chisa2008skoc.doc

# Therefore also the temperature inside the mold must

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therefore also the temperature) inside the mold must be elevated and almost uniform. The incomplete filling of the venting holes explains also a poor repeatability of results. On the other hand the experiments carried out with a smaller amount of suspension, such, that the mold was not completely filled by the expanded material, exhibited also a significant initial pressure peak during expansion and a mild elevation of pressure during the subsequent phase of free water evaporation. This observation can be explained by the model of expanding foam. The temperature profile evolution concept is shown in the fig.1. The process is distinguished into four stages. First, third and fourth stage are without changes according to Žitný et al. (2006). Fig. 1 Temperature profile of the sample during process The first stage is characterized by a linear temperature rising up to 100°C, and no phase or mass changes of the heated sample. ) ( 0 T T A h dt dT c M w I . (1) Mass of sample M 0 , contact surface A as well as the heat transfer coefficient h I are assumed constant. At the second stage, when the temperature exceeds 100°C, the sample expands due to growing bubbles. In the end of the second stage, the sample fills whole mould. Description of this process requires to identify the number of bubbles (from porosity experiments), the initial bubble radius and rheological properties of the expanding sample. We assume that water is entrapped inside impermeable bubbles and that the whole heat transferred into the sample is consumed by evaporation of free water inside the bubbles. The expansion rate of sample (in fact the expansion rate of a bubble in a liquid matrix d R b /d t ) is determined by the flow properties of suspension, characterized by the flow index n and by the consistency K , see Fan et al. (1999). n b b p F R dt dR / 1 , (2) where the parameter F is a fluidity coefficient of the liquid matrix n n K n F / 1 1 ) 3 2 ( 4 . (3) As soon as the contact surface A as well as the sample mass (or the mass of evaporated water M v ) are no more constant, the enthalpy balance of the whole sample (total enthalpy H) ) )( ( ] ) 273 )( [( ] ) ( [ 0 T T t A h dt dM h T c c dt dT c M c M M c M dt dH w II v w v v v w v w s s (4) must be completed by additional equations, namely by the flow equation of bubble (2), together with the pressure-temperature equilibrium relationship and the state equation of ideal gas. In this way the time derivative d M v /d t can be eliminated, giving T T A h p p h T c c RT pF R N dt dT c M w II n a w v b b II II 1 3 ) ( ) 273 ( 4 , (5) where

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Type 5 RT p R N T RT h h T c c c M c M M c M c M b b w v v v w v wo s s II II 3 2 3 4 ) 1 ( ) 273 )( ( ) ( (6) This Eq.(5) can be considered as an equation for temperature, because the pressure p can expressed in terms of temperature using Clausius Clapeyron equation ) exp( RT h B p , (7) and the contact surface A

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