THERMAL PRESSURE FORMING OF STARCH BASED
PACKAGING MATERIALS
Zitný R.1, Šesták J.1, Tsiapouris A.2, Linke L.2
1
CTU , Faculty of mechanical engineering, Technická 4, 166 07 Prague 6
2
Dresden University of Technology, Faculty of mechanical engineering, Institute of
Food Engineering and Bio-Engineering, D-01062 Dresden
E-mail: zitny@fsid.cvut.cz
Phone: (+42 02) 2435 2547 Fax: (+42 02) 2431 0292
E-mail: sestak@fsid.cvut.cz Phone: (+42 02) 2435 2547 Fax: (+42 02) 2431 0292
E-mail: Tsiapouris@mvll00.mw.tu-dresden.de Phone: (+49 0351) 463 6158 Fax: (+49
0351) 463 7126
E-mail: Linke@mvll00.mw.tu-dresden.de Phone: (+49 0351) 463 4985 Fax: (+49
0351) 463 7126
Scientific topic:
II.4.
Abstract:
Thermal pressure forming of starch based water suspension was
investigated experimentally and theoretically. Processed material
(thin plates) was baked in a metallic mould having a constant
temperature of walls. Time courses of temperature and pressure
inside the samples were recorded and compared with the suggested
crust and core model.
Keywords:
starch, packages, waffle-baking, crust-core model, biodegradation
INTRODUCTION
Thermal pressure forming of the starch based biologically degradable products
(e.g. trays, plates, packages, etc.) is similar to the contact baking of waffles in a toaster:
Raw material - water suspension of starch and additives (e.g. cellulose fibres) - is placed
into a closed planar mould and heated by contact with walls having a constant
temperature (180-1900C). The phenomena taking place inside the heated layer are rather
complicated, and the following three phases can be distinguished:
 Heating of liquid suspension up to the boiling point.
 Evaporation of free water accompanied by significant increase of pressure inside the
mould. Expansion of material (initial volume of suspension is increased 2-3 times).
Crust formation.
 Remaining bound water removal. Pressure decreases, temperature increases.
Process control, process design and optimisation require assessment of the
influence of product dimensions (thickness of material) and wall temperature on the
process time and the quality of product.
EXPERIMENTS
1 Experimental set-up
An experimental heater set-up is
T[ C]
p[bar]
shown in Fig.1. The cavity in the mould is a
rectangular box 270 x 200 x 2, 4 and 8 mm,
having venting channels around its
t[s]
t[s]
periphery. Both the lower and the upper
pC - crust
metallic plates are heated electrically and
their temperature is monitored by thermopG - gap
couples. The temperature of plates is
maintained at approximately 180-1900C. The
crust
second pair of thermocouples is located
inside the cavity, the first thermocouple in 4 mm
the centre (approximately 130 mm from the
shorter side) and the second in the vicinity of
the shorter side. This second thermocouple
130 mm
enables to estimate the time, when the front
Temperature at interface is Liquid core flows
of the expanding sample arrives to the side
controlled by pC+pG
driven by pressure
wall of mould. Pressure of steam is detected
D=150270 mm
by a pressure transducer, which is flash
mounted at the centre of the upper plate.
Fig.1 Baking in a mould - geometry
2 Measurement procedure - results
Tested samples, water suspensions of potato starch and additives, were inserted
into the centre of the mould (mass of samples varied from 80 to 120 g, usually 114 g, for
4 mm thickness). After closing the mould the sample forms a circular disk of diameter
approximately 160 mm. It was found experimentally that this amount of suspension is
sufficient to fill the whole cavity at the end of baking. Corresponding volumetric
expansion is approximately 2.7 times.
0
Initial composition of samples varied, but the concentration of solid phase was
always the same, 40% (i.e. 60% water w/w). Though a lot more additives were tested
(e.g. xanthan, carboxy-methyl-cellulose, methylstearat, different cellulose fibres, waxes
etc.) only the results for pure potato starch suspension (denoted KS) and a mixture of
30% potato starch and 10% cellulose fibres (denoted PS) are presented in Figs.2a, 2b,
2c, 2d. Time courses of temperatures (at the side of mould and in the centre) and
pressures were evaluated as time averages from several repeated measurements.
Centre
PS-2
Paper Fibres: 10% - Thickness: 2 mm
Pressure
Centre
Pressure
3,0
20
2,0
20
2,0
0
1,0
0
2:30
2:24
2:18
2:12
2:06
2:00
1:54
1:48
1:42
1:36
1:30
1:24
1:18
Fig.2b Starch 30%, paper 10%, thickness 2 mm
Starch 40%, thickness 2 mm
KS-4
Potato Starch: 40% - Thickness: 4 mm
1:12
Time [min:s]
Vicinity
Centre
Paper Fibres: 10% - Thickness: 4 mm
Pressure
PS-4
Vicinity
Centre
Pressure
Fig.2c
5:00
4:48
4:36
4:24
4:12
4:00
3:48
3:36
3:24
3:12
3:00
2:48
2:36
2:24
2:12
2:00
1:48
1:36
0:00
5:00
Time [min:s]
1:24
1,0
1:12
0
1:00
1,0
0:48
2,0
0
0:36
20
0:24
2,0
0:12
3,0
20
Temperature [°C]
40
Pressure [bar]
3,0
4:48
4,0
40
4:36
60
4:24
4,0
4:12
5,0
60
4:00
80
3:48
5,0
3:36
6,0
80
3:24
100
3:12
6,0
3:00
7,0
100
2:48
120
2:36
7,0
2:24
8,0
120
2:12
140
2:00
8,0
1:48
9,0
140
1:36
160
1:24
9,0
1:12
10,0
160
1:00
180
0:48
10,0
0:36
11,0
180
0:24
200
0:12
11,0
0:00
200
Pressure [bar]
Fig.2a
1:06
1:00
0:54
0:48
0:42
0:36
0:30
0:24
0:18
0:12
0:06
1,0
0:00
2:30
Pressure [bar]
Temperature [°C]
40
2:24
3,0
2:18
4,0
40
2:12
60
2:06
4,0
2:00
5,0
60
1:54
80
1:48
5,0
1:42
6,0
80
1:36
100
1:30
6,0
1:24
7,0
100
1:18
120
1:12
7,0
1:06
8,0
120
1:00
140
0:54
8,0
0:48
9,0
140
0:42
160
0:36
9,0
0:30
10,0
160
0:24
180
0:18
10,0
0:12
11,0
180
0:06
200
Time [min:s]
Temperature [°C]
Vicinity
11,0
0:00
Temperature [°C]
Vicinity
Pressure [bar]
KS-2
Potato Starch: 40% - Thickness: 2 mm
200
Time [min:s]
Starch 40%, thickness 4 mm
Fig.2d Starch 30%, paper 10%, thickness 4 mm
Different behaviour exhibit relatively thick samples (8 mm) of pure potato starch (Fig.3).
Centre
Pressure
Time [min:s]
Fig.3
Starch 40%, thickness 8 mm
11:42
11:15
10:48
10:21
9:54
9:27
9:00
8:33
8:06
7:39
7:12
6:45
6:18
5:51
5:24
4:57
1,0
4:30
2,0
0
4:03
3,0
20
3:36
4,0
40
3:09
5,0
60
2:42
6,0
80
2:15
7,0
100
1:48
8,0
120
1:21
9,0
140
0:54
10,0
160
0:27
11,0
180
0:00
Temperature [°C]
Vicinity
Pressure [bar]
KS-8
Potato Starch: 40% - Thickness: 8 mm
200
Some characteristic values are summarised in Tab.1 - process time, maximum pressure,
temperature of suspension corresponding to the second phase of free water evaporation
and also the mean velocity u of the edge during expansion of circular samples. This
velocity u was estimated from the time delay of the side-wall thermocouple response.
Tab.1 Experiments KS (native potato starch 40%), PS (starch 30%, paper fibres 10%),
BEM (starch 27%, cellulose fibres type Arbocel BEM 10%, pre-gelatinised starch 3%)
Material - Process time Boiling begins pmax
p“
T
u
Thickness
at time
[mm]
[s]
[s]
[bar] [bar]
[0C]
[mm/s]
KS - 2
140
6
7.7
5.4
155
5.500
KS - 4
350
20
6.7
4.8
150
0.724
KS - 8
800
40
5.5
3.6
140
0.367
PS - 2
140
6
6.8
4.8
150
5.500
PS - 4
400
8
6.3
7.9
120-170 1.375
PS - 8
1000
1.8
1.4
110
0.519
BEM - 2
140
8
6.8
5.4
155
5.500
BEM - 4
300
10
3.9
3.6
140
1.964
BEM - 8
1000
1.8
1.3
107
1.727
The fifths column, p“, is calculated as the tension of saturated water vapour at
temperature T in the sixth column of the table.
It is rather difficult to measure temperatures inside the flowing core of sample
(precise adjustment of thermocouples position) and even the interpretation of the
pressure transducer reading has been subject of discussion. However, some conclusions
seem to be solid:
 The temperature varies between 140 0C and 160 0C and is usually almost constant in
the second phase of free water evaporation.
 The most surprising is the observation, that the temperature of a heated sample
sometimes decreases even if the temperature of wall is substantially higher and
almost constant. Besides the local maximum of temperature one or even two peaks
of pressure were recorded.
 There exists some relationship between wall pressure and temperature of the flowing
core during the second phase of baking, and the temperature time courses are
controlled by the pressure drop of water steam.
 The expansion of heated materials is never accomplished during the first phase of
heating and it seems to be probable that the expansion - flow of liquid core - is
caused by bubbles formed in the suspension in the second phase of baking (boiling).
MATHEMATICAL MODELLING
1 Review of mathematical models
Mathematical models describing heat and mass transfer during frying or roasting
of meat, and baking biscuit were presented by Farkas [1], Õzilgen [2], Singh [3],[4] or
Zanoni [5]. There are some common features in these models, usually the assumption of
two regions - dried crust and moisten core - with a moving interface between them.
However, all the mentioned solutions are able to predict only monotone rising
temperature profiles. The reason is that the overall pressure was assumed to be
atmospheric, and no significant volumetric expansion of samples was expected.
2 Crust and core integral model
Suggested crust and core model tries to explain some non-usual phenomena
assuming that the boiling temperature of free water -and thus the temperature of
suspension- is controlled by the pressure of the evaporated steam. The simplest model is
integral, supposing spatially uniform temperature and moisture. This assumption seems
to exclude the effects caused by the moving evaporation front between the crust and
core, but this phenomenon can be included into the flow resistance and heat transfer
resistance. This approach is probably the most significant contribution to the modelling
of the baking process, as it removes severe numerical problems (instabilities) related to
a strong non-linear coupling between the temperature and the pressure fields. The
integral model accounts for the influence of finite heat capacity of the heating plates and
related changes of the wall temperature, see Fig.4.
Control volume: cylinder D0, height H
hG(t)
H
Tw(t)
h(t) crust
core T(t)
Mb(t)
p(t)
Mw(t)
 (t )
M
v
 c (t )
M
D0
D(t)
Fig.4
Dmax
Cylindrical sample
Three phases of thermal processing are analysed separately:
The first phase is heating of a more or less homogenous layer of water suspension up
to the onset of boiling.
 The second phase is characterised by evaporation of free water and by formation of a
growing solid crust. At the same time the liquid core expands, driven by pressure of
steam, which leaves the crust-core interface and flows through the porous crust and
along the walls of the mould. The friction loses in the crust and in the interstitial
spaces at the wall determine pressure at the crust-core interface, and are manifested
as the first peak of recorded pressure. The expansion rate of material is determined
by the thickness of the liquid core, by viscosity of suspension and by the pressure at
the crust-core interface.
 When the crust is fully developed and the expansion stops, the last phase of heating,
accompanied by the evaporation of the remaining bound water, begins. The sample
temperature no longer depends on the boiling temperature and steadily approaches
the temperature of wall.
2.a Basic assumptions and equations
Integral heat and mass balances were formulated for a constant control volume,
confined by the symmetry plane and the surface of cylindrical sample, see Fig.4. The
model assumes that:


There is a thin gap of the width hG between the surface of cylindrical sample and the
wall of mould. This gap filled by steam represents thermal and hydraulic flow
resistance.
 Crust contains only solid, bound water and steam. Thermal conductivity of this
porous layer depends on porosity c. Thickness of crust, h, can be calculated from
material balance if the mass flow-rates of suspension, and the escaping steam are
known. It is assumed that at the surface a very thin layer of melted starch is
gradually built; this layer has negligible effect on heat transfer resistance, but
influences pressure drop across the crust.
 Liquid core has a uniform temperature which is the same as the crust-core interface
temperature. Suspension is a Newtonian liquid, which flows in the radial direction
driven by internal pressure in bubbles. This pressure equals saturated vapour
pressure at a temperature of core. Relative composition of solid, bound and free
water content is independent of time, but the porosity of core c is changing.
The most important and sufficiently general equation for the temperature time
course T(t) follows from the enthalpy balance of the control volume shown in Fig.4,
dH
 v (rw  cw Tw )  ( M
 ss cs  M
 bs cb  M
 ws cw )T ,
  e S (Tw  T )  M
(1)
dt
where H is the total enthalpy of material inside the control volume, T and Tw are
temperatures of core and wall of mould respectively, Se represents effective thermal
conductivity of steam in the gap hG and porous layer of crust h and thermal conductivity
c (1/e=1/+h/c). The heat transfer coefficient =v/hG is fully determined by the
thermal conductivity of steam v and by the thickness of gap hG. M v is the mass flow is the mass
rate of vapour (evaporated bound and free water taken together), and M
xs
flow-rate of component x (water, solid) in the suspension flowing out of the control
volume during expansion. cs, cw are specific thermal capacities of solid and water, rw is
the latent heat. Eq. (1) can be rearranged into equation
C A 
dT



[Cs  (1  A)Cc ]
 [ e S  s ( M
v  M bc )  M v (1  A) c w ]( Tw  T )  M v rw (2)
dt
M ws
 is the mass flow-rate of evaporated bound water from the crust, Cs and Cc
where M
bc
heat capacity of suspension and core, respectively.
To solve Eq.(2) the mass flow-rates of steam must be expressed in terms of
temperatures T and Tw . The flow-rates are first related to the pressure drop across the
porous crust pC=p-pG and along the surface in the gap pG=pG-pA , where p, pG, pA are
pressures at the crust-core interface, at the surface and at the edge of sample,
respectively (pA is in fact atmospheric pressure, because the calculated pressure drop in
the venting channels of mould are negligible). Pressure drop pC is calculated from the
Ergun’s equation for the flow resistance of a porous bed with porosity c, see Perry [6],

150
1 
M
v
  f M
 .
p  pG  (
 175
. ) 3c
M
(3)
c
v
Re
c Dp v S 2 v
pG was estimated from the simplified solution of radial laminar flow between parallel
 /S
discs with a constant transversal mass flux M
v

3 M
v.
pG  p A  v 3 v  f G M
hG
(4)
Additional pressure drops (venting channels, compact layer built at the crust surface,
etc.) can be included into friction coefficient fG, too. The pressure p in Eq.(3) can be
substituted by equilibrium temperature from the following approximation (5),
(5)
T  100m p ,
0
where T is to be expressed in C and pressure p in bars (exponent m=4 for water).
The only unknown quantity in Eq.(2)
remains mass flow-rate of bound water. wall gap
crust h
core
It is assumed that the intensity of
evaporation is directly proportional to
Temperature of bound
the amount of bound water in the crust
water increases and
vapour tension p" too
and to the difference between the
partial pressure of bounded water
p"
p=p"
vapour at a porous surface inside the
p
p"-p
crust layer (this pressure is determined
p
Free water
by temperature) and the pressure of
Pressure decreases in
flowing steam in the same place of
the direction of flow
pG
crust (this pressure is determined by
mb
friction losses), see Fig.5. The mean
pA
value of this pressure difference is
y
estimated assuming linear temperature
Bound water
profile in the crust and cubic profile of
mb(p"-p)
pressure (this profile is determined
uniquely knowing values of pressure
Fig.5 Pressure and moisture profiles in crust
and pressure gradients for y=0 and
y=h).


  M   p" p ,
M
bc
bc
(6)
where  is a rate coefficient and exponent =1 was considered in simulations.
Combining Eqs.(3-6) we could solve Eq.(2) for temperature T(t). However, the
thickness of crust h, must be calculated too, because it determines overall heat capacity
of the control volume and first of all the heat flux from the wall (this quantity is
included into effective conductivity e). The time change of the thickness h is described
by differential equation, following from the mass balance of the expanding core
 M
 bc
dh M
V V
(7)
 v
(1  ss bs )
dt
S (1  s )
Vws
and s is the porosity of core, related to the volumetric flowrate of suspension
16 ( H  h) 2

(8)
Vs 
( p  pA ) .
3S (1  s )
2.b Implementation and simulation
The model described above is a part of family of more than ten similar integral
models, differing slightly by assumptions concerning expansion of material, bound
water evaporation, core and gap resistance calculation. All these models were
implemented on PC and intensively tested. These models are able to describe either
temperature and pressure time courses exhibiting local maximum, see Fig. 6.
Potato Starch: 40% - Thickness: 4 mm
experimental
predicted
200
180
Temperature [°C]
160
140
120
100
80
60
40
20
0
0
60
120
Time [s]
180
240
300
Fig.6 Temperature courses: experiment and
numerical prediction of crust-core integral model
CONCLUSIONS
Baking process of starch-based materials depends significantly on the amount of
bounded water and pressure of evaporated steam. Suggested integral model enables to
describe temperature and pressure time courses having local minimum. It also enables to
predict the baking time and its dependence on the thickness and other geometrical
parameters of product. It allows for a more complete description of the process to be
developed and an increased understanding of the parameters which affect product
quality.
List of most important symbols
C
heat capacity
h
hG
thickness of crust
thickness of gap at wall
H
M
p
rw
S
t
T
V
half thickness of sample
mass
pressure
latent heat of evaporation
contact surface
time
temperature
volume
[J.K-1] 
[W.m-2.K1
]
[m]
[-]
 porosity
[m]
thermal
conductivity
[W.m-1.K
1
]
[m]
[Pa.s]
 viscosity of suspension
[kg]
 rate coefficient of evaporation [-]
[bar]
Indices
[J.kg-1] b bound water
[m2]
bc bound water in crust
[s]
c crust
0
[ C]
s solid or suspension
3
[m ]
v vapour
w free water
ws water suspension
heat transfer coefficient
References
[1] Farkas B.E.: Heat and Mass Transfer in Frying. Journal of Food Engineering, 29
(1996)
[2] Özilgen M., Heil J.R.:Mathematical Modeling of Transient Heat and Mass Transport
in a baking Biscuit. J. Food Processing and Preservation, 18, pp.133-148, (1994)
[3] Singh N., Akins R.G., Erickson L.E.: Modeling Heat and Mass Transfer during the
Oven Roasting of Meat. Journal of Food Process Engineering, 7, pp. 205-220, (1984)
[4] Singh R.P.: Heat and Mass Transfer in Foods during Deep-Fat Frying. Food
Technology, pp. 134-137, (1995)
[5] Zanoni B., Pierucci S., Peri C.: Study of the Bread Baking Process - II. Mathematical
Modelling. Journal of Food Engineering, 23, pp. 321-336, (1994)
[6] Perry R.H., Green D.W.: Chemical Engineers’ Handbook. McGraw-Hill, 1997
Acknowledgement: The project is supported by fund J04/98: 212200008