Reporter: Hsieh, Tsung-Lin

Question A wire with weights attached to each end is placed across a block of ice. The wire may pass through the ice without cutting it. Investigate the phenomenon.

Outline Experimental setup Typical results Hypothesis Pressure effect Weight Thermal conductivity Curvature Other effect Summary

Experimental Setup Weights Camera Ice

Typical Result The wire position is obtained by MATLAB program. Duration: 1 hr

Pressure Effect Ice under the wire tends to melt. Heat

Temperature Pressure Gas Solid Liquid Atmospheric pressure Wire pressure Ice Schematic Phase Diagram

Temperature Pressure Gas Solid Liquid Atmospheric pressure Wire pressure Absorbing heat Cutting Ice+Water Schematic Phase Diagram Hot Cold

Temperature Pressure Gas Solid Liquid Atmospheric pressure Releasing heat Ice Schematic Phase Diagram Hot Cold

Pressure effect Weight Thermal conductivity Curvature Hot Cold

Speed at Center Speed of the center of the wire after it sinks into the ice. distance

Weight 3kg: kg: kg: kg: kg: kg: 0.49 (cm/min) ‏ Stainless steel wire 0.4mm

Weight vs. Speed at Center Stainless steel wire 0.4mm Temperature Pressure g s l

Mathematical Estimation Heat conducting rate: From Clausius-Clapeyron equation, Center speed upper limit Pressure effect plays an important role. l d A

Hot Cold

Material vs. Speed at Center Thermal Conductivity (W/m-K) ‏ Aluminum : 235 Steel : 16.3 Good thermal conductor cuts faster. speed: 0.30 cm/min speed: 0.34 cm/min

Water Flow Video

Wire Diameter 0.3mm: mm: mm: 0.06 (cm/min) ‏ Explanation...

Pressure and Curvature θθ θ θ T T r d Ice Cross-section of the Wire

Cutting Speed After the whole wire sinks into the ice: Pressure effect dominates center Left side External heat input is more significant

External Heat Effect Water melts due to external heat input It can solidify again because the temperature inside the ice is below 0 0 C (-15 0 C~ C). External heat Hot Cold

Summary The wire passes through the ice Pressure effect External heat effect The ice regelates (without being cut) Pressure releases Temperature inside the ice is below 0 0 C

Thank you for your attention.

Ambient Temperature The “speed at center” is almost constant. Repeatable in different temperature (23 0 C~28 0 C). Ambient heat can be neglected.

Weight 6kg: kg: kg: 0.05 (cm/min) ‏

Temperature inside the Ice

Time interval: 5 min

Time interval: 5 min

Curvature vs. Speed At the Beginning of Cutting: Pressure effect dominates center Left side

Patterns formed on regelated ice

Problems on the Hypothesis Water can be supercooled and it don’t have to follow the phase line. Of course not, but the final state is, as observed. The direction of pressure… The cross-section shape of the wire… The surface property (roughness) of the wire… It takes some time for it to travel along the phase line. In our case, it is a good assumption. Heat may flow to not only the ice below it. There may be water flow. My position error? Less than 5% What about put the ice in 0 0 C? Wire moving causes cutting, not only pressing. Does your wire has the same diameter after hanging weights? PICK UP the main physics

Speed v.s. Curvature –at time 1 In the middle of the ice, speed is positively related to the curvature. The speed is faster at both side because of external heat. Fig. Speed of the whole wire Fig. Acceleration

Speed v.s. Curvature –at time 2 In the middle of the ice, speed is positively related to the curvature. The speed is faster at both side because of external heat. Fig. Speed of the whole wire Fig. Acceleration