1. A device for stirring and aerating a liquid and eliminating the foam in a tank for treating said liquid, including inside the tank: a vertical sheath extending in a part of the height of the tank and including, in its upper part, at least one first opening providing an entry passage for the liquid and, near the bottom of the tank, at least one second opening providing an exit passage for the liquid, a funnel disposed around the upper part of the sheath and connected to said sheath, the upper edge of said funnel defining with the wall of the tank a free space for the passage of the liquid, a main propeller disposed inside the sheath below the bottom of the funnel, a vertical shaft drivable in rotation, extending inside the sheath above this propeller and operable to drive the latter in rotation, an anti-vortex means disposed inside the sheath, below said propeller. means for injecting a gas under pressure in the sheath, below the anti-vortex means, wherein the device further includes static stirring means for stirring the liquid by turbulence inside the sheath, the stirring means being disposed below the anti-vortex means. 2. A device according to claim 1, wherein the at least one first opening includes  a first series of ports provided in the upper part of the sheath and situated at the level of the liquid in the funnel, and a second series of ports provided in the sheath, above the bottom of the funnel; and wherein the device further includes means for regulating the level of the liquid in the funnel. 3. A device according to claim 2, further including means for regulating the flow of the liquid and of the foam sucked by the propeller into the sheath. 4. A device according to claim 3, wherein the means for regulating the flow of the liquid and of the foam sucked in by said propeller includes, on one hand, by a first sleeve disposed around the sheath at the level of the first series of ports and, on the other hand, by a second sleeve disposed around said sheath at the level of the second series of ports, the position of said sleeves relative to the corresponding ports being vertically adjustable. 5. A device according to any one of the preceding claims, wherein the means for effecting a static stirring by turbulence includes, on one hand, a vertical tube disposed inside the sheath and extending from the bottom of the tank to below the anti-vortex means and, on the other hand, superimposed static obstacles disposed inside said sheath and fixed to said tube. 6. A device according to claim 5, wherein the static obstacles define with the inner wall of the sheath passages for the circulation of the liquid. 7. A device according to claim 5 or claim 6, wherein the static obstacles are evenly spaced apart throughout the portion of the tube disposed inside the sheath. 8. A device according to claim 5 or claim 6, wherein the static obstacles are arranged on the tube, on one hand, below the anti-vortex means and, on the other hand, in the lower part of the sheath. 9. A device according to claim 5, wherein the static stirring means employing turbulence includes static obstacles fixed to the inner wall of the sheath and defining an axial passage for the circulation of the liquid. 10. A device according to claim 9, wherein the static obstacles are evenly spaced apart throughout the portion of the sheath situated below the anti-vortex means. 11. A device according to claim 10, wherein the static obstacles are arranged inside the sheath, on one hand, below the anti-vortex means and, on the other hand, in the lower part of the sheath. 12. A device according to any one of the claims 5 to 11, wherein the static obstacles are formed by cups the concavity of which faces toward the bottom of the tank. 13. A device according to any one of the claims 5 to 11, wherein the static obstacles are formed by discs. 14. A device according to any one of the preceding claims, wherein the tank is insulated. 15. A device according to any one of the claims 2 to 4, or to any one of claims 5 to 14 when appended to any one of claims 2 to 4, wherein the means for regulating the level of the liquid in the funnel includes an overflow pipe disposed inside the funnel in a position which is vertically adjustable. 16. A device according to any one of the preceding claims, further including a second anti-vortex means disposed inside the sheath and above the main propeller, said second anti-vortex means having at least two vertical plates each extended upwardly by a stiffening rib extending up to the upper end of said sheath. 17. A device according to any one of the preceding claims, further including a liquid accelerator inside the sheath. 18. A device according to claim 17 when appended to claim 16, wherein the liquid accelerator includes, on one hand, a secondary propeller disposed above the second anti-vortex means, connected to rotate with the shaft, and having a pitch oriented in the same direction as the pitch of the main propeller and, on the other hand, an anti-vortex means disposed above the secondary propeller and inside a cylindrical stack fixed to the reinforcing ribs, the secondary propeller, the anti-vortex means and the stack being situated between the two series of ports. 19. A device according to any one of the claims 1 to 16, further including means for aerating the surface of the liquid in the tank. 20. A device according to claim 19 when appended directly or indirectly to claim 16, wherein the means for aerating the surface of the liquid comprises, on one hand, a secondary propeller disposed above the second anti-vortex means, connected to rotate with the shaft and having a pitch inverted relative to the pitch of the main propeller and, on the other hand, an anti-vortex means disposed above the secondary propeller and inside a cylindrical stack fixed to the reinforcing ribs, the secondary propeller and the anti-vortex means being situated between the two series of ports and the stack extending substantially from the median part of the first series of ports to the upper edge of the second series of ports. 21. A device according to claim 20, wherein a cover is mounted on the shaft above the upper edge of the stack and defines with said upper edge an adjustable passage. 22. A device according to claim 16, or to any one of claims 17 to 21 when appended directly or indirectly to claim 16, further including a vortex pump for the suction of the surface of the liquid into the sheath, disposed above the second anti-vertex means and at the level of the at least one first opening. 23. A device according to claim 22, wherein the vortex pump includes, on one hand, a circular plate connected to rotate with the shaft and provided on its upper side with radial and vertical blades and, on the other hand, a stack fixed to the upper edge of the blades and extending from a position adjacent the upper end of the tank substantially from the median part of the first series of ports to said upper edge of the blades. 24. A device according to claim 23, wherein the stack is conical and tapers toward the upper part of the tank. 25. A device according to claim 23, wherein the stack is cylindrical. 26. A device according to claim 23, wherein the blades are planar or curved. 27. A device according to any claim 1 to 3 and 5 to 16 further including a single-passage propeller for the suction of the liquid into the sheath, disposed above the second anti-vortex means and at the level of the first series of ports. 28. A device according to claim 27, wherein the single-passage propeller includes, on one hand, a circular plate connected to rotate with the shaft and disposed above the level of the liquid in the tank and, on the other hand, in the liquid, a vertical plate forming a spiral and fixed to the lower face of said plate around the shaft, said plate defining a lateral inlet for the liquid, a vertical passage for the downward circulation of the liquid and a lower outlet for the liquid. 29. A device according to claim 28, wherein the inner edge of the vertical plate has a vertical deflector which is inclined in the direction toward the center of the spiral. 30. A device according to any claim 1 to 3 and 5 to 16 further including a double-passage propeller for the suction of the liquid into the sheath, disposed above the second anti-vortex means and at the level of the first series of ports. 31. A device according to claim 30, wherein the double-passage propeller has, on one hand, a circular plate connected to rotate with the shaft and > disposed above the level of the liquid in the tank and, on the other hand, in the liquid, two vertical plates fixed to the lower face of said plate and having the shape of two half-shells which are in opposed and offset relation to each other, said plates defining two lateral inlets for the liquid, two vertical passages for the downward circulation of the liquid and a lower outlet for the liquid. 32. A device according to claim 31, wherein the edge of each plate situated in facing relation to the passage defined by the other plate includes a vertical deflector. 33. A device according to claim 27 or claim 30, wherein a pumping propeller is fixed on the shaft below the single passage propeller or the double-passage propeller.