[MUSIC] Hello. In this experimental session we are going to show the effects of coupling between a still fluid and a solid for two cases: When viscosity plays a role and when sloshing plays a role. Here is the first set of experiments with eggs. Why eggs? Because an egg contains inside the shell a very viscous substance, the white. But when the egg is boiled, the inside is actually solid. This is the reason why cooks, at least in France, use a trick based on the fluid-solid interactions to check if an egg is raw or boiled. Let's us see this. Here is a test, on two different eggs. The test is to try and rotate the egg on a flat table. For my first egg, here, a simple twist with the hand and the egg spins. For my second egg it does not work so well. The rotation needs several tries to start. Certainly these two eggs are different inside. Here is another test on these two eggs. Once the first egg is spinning I try to stop it with my hand, and when I release it, it stays there. On the second egg, the one which was difficult to spin, the motion is different. If I stop it and release it, it restarts to spin. What is happening? This is just a case of viscous diffusion inside the egg. For the raw egg, the motion of the shell is transmitted to the liquid only by viscous diffusion, and this is not instantaneous. Actually, this is very similar to the case of the translating plate, with an impulsive start, that you solved in the lectures. Except that here the solid is around the fluid. What is the time of diffusion inside the raw egg? Well, the viscosity is about 0.1 Newton times second per meter squared. The density is about that of water. And the size of a few centimeters. Therefore, what we call T viscosity, is of the order of a second. Over more than a second, the motion of the shell and of the white, are the same. This is what happens when I continue to rotate the shell, I eventually spin the whole egg. But if I stop the rotation for a too short moment, then the white is not stopped and re-entrains the shell. Of course, for the boiled egg, nothing of this happens. Here are my two eggs, the boiled one and the raw one. No doubt you can tell which is which by their ability to spin. And then you can check by breaking the eggs, the boiled one and the raw one. Now something about sloshing. If you take a bottle of water and try to make it roll on the ground. Its motion is not as regular as if it was a rigid cylinder. Let us see another experiment of this. Here is a cylinder half full of liquid that I try to roll on a table. I can have a very regular motion if I start the motion smoothly. As here. Note that the surface of the liquid is not moving much. It remains almost horizontal. But if I start the rolling by a sudden impulse, as here, the motion is different. The cylinder rolls step by step, and the surface of the liquid oscillates strongly. What happens? This is a particular case of the coupling between a sloshing mode and a solid mode that you saw in the lectures. Here the solid mode is a rigid body mode with zero frequency. It is just the rolling motion. So I have a sloshing mode exciting by the rolling motion. And the rolling motion excited by the sloshing mode. The resulting motion is a combination of a regular rolling plus an oscillation due to the sloshing. And this oscillation is larger when the sloshing mode has been excited by a sudden impulse. Now if I add some stiffness to my rolling mode, for instance, by attaching a mass on the cylinder, like a pendulum, as you can see I get a coupling between the sloshing mode and the solid mode. This is the same coupled motion that the one we had in the lectures on the translation mode of the rectangular tank. These two experiments, that you can try with eggs and a bottle, show you that fluid solid coupling with viscosity and with sloshing are present all around you. This experimental session is over, thank you and see you soon. >> [MUSIC]
