Reporter: Hsieh, Tsung-Lin

QuestionA 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 setupTypical resultsHypothesisPressure effect

WeightThermal conductivityCurvature

Other effectSummary

Experimental Setup

Weights

Camera

Ice

Typical ResultThe wire position is

obtained by MATLAB program.

Duration: 1 hr

Pressure EffectIce under the wire tends to melt.

Heat

Temperature

Pressure

GasSolid

LiquidAtmospheric pressure

Wire pressure

Ice

Schematic Phase Diagram

Temperature

Pressure

GasSolid

LiquidAtmospheric pressure

Wire pressure

Absorbing heat

Cutting

Ice+Water

Schematic Phase Diagram

Hot

Cold

Temperature

Pressure

GasSolid

LiquidAtmospheric pressure

Releasing heat

Ice

Schematic Phase Diagram

Hot

Cold

Pressure effectWeightThermal conductivityCurvature

Hot

Cold

Speed at CenterSpeed of the center of the wire after it sinks

into the ice.

distance

Weight

3kg: 0.114kg: 0.185kg: 0.266kg: 0.307kg: 0.398kg: 0.49

(cm/min)

Stainless steel wire 0.4mm

Weight vs. Speed at Center

Stainless steel wire 0.4mm

Temperature

Pressure

gs

l

Mathematical Estimation• Heat conducting rate:

• From Clausius-Clapeyron equation,

• Center speed upper limit

• Pressure effect plays an important role.

l

d

A0

0lnT

TTLP

)( AvLdt

dmLT

d

Ak

dt

dQ

min/10 1cmv

Hot

Cold

Material vs. Speed at Center

Thermal Conductivity

(W/m-K)Aluminum : 235 Steel : 16.3Good thermal

conductor cuts faster.

speed: 0.30 cm/min

speed: 0.34 cm/min

Water Flow Video

Pressure and Curvature

θ θ

θ θ

T T

rd

T

dr

T

A

F

*2

sin2

r

d

IceCross-section of the Wire

curvature1

r

Cutting SpeedAfter the whole wire sinks into the ice:

Pressure effect dominates

center

Left side

External heat input is more significant

External Heat EffectWater melts due to

external heat input It can solidify again

because the temperature inside the ice is below 00C (-150C~ -0.60C).

External heat

SummaryThe wire passes through the ice

Pressure effectExternal heat effect

The ice regelates (without being cut)Pressure releasesTemperature inside the ice is below 00C

Thank you for your attention.

Ambient TemperatureThe “speed at

center” is almost constant.

Repeatable in different temperature (230C~280C).

Ambient heat can be neglected.

Weight

6kg: 0.124kg: 0.063kg: 0.05

(cm/min)

Temperature inside the Ice

Time interval: 5 min

Time interval: 5 min

Curvature vs. SpeedAt the Beginning of Cutting:

Pressure effect dominates

centerLeft side

Patterns formed on regelated ice

Speed v.s. Curvature –at time 1In 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 2In 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