Water bridge 岑剡

Water bridge FIG. 1. (Color online) Floating water bridge from front and top views. Distance between the beaker tips: 14 mm.

Liquid bridges Fig. 2 Water bridges forming in different polar liquids under atmospheric conditions and DC voltage. aetrahydrofuran 16 kV,b dichloromethane 19 kV, c 2-propanol 8 kV, d acetone 10 kV, e 1-propanol 10 kV, f ethanol 9.5 kV, g methanol 9.5 kV, h dimethylformamide12.5 kV, i glycerol 11.5 kV, j dimethylsulfoxide 12 kV, k water 12 kV

Formation of a water bridge Figure 3. Formation of a water bridge between two Teflon beakers. (a) No current applied,(b) rise of the water surface mainly in the anodic beaker at approximately 15 kV dc, (c)spark, (d) water jet ejection leading to (e) a stable connection between the beakers (leftcathode, right anode beaker) （Fuchs, E.C.; Gatterer, K.; Holler, G.; Woisetschläger, J. Dynamics of the floating water bridge. J. Phys.-D-Appl. Phys. 2008, 41, 185502-185507） Fig. 4 Bridge formation between two Teflon beakers. The shape of the water surface is contoured by the distortions of the otherwise parallel line reflections. In (b) the high voltage was applied to the electrodes, in (e) a watery connection formed, in (f) the bridge was stabilized （Woisetschläger, J.; Gatterer, K.; Fuchs, E.C. Experiments in a floating water bridge. Exp. Fluids 2010, 48-1, 121-131.）

Experimental setup FIG. 5. Schematic of the experimental setup. Reza Montazeri Namin , Phys. Rev. E 88, 033019 (2013)

Thermographic image Fig. 8 Thermographic image of a water bridge (12 kV DC, 9 mm beaker to beaker distance) J. Woisetschlager, A. Wexler, G. Holler, M. Eisenhut, K. Gatterer, and E. Fuchs, Exp. Fluids 52, 193 (2012).

The length of water bridge Fig. 9 DC voltage applied to the electrodes in the beaker vs. the spout to spout distance (length of the bridge) for a water bridge. Current was constant at 0.5 mA J. Woisetschlager, A. Wexler, G. Holler, M. Eisenhut, K. Gatterer, and E. Fuchs, Exp. Fluids 52, 193 (2012).

Oscillations of a water bridge Fig. 10 Oscillations of a water bridge with a small amount of soap added. a 13 kV, b–d 17 kV applied to the electrodes. a shows a amphora type oscillation (1/10 s interval), b fundamental string oscillation (1/15 s interval),c first harmonic (1/30 s interval) and d bridge break-up (1/75 s interval). All images are multiple exposures J. Woisetschlager, A. Wexler, G. Holler, M. Eisenhut, K. Gatterer, and E. Fuchs, Exp. Fluids 52, 193 (2012).

The water bridge between two crossed linear polarizer plates Figure 11. The water bridge between two crossed linear polarizer plates (a,b). P indicates the direction of the polarizer, A the direction of the analyzer. (c) Focused laser beam shining through the length of the bridge. J. Woisetschlager, K. Gatterer, and E. C. Fuchs, Exp. Fluids 48, 121 (2010).

The development of theory of water and charged liquid bridges Armstrong firstly found the phenomenon [1] Fuchs et al. [2] reported their investigation in 2007. In 2009 Widom et al. [3] suggested the existence of a tension along the bridge caused by the electric field based on the Maxwell pressure tensor In 2010 Mar´ın and Lohse [4] apply a similar theory, while the tension is calculated as half the value derived by [3], In 2012 Morawetz [5,6]discusses the effect of electrical charges in a charged catenary and solves the flow and derives the stability criteria. Aerov [7] in 2011 performed calculations and stated that “It is proven that electrostatic field is not the origin of the tension holding the bridge”and the only force holding the bridge against gravity is surface tension. Reza Montazeri Namin[8] Experimental investigation of the stability of the floating water bridge [1] W. Armstrong, Electr. Eng. 10, 153 (1893). [2] E. Fuchs, J. Woisetschl¨ager, K. Gatterer, E. Maier, R. Pecnik, G. Holler, and H. Eisenk¨olbl, J. Phys. D: Appl. Phys. 40, 6112 (2007). [3] A. Widom, J. Swain, J. Silverberg, S. Sivasubramanian, and Y. N. Srivastava, Phys. Rev. E 80, 016301 (2009). [4] A´ . G. Mar´ın and D. Lohse, Phys. Fluids 22, 122104 (2010). [5] K. Morawetz, Phys. Rev. E 86, 026302 (2012). [6] K. Morawetz, AIP Adv. 2, 022146 (2012). [7] A. A. Aerov, Phys. Rev. E 84, 036314 (2011). [8] Reza Montazeri Namin , Phys. Rev. E 88, 033019 (2013)

Theory of water and charged liquid bridges Theoretical questions have to be answered: (i) How is the electric field influencing the height zmax in which water can creep up? (ii) What is the radius R(x) along the bridge? (iii) What is the form z = f (x) of the water bridge? K. Morawetz, Phys. Rev. E 86, 026302 (2012).

Creeping height and Radius of bridge Creeping height z: E is in units of 104 V/cm. Radius R(x) along the bridge : K. Morawetz, Phys. Rev. E 86, 026302 (2012).

Profile of bridge K. Morawetz, Phys. Rev. E 86, 026302 (2012).

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