Polymers 2021 , 13 , 2485
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of the different components are (assuming bulk phase dominates the volume for both components when the moisture content is high).
M i ρ i
(A3)
V i =
For cellulose, we obtain the volume
( 1 − c l ) M f ρ c
(A4)
V c =
where M f is dry fibre mass and ρ c is cellulose density. The water mass in terms of moisture content mc and dry fibre mass M f becomes
mcM f 100 − mc
(A5)
M w =
leading to the water volume
mcM f ( 100 − mc ) ρ W
(A6)
V w =
where ρ w is water density. The total volume of the water-cellulose gel can be approximated as V T ≈ V c + V w = 1 − c l ρ c + mc ( 100 − mc ) ρ w M f = ( 1 − c l )( 100 − mc ) ρ w + mc ρ c ρ c ( 100 − mc ) ρ w M f (A7) Thus, we can write volume fractions as
V w V T ≈ V c V T ≈
mc ρ c ( 1 − c l )( 100 − mc ) ρ w + mc ρ c ( 1 − c l )( 100 − mc ) ρ w ( 1 − c l )( 100 − mc ) ρ w + mc ρ c
(A8)
φ w =
(A9)
φ c =
In Figure A1 we show the behaviour of vapour pressure for varied temperatures and solids contents. The used values of the parameters are presented in Table A1.
( a ) ( b ) FigureA1. ( a ) Vapour pressure as a function of temperature for three different levels of solids content, 90%, 70%, and 50%. ( b ) Vapour pressure as a function of solids content for three different temperature levels, 20 ◦ C, 190 ◦ C, and270 ◦ C.
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