The formation of a vortex ring when a large bubble rises in water. PMTF, No. 3, pp. 75-78, 1977.
http://www.site
V.V. Marmyshev, D.E. Meshkov, E.E. Meshkov, E.L. Ognev, V.S. Sivolgin, Ya.S. Shapovalov. The passage of an air bubble through the boundary of two mutually insoluble liquids. Bulletin of the Sarov Institute of Physics and Technology (in print).
Richtmyer R.D. Taylor instability in shock acceleration of compressible fluids. Commun.Pure Appl. .Math. V.13, 1960,297.
Meshkov E.E. Instability of the interface between two gases accelerated by a shock wave. Izv.AN USSR, MZhG. No. 5, 1969, p. 151-158.

New generation washing machines use various technologies, which are becoming more and more every year.

They are most common in Asia and among American housewives, while in Russia this technology has come relatively recently and is only gaining popularity and authority.

Principle of operation

As the name of the technology implies, quick stain removal is achieved through the circulation of bubbles. Air bubbles that are in the water constantly pass through the linen, acting on contaminated areas together with washing powder or liquid detergent.

Such an effect is akin to boiling, only boiling water spoils and significantly wears out the fabric, weakening its fibers.

automatic machines

The main element of the machine is a tank where water is poured and linen is laid. Inside it is a stainless steel drum that produces rotational movements. Water enters the machine through the filling hole. Along the way, she washes off the powder from a special tray and enters the tank.

In air bubble machines, after the water has entered the detergent tray, it descends into the bubble generator located under the drum. There, water with detergent is mixed with air and fed into the drum through small holes, in the form of a washing solution, foam and air bubbles.

The bubbles penetrate the fabric, removing dirt and coping even with dried stains. Also, during washing, the bubbles burst, releasing heat, which creates the effect of boiling. Washing is carried out in warm and cold water.

activator machines

The main difference between such machines is vertical loading. At the very bottom of the drum there is a pulsator designed to create vortex flows of water. It creates perfect jets for washing.

Separate from the activator is a nozzle that feeds the bubbles into the drum. Air bubbles are evenly distributed throughout the drum by the activator.

Such machines are connected to cold and hot water pipes, so they do not have heating elements. The built-in air bubble generator actively ejects portions of bubbles throughout the wash cycle, which makes the destruction of contaminants more effective.

Advantages and disadvantages

Pluses models of washing machines with the available air bubble wash mode are:

Significant energy savings.
Saving detergents due to the abundant formation of foam.
High degree of stain removal, boiling effect.
Reduced wash time. At the same time, the result remains the same as with long programs of washing machines not equipped with an air bubble system.
Washing things becomes delicate, thanks to the bubble pillow. It reduces the friction of the laundry against the walls of the drum and each other.
Things after washing have the same size, do not shrink.
In activator-type machines, you can report and remove laundry during washing. You can also stop washing at any time.
The machine with the activator does not have to be connected to the water supply, it is enough to pour water into the tank.
Low noise level.

Flaws:

High requirements for water hardness. It should be as soft as possible.
In activator-type machines, there may be no spin mode for laundry or a drain without spin function.
The cost of air bubble machines is higher than that of conventional ones.
The dimensions of the machines are slightly larger than those of simple activator machines and drum-type machines.

How to choose?

There are many models of air bubble machines on the market. In order to make a choice, you need to decide for yourself the following questions:

What type of car do you need. Automatic machines are more expensive than activator type machines, they also take up more space and require a connection to the water supply.
Machine dimensions.
Is pressing necessary? If so, what should be its maximum speed.
What should be the way to load things (horizontal or vertical).
Required energy saving class in washing and spinning mode.
Does the manufacturer matter?
Washing machine price range.

Customer Reviews

Galina, Moscow

For the last 15–20 years I have been using an ordinary activator baby, but a couple of years ago it broke down, and they could no longer repair it. The children brought a similar-looking machine, but they said that there was a thing in it that launched air bubbles inside. That should make her wash even better. I wash every weekend and I don’t know if these bubbles really affect something, but things are always clean, everything is washed well.

Marina, Far East

I have been using the Daewoo air bubble machine for 5 years, I bought it to replace the old one. Once it leaked, but it was my fault - I put it on an uneven surface, and during the spin cycle, the drain hose unscrewed. I really like the fact that you can throw a thing when the wash has already begun. For example, I forgot to throw a sock or a baby's undershirt. Bleach, conditioner and powder can be poured into the machine. For all the time of use proved to be excellent, I recommend!

Timofey, Kaluga

We have been using a Samsung machine for six months, everything seems to suit us, except for two points. When spinning, the car is ready to take off, it shakes very strongly. As I did not install the legs - nothing changes. Secondly, the delay time for washing is incorrect. Starts working earlier. Through trial and error, it turned out that for some reason the machine adds washing time to the delay time. There are no complaints about the rest - it washes perfectly, even children's things were washed.

Inna, Moscow

We bought an Eco Bubble machine a year ago. They took fancy, for more than 30,000 rubles. As a result, I wash LG, which is in the kitchen and is much cheaper. I do not like the noise when spinning. Sometimes after rinsing without spinning, foam remains on things.

Tatiana, Yekaterinburg

I have long wanted Samsung Eco Bubble. Bought six months ago. I can't get enough of her! It washes all the spots and saves a lot of electricity, especially if washed after 12 at night or on weekends. I don’t know who makes noise during the spin cycle, we don’t hear anything. If you close both doors (to the room and the bathroom), there is generally silence - the child sleeps peacefully. There is also no foam or streaks on things. I like the drum and the big boot.

Anna, Kyiv

Creepy car. I wanted to wash the bedding, pulled it out with huge dry spots, not stretched. They called a specialist, did the calibration. As a result, I got the same thing for the second time. The rest of the things do not stretch, stains remain on them. Even an elementary foundation or food on children's things. Several times things leaned back on the rubber band of the drum to the glass and remained dirty. There are no complaints about the noise and the remaining powder. I like the design, the drum, saving on electricity, but not washed stains spoil the whole impression.

Successful Models

The first production of air-bubble washing machines was started by the company Daewoo. It is still the leader in sales and quality of activator type machines with built-in bubble generator. Most requested model Daewoo DWF-806WPS. Much about this model positive feedback. The average price for a model is 10,000 rubles.
earlier model Daewoo DWF-760MP. The cost is from 7000 to 8000 rubles.
Company models gain popularity Samsung with technology EcoBubble. One of these models is SamsungAEGIS 3. The price of the model varies from 57,000 to 59,000 rubles.
Samsung WW 60H2210 EW. Drum washing machine. The price is from 22,000 to 31,000 rubles.
Samsung WF 60 F1R1 W2W. Drum washing machine. The price is 17500–23000 rubles.
Samsung WF 6 MF1R2 W2W. Drum type washing machine. The cost is 23,000 rubles.
Fairy 2 M. activator machine. The cost is 4200 rubles.

Failed Models

Firm Models EVGO and magna have been discontinued and are no longer sold.
Samsung WF 6 RF4E2 W0W. Drum machine. The cost is from 21,000 to 28,000 rubles.
Samsung WF 60 F4E0 W2W. Drum type washing machine. The price is 25,000 rubles.
Samsung WW 80 H7410 EW. Drum type washing machine. Reviews about this model are mixed. Lots of positive and negative opinions. The cost is from 50,000 to 67,000 rubles.

Washing machines with air bubble technology make washing any item much easier. Air bubbles form a soft foam-bubble pillow, which prevents the drum and other clothes from mechanically affecting delicate fabrics.

Kotkin, G., A rising air bubble and Archimedes' law, Kvant. - 1976. - No. 1. - S. 19-23. (1996. - No. 3. - P. 50-51.)

By special agreement with the editorial board and the editors of the journal "Kvant"

Imagine that you are preparing for an exam in physics, sitting on the edge of a forest near a lake. Repeating Newton's second law, you would like to apply this law to the movement of gas bubbles emerging from the bottom. And then something strange begins...

The force of gravity acting on the bubble is a thousand times less than the weight of the water displaced by it (the densities of air and water differ by about a thousand times). The resistance force during liquid friction, proportional to the bubble velocity, is initially small, so it should not be taken into account (The role of the resistance force will be discussed later.). Thus, the acceleration is determined mainly by the Archimedean buoyancy force:

Here m- weight, a is the acceleration of the bubble, V is its volume, ρ is the density of water. Let the gas density ρ 0 . Then

So, the acceleration of the bubble is about a thousand g. This is a very large value. Recall that the acceleration that the cosmonauts have to transfer to the pilots reaches several g(say up to 10g). If the projectile moves in a barrel 1 m long with such an acceleration, then it will be able to fly up to a height h= 1 km (check it yourself); if an insect gets inside our pop-up bubble, it will be crushed in such an “elevator”; etc. etc. A truly rich opportunity for inventors.

However, sitting on the shore of the lake, you can see with your own eyes that in fact the acceleration of the bubble is not at all so great.

Instead of immediately answering the riddle that has arisen, let's ask another one.

May you easily lift a pood weight ( m\u003d 16 kg) to a height of 1 m. And what if we apply a force equal to the weight of this weight to a 1 g pebble (or to a penny coin) on the way also 1 m? It is not difficult to imagine that the pebble will then fly up to a height of 16 km. (Air resistance is not taken into account. It is clear that this is not the point.) What is this - another fantastic project? No, this time it is quite easy to expose the author of the project: you will have to raise not only a stone, but also your own hand! A force of about 160 N must be applied to each gram of it. The whole arm will weigh several tons, and there will not be enough strength to lift it.

Thus, a hand that is stationary or moving with little acceleration can exert a much greater force on the load than a hand that moves with high acceleration.

But after all, when an air bubble moves in water, a similar picture arises. When the bubble rises, a certain mass of water rushes down, filling the vacated space. The bubble interacts with moving, not stationary water. Apparently, the force exerted by the water on the bubble also depends on the acceleration of the water itself. Archimedes' law, written in the usual form, is not applicable to a bubble moving at an accelerated rate!

It turns out that the problem of a bubble is very close to the problem of the motion of weights connected by a thread thrown over a fixed block (Fig. 1). It is easy to see the analogy between them. Indeed, one of the weights (with mass m) as if plays the role of a bubble, the other (with mass M) is the role of water, and the tension of the thread T- the role of the buoyant force.

Newton's second law as applied to a weight of mass m can be written like this:

If the mass weight m hold, then the thread tension T will be numerically equal to the weight of a Georgian mg(weight of "displaced" water). Substituting into equation (2), we obtain:

(wrong!). (3)

When it turns out. This conclusion, by its absurdity, is similar to the conclusion about the huge acceleration of the bubble (see (1)). The reason for both errors is the same: the movement of the mass weight must be taken into account M and the movement of "displaced" water. Recall that for the correct solution of the problem of weights, it is also necessary to write down the equation of Newton's second law for the mass weight M

and solve the system of equations (2) and (4). From here

When it turns out that is quite true.

You can solve this problem in another way - to use the law of conservation of energy. When the mass weight is displaced m up (and, accordingly, the weight of the mass M down) to a distance h the potential energy of the system will decrease by . The kinetic energy becomes , where υ is the speed of the weights (the initial speed is assumed to be zero). Equating the quantities

or (see (5))

Such a relationship between speed and displacement is characteristic of motion with constant acceleration. a. (In this case )

We use this to solve the problem of the motion of a body in a fluid. True, we cannot give a complete solution of the problem of an air bubble. The point is that the distribution of liquid velocities around the bubble is too complicated (Fig. 2).

However, we will solve a similar problem. Consider the motion of a long rod of radius r, length l and the masses m along the axis of the liquid-filled density with a tube of radius (Fig. 3).

In this case, the fluid motion is easy to calculate. The liquid displaced by the upper part of the rod moves down and fills the space vacated by the lower part of the rod. If we exclude small areas near the ends of the rod t, then the fluid velocity everywhere between the rod and the walls of the tube turns out to be the same. Denote by υ the speed of the rod, and through υ 1 - the speed of water moving between the rod and the walls of the tube, at the moment when the rod rose to a height h from the level at which its speed was zero. Equating the volume of fluid displaced by the rod in a short time interval Δ t, volume liquid that has passed during the same time between the rod and the tube, we find

During the time that the rod rose to a height h, the mass of liquid equal to ( is the volume of the rod), will also fall by h, then the decrease in the potential energy of the rod and the liquid is equal to . The kinetic energy of the system is , where m 1 is the mass of the moving fluid. It is convenient to write the kinetic energy of a liquid in the following form:

Using the law of conservation of energy, we get

Such a dependence of the speed v on the displacement h corresponds to motion with acceleration (see (6))

(7)

Thus, the rod moves as if its mass has increased by an amount m", and the buoyant force remained equal to the hydrostatic Archimedean force. The value m" is called the added mass. This is a purely formal, but convenient interpretation of equality (7). Formula (7) is obtained from the incorrect formula (1) by adding the term in the denominator m". Note that in a similar way formula (5) is obtained from (3) by adding the term in the denominator M.

Strength F vt, with which the moving fluid acts on the rod, is now easy to obtain from Newton's second law

In particular, if , then ; at , the buoyant force turns out to be of the order of the weight of the rod (and has nothing to do with the weight of the displaced water). If that is, we return to the law of Archimedes in its usual form.

< style="text-transform: uppercase">For a ball (in particular, for a bubble), the calculation gives the following result: the kinetic energy of the liquid is where V is the volume of the ball, υ is its speed. Then the added mass for the bubble i.e. it is equal to half the mass of the displaced water. The bubble rises with acceleration

The buoyancy force is determined from equation (8), it is approximately equal to i.e. three times the weight of an immobile bubble (and many times less than the weight of displaced water).

Now let's remember the resistance force. For a gas bubble in a liquid, it is determined by the formula where r is the radius of the bubble, υ is its velocity, η is the so-called coefficient of viscosity of the medium (The above formula is valid for if , the coefficient 12π should be replaced by 4π. For a solid ball with the coefficient is 6π (Stokes formula).). Taking into account the resistance force, the bubble motion equation can be written as follows (see (7)):

It's obvious that F c reduces the acceleration (and hence the speed) of the bubble compared to the case when we do not take into account the resistance of the liquid. However, if those. when the resistance force can be neglected. For example, if we are talking about a bubble of radius r\u003d 3 mm (A bubble of a larger radius cannot maintain a spherical shape (like a falling raindrop deformed by the force of air pressure; see, for example, the article by I.Sh. Slobodetsky "On the shape of a raindrop", "Kvant", 1970, No. 8) .), moving in water (ρ = 1 g / cm 3, η = 1.0 10 -2 g / (cm s), then its speed should be much less than the value Let's guess which way h 0 , the bubble will reach this speed. For a rough estimate, we use the equality where