^{1,a)}and Charalambos Aristidou

^{1}

### Abstract

What happens after lighting a paraffin candle that is barely floating in water and kept upright with the aid of an appropriately weighted nail attached to its bottom? Presumably, it should sink because the buoyant force will decrease more than the weight. Surprisingly, the candle will continue to burn, rising slowly above the surface of the water. The reason for this is that the flame forms a well around the wick filled with molten paraffin, while the water keeps the outer walls of the candle cool and unscathed. Thus, the buoyancy hardly changes while the weight is reduced through burning, resulting in a floating candle that will rise above water. We present a quantitative model that describes the formation of the well and verify it experimentally, examining first the case of a candle in the air and then the case of a candle immersed in water.

I. INTRODUCTION

II. THEORETICAL MODEL

A. Radial energy flux and well radius

B. Vertical energy flux and well depth

III. COMPARISON WITH EXPERIMENTS

A. A candle in air

B. A candle wholly immersed in water

IV. A CANDLE PARTLY IMMERSED IN WATER

V. CONCLUSION

## Figures

The well formed around the flame of the candle, as depicted in Ref. 3.

The well formed around the flame of the candle, as depicted in Ref. 3.

Schematic diagram of the well carved around the wick by the flame.

Schematic diagram of the well carved around the wick by the flame.

The radius of the well formed around the wick of a candle surrounded by air as a function of time. The dots are the experimental points while the curve is the prediction of Eq. (8) using and *d* = 0.29 cm.

The radius of the well formed around the wick of a candle surrounded by air as a function of time. The dots are the experimental points while the curve is the prediction of Eq. (8) using and *d* = 0.29 cm.

The depth of the molten paraffin layer as a function of time for a candle surrounded by air. The dots are the experimental points while the curve is the prediction of Eq. (19) using , *d* = 0.29 cm, and .

The depth of the molten paraffin layer as a function of time for a candle surrounded by air. The dots are the experimental points while the curve is the prediction of Eq. (19) using , *d* = 0.29 cm, and .

The depth of the well as a function of time for a candle surrounded by air. The dots are the experimental points, while the curve is the prediction of Eq. (11) using , *d* = 0.29 cm, and .

The depth of the well as a function of time for a candle surrounded by air. The dots are the experimental points, while the curve is the prediction of Eq. (11) using , *d* = 0.29 cm, and .

The distance from the surface of the pond to the top of the candle as a function of time for a candle surrounded by air. The dots are the experimental points while the curve is the prediction of Eq. (1) using , *d*= 0.29 cm, and .

The distance from the surface of the pond to the top of the candle as a function of time for a candle surrounded by air. The dots are the experimental points while the curve is the prediction of Eq. (1) using , *d*= 0.29 cm, and .

The radius of the well formed around the wick of a candle immersed in water as a function of time. The dots are the experimental points while the curve is the prediction of Eq. (8) using and *d* = 0.597 cm.

The radius of the well formed around the wick of a candle immersed in water as a function of time. The dots are the experimental points while the curve is the prediction of Eq. (8) using and *d* = 0.597 cm.

The thickness of the molten paraffin layer as a function of time for a candle surrounded by water. The dots are the experimental points while the curve is the prediction of Eq. (19) using , *d* = 0.597 cm, and .

The thickness of the molten paraffin layer as a function of time for a candle surrounded by water. The dots are the experimental points while the curve is the prediction of Eq. (19) using , *d* = 0.597 cm, and .

The depth of the well as a function of time for a candle surrounded by water. The dots are the experimental points while the curve is the prediction of Eq. (11) using , *d* = 0.597 cm, and .

The depth of the well as a function of time for a candle surrounded by water. The dots are the experimental points while the curve is the prediction of Eq. (11) using , *d* = 0.597 cm, and .

The distance from the surface of the pond to the top of the candle as a function of time for a candle surrounded by water. The dots are the experimental points while the curve is the prediction of Eq. (1) using , *d* = 0.597 cm, and .

The distance from the surface of the pond to the top of the candle as a function of time for a candle surrounded by water. The dots are the experimental points while the curve is the prediction of Eq. (1) using , *d* = 0.597 cm, and .

Once a portion of the candle rises above water, the flame carves out a wider cylinder of radius above the water level, while it carves out a cylinder of radius below the water level. The top of the candle is at a height *x* above water while the depth of the well is *y*.

Once a portion of the candle rises above water, the flame carves out a wider cylinder of radius above the water level, while it carves out a cylinder of radius below the water level. The top of the candle is at a height *x* above water while the depth of the well is *y*.

The portion of the candle above the water level as a function of time. The dots are the experimental points while the curve is the piecewise continuous function of Eq. (29) using , , and .

The portion of the candle above the water level as a function of time. The dots are the experimental points while the curve is the piecewise continuous function of Eq. (29) using , , and .

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