Shapes and shaping of biopolymer drops in a hyperbolic flow

Shapes and shaping of biopolymer drops in a hyperbolic flow

Lars Hamberga, Mathias Wohlwendb, Pernilla Walkenstroma, Anne-Marie Hermanssona,*

aSIK, The Swedish Institute for Food and Biotechnology, P.O. Box 5401, SE-402 29 Goteborg, SwedenbETH, Laboratory of Food Engineering, Swiss Federal Institute of Technology, 8092 Zurich, Switzerland

Received 11 July 2002; revised 4 October 2002; accepted 18 December 2002

Abstract

The shaping of drops in a model system based on k-carrageenan-emulsion drops in the millimetre range in silicon oil has been studied. The

drops were shaped by exposing them to drag forces in a hyperbolic flow, while their shape was fixed simultaneously by introducing gel

formation of the biopolymer in the drop.

The shape and the shaping process were studied and evaluated with image analysis of macrograph sequences of the shaping. The effect of

process conditions, flow speed and cooling temperature on the final shape and shape progress was investigated as well as the effect of

different k-carrageenan drop characteristics, such as drop viscosity and gel strength. Drop viscosity was altered by addition of locust bean

gum, LBG, and the gel strength was altered by addition of ions. The k-carrageenan solutions in the drop were characterised by rheological

investigations.

With the same type of flow, different shapes could be achieved with small process changes and with high reproducibility. The fixation of

the characteristic drop features, perimeter, area, Feret’s X and Y ; does not occur at the same time and position. For the different process

parameters investigated, a change in speed affected the process in a similar way to a change in the viscosity ratio. This applies if the viscosity

ratio is changed at a constant temperature, but if the change in the viscosity ratio is temperature-induced, the effect is different. The final

shape of the produced drops could be graded into three classes, correlated to the position in the flow field where the drops were fixed. A shape

map of the different drop shapes obtained was presented.

q 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Shape; Shaping; Elongation; Deformation; Drop; k-carrageenan

1. Introduction

Emulsion droplet deformation during flow processing

could lead to emulsion-based products with new properties

if the shape of the deformed drop is conserved. Small

deformation of drops induced by flow has been studied for a

long time (Rallison, 1984; Stone, 1994; Walther, 2001).

However, large deformation of a drop into a specific drop

shape is an area where, until recently, only a limited number

of studies have been reported (Hamberg, Walkenstrom, &

Hermansson, 2002; Walther, Walkenstrom, Hermansson,

Fischer, & Windhab, 2002; Wolf, Scirocco, Frith, & Norton,

2000). To increase the functionality of a fluid drop, it is not

enough to simply deform and shape it. It is also necessary to

fix and make the drop resistant to further changes when a

desirable shape has been accomplished. One way to achieve

fixation is by gel formation of the biopolymers in the drop.

The fixation and deformation process often interact, affect

one another and could therefore be treated as one process,

shaping (Hamberg et al., 2002).

When drops or particles are shaped, their contribution to

the functionality of the suspension is believed to be different

from the contribution for a spherical drop or particle. Little

is investigated for biopolymers (Stokes, Wolf, & Frith,

2001; Wolf, Frith, Singeleton, Tassieri, & Norton, 2001),

but in the nearby fibre-suspension area, interesting parallels

could be found. The shape effect of a hard symmetric fibre

suspension on rheology is known from previous studies and

reviewed both for theory (Petrie, 1999) and for practice

(Djalili-Moghaddam, 2001). On addition of fibres and

spheres of the same number and individual volume, the

viscosity increases more markedly with addition of fibre.

Even small alterations in the shape of the fibres make a

difference. When the shape of a fibre is a changed from the

normal symmetry to become somewhat curved, even a small

0268-005X/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S0268-005X(03)00009-2

Food Hydrocolloids 17 (2003) 641–652

www.elsevier.com/locate/foodhyd

* Corresponding author. Tel.: þ46-31-33-55-600; fax: þ46-31-83-

37-82.

E-mail address: [email protected] (A.-M. Hermansson).

http://www.elsevier.com/locate/foodhyd

curvature ,5% can increase the solution viscosity by an

order of 10 to 15% compared with a solution with straight

fibres (Joung, Phan-Thien, & Fan, 2002). The curvature

does not have to be fixed; flexible fibres have been

theoretically treated, and it was found that a sufficient

viscosity increase could be expected (Joung, Phan-Thien, &

Fan, 2001). If parallels could be found and explored in the

case of biopolymer drops, shaping would be an area of great

interest.

The drop-shaping method used in this work has recently

been presented by Walther et al. (2002). In their work,

shaping was done with millimetre-sized gelatine drops in

hyperbolic flow, and both elongated drops and drops of

complex form were formed. They found that the region

where the drop was fixed was directly related to the created

shape. The impact of the process conditions on the final

shape of the drop was clear and it was possible to control

process with high reproducibility. Hamberg et al. (2002)

also used the same type of hyperbolic flow to shape small

ellipsoidal drops. They investigated the impact of different

gel formation kinetics by comparing sub-millimetre drops

of gelatine and k-carrageenan under the same conditions.

Wolf et al. (2000) have presented a method using pure shear

flow instead of hyperbolic flow. It resulted in stretched and

ellipsoid drops with large differences in the length to width

ratio.

Although shear flow has long been used to deform drops,

the focus has shifted more and more to other flow types,

such as hyperbolic flow. Hyperbolic flow can easily be

generated in the centre of a four-roll mill 4-RM (Taylor,

1934). By following the centre flow-line from the centre and

out between one pair of rollers, one obtains first an

elongation flow, then a contraction flow. Elongation flow

has the advantage of being more effective in terms of

creating interfacial area than shear flow (Erwin, 1991).

However, elongation flow is limited in residence-time and

space for practical reasons. Therefore, processes with

elongation flow are limited to a time scale of seconds.

This places high demands on analysing tools as well as on

the time scale of properties of the flow, the drop and the

biopolymer.

In this work, the shaping of drops in a model system

based on k-carrageenan-emulsion drops in the millimetre

range in silicon oil has been studied. k-carrageenan is cold-

set biopolymer, i.e. a water/k-carrageenan system in the

drop is in solution at temperatures over Tgel; and fixes when

forming a gel at temperatures below Tgel: The viscosity of

the biopolymer solution above Tgel is strongly temperature-

dependent and rises drastically just before Tgel: The gel

formation properties of carrageenan are strongly dependent

on the type of carrageenan and the counter-ions present in

the solution, (Hermansson, Eriksson, & Jordansson, 1991;

Rochas, & Rinaudo, 1980, 1984; Rochas, Rinaudo, &

Landry, 1989). The ion-dependence makes it possible to

choose a suitable Tgel by introducing the proper ion-

compound and ion-strength of the solution. In this food

emulsion model system, the silicon oil used is neither food

grade nor is the size of the drops at the same size as the

drops found in food products. The oil is present in the

system primary as ‘a shaping agent’ and is not mixed with

the product, i.e. the drops. The oil is chosen because the high

viscous silicon oil made it possible to study the process in

the 4-RM at lower speeds than low viscous oil. The use of

other oils will probably not change the mechanism in other

means than scaling the force from the flow and changing

interfacial properties.

The aim of this study was to investigate the final shape

and the shape development of millimetre k-carrageenan

drops during a combination of cold-set gel formation and

deformation by elongation flow. The shape and the process

have been evaluated and studied in terms of macrograph

sequences and image analysis to be able to investigate not

only the final shape but also the changes in the shape during

the process. The effect of process conditions, flow speed and

cooling temperature, on the final shape and shape progress

was investigated as well as the effect of different k-

carrageenan drop characteristics, drop viscosity and gel

strength. The k-carrageenan solutions were characterised by

rheological investigations. The reason for exploring differ-

ent shapes is not only to study the shape as a final product,

but also to pave the way for future studies of the special

functional properties that could be related to the final drop

shape in future emulsions with smaller shaped drops.

2. Materials and methods

2.1. Biopolymer

The k-carrageenan used was a product of Danisco Cultor

(8220 Brabrand, Denmark). It is a commercial potassium-k-

carrageenan. The ion content was 8.5% K, 0.18% Ca and

1.5% Na. The locust bean gum, LBG, was also a

commercial product of Danisco Cultor (8220 Brabrand,

Denmark), called Grindstede LBG 246.

2.2. Oil

The oil used as the continuous phase was silicone oil,

polydimethylsiloxane, PDMS, named Wacker Silicone

Fluid AK5 000 from Wacker-Chemie GmbH, Burghausen,

Germany. The oil had a measured viscosity of 6.4 Pas at

10 8C and 5.2 Pas at 20 8C.

2.3. Additive

To increase the quality of the macrographs and reduce

the image measurement error, aniline blue was used as a

contrast agent. Aniline blue was obtained from Riedel de

Haen AG, Seelze-Hannover, Germany. Addition of standard

NaCl was used to alter the Naþ concentration.

L. Hamberg et al. / Food Hydrocolloids 17 (2003) 641–652642

2.4. Solution preparation

2.4.1. Preparation of the k-carrageenan solution

Three different types of 1% w/w k-carrageenan water

solutions with different additions of sodium chloride were

prepared. The three solutions had a final sodium concen-

tration, including sodium from the k-carrageenan, of 17,

109 and 212 mM, respectively. The amount of Kþ ion

present from the k-carrageenan powder resulted in a final

concentration of Kþ of 22 mM. Although only the Naþ ion

concentration is adjusted, presence of Kþ ions is necessary

for the gel formation and vital for the final gel strength

(Hermansson et al., 1991). Aniline blue was added to the

solutions at a concentration of 0.5% w/w. To dissolve all the

ingredients, the solution was heated to and then held at

95 8C for 15 min while stirring.

2.4.2. Preparation of k-carrageenan blended with LBG

For the solution of 1% k-carrageenan blended with LBG,

0.25% w/w LBG was added and the sodium chloride

addition was adjusted to obtain the same final properties

as for the k-carrageenan solution with 109 mM Naþion

concentration. In order to dissolve the k-carrageenan/LBG

mixture, the solution was first pre-stirred for 30 min at room

temperature before the solution was held at 95 8C for 15 min

during stirring.

2.5. Shaping

2.5.1. Flow

The hyperbolic flow was generated in a four-roll mill,

4-RM (Taylor, 1934). The 4-RM was built and adapted to

fit a microscope by the workshop at the Institute of Food

Science/Food Process Engineering at ETH, Zurich,

Switzerland and has been described in more detail earlier,

(Hamberg, Walkenstrom, Stading, & Hermansson, 2001).

By letting one pair of the rolls rotate in one direction and

the other pair in the opposite direction, the hyperbolic

flow-field will be generated in the centre of the chamber

(Feng & Leal, 1997). In the investigations, the speed of

the rolls was 5, 10, 15, 20 and 25 rpm. The corresponding

flow along the centre line for different roll speeds

constantly increases through the inlet area at an elongation

rate of around 0.5 s21 for the lowest roller speed and

around 2.5 s21 for the highest speed. The flow speed of

the continuous phase reaches its maximum in the

narrowest gap, with values around 12 and 48 mm/s for

the lowest and highest speed, respectively. In the same

area, the elongation rate drops from positive to negative

with the same magnitude as for the inflow. The flow along

the centre line slows down and approaches immobility at

a distance approximately 70 mm from the stagnation

point. The elongation rate along the centre line drops to

zero from the peak values at the beginning of the outlet

from around 20.5 and 22.5 s21.

2.5.2. Process

The shaping process started with injection of a 10 ml

large drop of the biopolymer solution into the oil in the 4-

RM. The rolls were started in advance so that a fully

developed hyperbolic flow field was generated. The

biopolymer solution was heated to 90 8C and the

surrounding oil to 10 or 20 8C. The drop was injected at

the centre line, 4 mm from the stagnation point in the

centre. First, the drop was accelerated from the injection

point to the narrowest gap between the rollers and then,

after passing the narrowest gap, the drop was exposed to

retardation in the outflow from the rollers. The tempera-

ture of the biopolymer phase was chosen in order to have

a large gap to the gel formation temperature. This ensures

that the drops is deformable until the relaxation flow in

the outlet and enable the possibility to form complex-

shaped drops. The oil temperatures were chosen to be

sufficiently under gel formation temperature to ensure a

rapid cooling of the drop around gel formation

temperature.

2.5.3. Macroscopy

The shaping was recorded with a macroscopic technique,

in which a sequence of macrographs was taken to observe

the shaping progress. The macrographs were taken with a

Hamamatsu C6157, 3 CCD Colour Video Camera, Hama-

matsu Photonics K.K., Hamamatsu-city, Japan, connected

to a frame-grabber in a workstation equipped with the image

analysis program MicroGOP 2000/S, Contextvision AB,

Linkoping, Sweden. The camera was tilted at an angle of 58

from the normal of the oil surface in the 4-RM to obtain

good picture quality. To avoid motion-induced blurring, the

electronic shutter of the camera was set to 1/10,000 s. The

time resolution was higher than 0.1 s, corresponding to a

measured frame rate of around 12 frames/s.

2.5.4. Image analysis

The macrographs were converted into binary images and

the drop was isolated before drop parameters were

measured. The parameters used were defined as follows:

Area The projection area of a drop on an x–y plane.

Perimeter The projection perimeter of a drop on an x–y

plane.

Feret’s X The projection length of a drop along the centre

line.

Feret’s Y The projection length of a drop perpendicular to

the centre line.

Position x-coordinate of the centre of gravity of a drop.

Graphic illustrations of the response parameters are

given in Fig. 1.

L. Hamberg et al. / Food Hydrocolloids 17 (2003) 641–652 643

2.6. Rheological characterisation

2.6.1. Viscosity

To characterise the properties of the solutions before gel

formation, viscosity measurements were made. The instru-

ment used was a Bohlin VOR Rheometer, Bohlin Rheology,

Chichester, UK, equipped with Millennium VOR software,

Reologen i Lund, Oved, Sweden, with a double gap

geometry measuring system. The system had an inner and

outer rotating wall with diameter 21.7/27.4 mm and a fixed

bob with a diameter of 23.9/24.9 mm. A volume of 10 ml

from the different solutions was used and shear sweeps were

performed at 90, 60, 50, 40 and 35 8C.

2.6.2. Gel formation temperature

Oscillatory measurements were also made while the

solution was cooled from 50 to 10 8C to measure the gel

formation temperature, Tgel: A stress-controlled StressTech

HR Rheometer, Rheologica Instruments AB, Lund, Swe-

den, with Peltier cooling was used with a cone and plate

geometry, angle 48, diameter 30 mm. 0.5 ml of the warm

solution was placed on the plate and measurement was made

with a cooling rate of 5 8C/min, frequency of 1 Hz, and with

a strain of 0.001. Tgel was determined as the temperature

where the storage modulus, G0; crosses over the loss

modulus, G00:

2.6.3. Gel strength

To measure the bulk gel strength of the drops, gel tubes

were prepared from solutions with the same properties as

the different drops by pouring a hot solution, heated to

95 8C, in a metal cylinder. The metal tube was put in an ice-

bath to cool the solution and to build a gel. Then the gel

tubes were taken out of the cylinders and cut into 5 mm

thick slices. The measurements were made with a Bohlin

VOR Rheometer, as described earlier. The measurement

system had riffled plate-plate geometry, with a diameter of

30 mm. The measurements were carried out at a tempera-

ture of 10 and 20 8C with a strain of 0.025, amplitude of 5%

and a frequency of 1 Hz. The gel slices were applied to

the measurement system and compressed 5% before the

start of the measurements.

3. Results and discussion

This part is divided into four sections of which Section

3.1 describes typical shaping of a drop. Section 3.2 covers

the rheological characterisation of the k-carrageenan

solution. Section 3.3 focuses on the end shape of a

processed drop, and Section 3.4 concerns measurements

and image analysis of the shaping process.

3.1. Shaping

Typical shaping of a drop is shown in the 10 macrograph-

long sequence in Fig. 2. The macrographs cover an area

from the centre of the 4-RM, on the left-hand side of the

macrographs, where the injection is situated, along

the centre line, to the outflow region on the right-hand

side. The process ends approximately 70 mm from the

centre of the 4-RM. Just to the left of the middle of the

macrograph the tip of two of the rollers is visible, indicating

where the narrowest gap is located.

The macrographs have been taken from a sequence with

the experimental conditions 1% k-carrageenan in 109 mM

Naþ, 15 rpm roller speed and 10 8C cooling temperature.

The time between each macrograph is approximately 0.8 s.

The first macrograph was taken when the injection needle

was positioned. The second macrograph was taken during

the injection. Sequences 3–5 show the actual elongation

process and the contraction is shown in sequences 5–7.

From macrograph 7 to the end in macrograph 10, no large

Fig. 1. Definitions of the different responses measured: (a) area, (b)

perimeter, (c) Feret’s X and (d) Feret’s Y :

Fig. 2. Sequence showing the progress of shape formation. The

macrographs were taken with approximately 0.8 s delays starting at the

top. Conditions of 15 rpm, 10 8C and 109 mM Naþ.


change in shape is visible, but transportation along the

centre line is noted.

Fig. 2 also shows the development of the different

characteristic parts of the drop: the body, the limbs and the

blob. The characteristic parts are illustrated in Fig. 3. The

first limb to be developed is the bow-limb, macrographs 3–

5. The limb is stretched out from the bow as the bow

formation accelerates into the gap. When the bow of the

drop has passed the narrowest gap, a blob is developed at the

bow limb, macrographs 4–7. The forming of the aft limb

starts later than the bow limb, as can be seen in the

macrographs 4–6, and seems to form when the body of the

drop is accelerated around the narrowest gap. The body of

the drop is already present from the beginning. First, it is

located in the centre, later when the bow is accelerated the

body is closer to the aft. In the end, at the outflow, the body

contracts along the centreline and expands in the perpen-

dicular direction. The body seems to be the last part of the

drop to be fixed.

3.2. Rheological characterisation of k-carrageenan

3.2.1. Viscosity

The result of the viscosity measurements of pure k-

carrageenan solution and k-carrageenan solution blended

with LBG at temperatures between 90 and 35 8C is

presented in Table 1. The measurements were made with

solutions at the 109 mM Naþ ion concentration. In the table,

only one viscosity value from the different measured flow

curves is presented. For the pure k-carrageenan solution, no

shear dependence was found for shear rates between 5 and

100 s21 at temperatures between 90 and 40 8C. At 35 8C a

very weak shear dependence was detectable along the

lowest shear rates, and therefore the value in the table is

presented for a shear rate at 50 s21. Limited shear-

dependence was also found for the k-carrageenan solution

blended with LBG, and hence all the values in Table 1 for k-

carrageenan/LBG are presented for 50 s21. The k-carragee-

nan solution tended to be more shear thinning at lower

temperatures than at higher temperatures.

The viscosities for both the pure k-carrageenan solution

and the solution blended with LBG were highly tempera-

ture-dependent, and increased rapidly when the temperature

came close to Tgel: The viscosities of the pure k-carrageenan

solution were in general more than six times lower than for

the k-carrageenan/LBG solution. It was consequently

concluded that differences in drop viscosity due to the

cooling temperature, 10 and 20 8C, of the oil, were much

less than those due to addition of LBG for all temperatures

away from Tgel surroundings. The viscosity ratio between

the pure k-carrageenan solution in the drop and the oil

changes during the process varied from 0.0006 at 90 8C to

0.003 at 35 8C. The rapid increase in viscosity near Tgel

increases the ratio further. Corresponding values for the

blended drops were 0.004 at 90 8C and 0.03 at 35 8C. All

viscosity ratios refer to the oil temperature of 10 8C.

3.2.2. Gel-formation temperature

The aim was to have as little variation as possible in Tgel:

Tgel measurements are presented in Table 1. All gel-

formation temperatures are around 30 8C and therefore well

above the cooling temperature for the experiments. The

variation is less than 10% of the total temperature drop. The

measurements showed that Tgel is also slightly dependent on

Naþ concentration, but the effect of LBG addition on Tgel is

minor.

3.2.3. Gel strength

The foremost reason for investigating the gel strength

was to control the parameter for determining the influence

on the final drop shape. The ion-dependence of the shape

was expected to be minor since the ions did not affect the

viscosity but only the gel strength, and thereby should only

be crucial in the very last stages of the process. Another

reason for measuring and varying the gel strength was to

pave the way for future investigations not only of drops of

different shapes, but also of the rheological effects in a

dispersion of shaped drops of different flexibility.

The results of the gel strength measurements for the

different cooling temperatures and the three different Naþ

salt concentrations are presented in Table 2. The values of

the storage modulus, G0; was shown to be highly dependent

on the Naþ salt concentrations, with values from below

3 kPa for the lowest concentration to values around 9 kPa

for the highest concentration. Differences in G0 due to

Fig. 3. Different characteristic parts of a drop: (a) the body, (b) the aft limb,

(c) the bow limb and (d) the blob.

Table 1

Viscosity and gel transition temperature and surface tension

k-carrageenan k-carrageenan þ LBG

h 90 8C, 109 mM NaCl 3.7 (mPas) 23 (mPas)

h 60 8C, 109 mM NaCl 6.7 (mPas) 51 (mPas)

h 50 8C, 109 mM NaCl 10 (mPas) 74 (mPas)

h 40 8C, 109 mM NaCl 16 (mPas) 110 (mPas)

h 35 8C, 109 mM NaCla 21 (mPas) 200 (mPas)

Tgel 17 mM NaCl 29 (8C) –

Tgel 109 mM NaCl 32 (8C) 31 (8C)

Tgel 212 mM NaCl 35 (8C) –

a Large deviation occurs between different measurements.


cooling temperature 10 and 20 8C are less than the gel

strength differences due to addition of Naþ ions. The loss

modules, G00; were shown to be more temperature-

dependent than ion-dependent, with lower values for the

high temperature.

3.3. Final drop shape

To find out the diversity of possible shapes that could be

produced under the limited process conditions, the process

and drop parameters: speed, cooling temperature and the

amount of added Naþ salt, were altered. The reason for

exploring different shapes is not only to study the shape as a

final product but also to open up the possibility for future

studies of the special functional properties that could be

related to the final drop shape.

3.3.1. Shape map

Fig. 4 show the final shape of the drop cooled in the

continuous phase with a temperature of 10 8C. The Naþ ion

concentrations in the drop are 17, 109 and 212 mM,

respectively, and the speed of the rollers varies from 5 to

25 rpm. The macrographs of the individual drops in the

figure are picked from a number of trials and are chosen to

be representative and to have good contrast. Fig. 5 shows

drops from the same salt and speed conditions but cooled in

a continuous phase instead with a temperature of 20 8C.

The total number of drops investigated for the figures is 63.

Common to all drops in Figs. 4 and 5 is that the shape of the

drops could be divided into three classes:

† Class I—a solid body with no limb.

† Class II—a solid body with one bow limb to the right.

† Class III—a solid body with one bow limb to the right

and one aft limb to the left.

The first class, with no limb, consists of all the drops

formed with the speed condition of 5 rpm and the drop

formed with the speed of 10 rpm, 17 mM Naþ ion

concentration, and the cooling temperature of 20 8C. In

general, these drops have an ellipsoidal shape with the

longest axis oriented perpendicularly to the centre line.

However, two of the drops in the class differ substantially

from the others. The first drop that differs has the strongest

gel strength, Table 2, and is formed under the conditions

5 rpm, 212 mM Naþ, and 10 8C. This drop has the

ellipsoidal shape, but its longest axis is oriented along

the centre line instead of being perpendicular to it. The

second drop that differs is the triangular drop formed under

the conditions 10 rpm, 17 mM Naþ and 20 8C. This drop

has the weakest gel strength within the class (Table 2).

Within class I the impact of different Naþ concentrations

and cooling temperature is small. The only notable fact is

that the differences are larger for the drops cooled at the

low temperature compared with the ones cooled at the high

temperature.

The second class consists of the three drops with one

limb and all are formed with the speed condition 10 rpm. In

Fig. 4, with a drop cooling temperature of 10 8C, only the

drop with 17 mM Naþ ion concentration, and in Fig. 5,

20 8C, the drops with the two highest Naþ ion concen-

trations belong to the class. All the drops in class II have the

limb at the bow of the drop and the limb ends with a distinct

blob. Although the class has a limited number of objects,

some trends could be found. Within the class, an increase inFig. 4. Shape map of end shapes of the drops regarding speed and Naþ

concentration at 10 8C.

Fig. 5. Shape map of end shapes of the drops regarding speed and Naþ

concentration at 20 8C.

Table 2

Gel strength

Naþ conc.(mM) Temperature (8C) G0 (Pa) G00 (Pa)

17 20 2878 54

17 10 3674 465

109 20 7367 224

109 10 7561 986

212 20 8856 309

212 10 9460 901


the Naþ salt concentration tends to favour a higher Feret’s Y

at the expense of Feret’s X. The same trend is found for a

decrease in temperature, so the effects are hard to separate,

since temperature and Naþ ion concentration both affect the

gel strength of the drop (Table 2).

The last and biggest class involves all the drops with two

limbs, and they are formed at the roller speeds 15, 20 and

25 rpm. In addition, the two drops at 10 rpm, with 109 and

212 mM Naþ ion concentration and 10 8C cooling tempera-

ture belong to this class. The limb at the bow of the drop

ends with a distinct blob but the aft does not, or has a very

indistinct one. The bow limb is also longer than the aft limb.

In general, the drops within the class have an increasing

projection perpendicular to the centre line, Feret’s Y ; with

higher roller speed and for increasing temperature. How-

ever, an increase in Naþ ion concentrations both projections

seem to increase. The drops with a low Naþ ion

concentration have a more narrow distribution in Feret’s X

and Y than the drops with higher Naþ ion concentrations.

Furthermore, drops with higher Naþ ion concentration have

thinner limbs.

3.3.2. Fixation time and position

Previous investigations have shown that the final drop

shape is related to the drop fixation position (Hamberg et al.,

2002; Walther et al., 2002). Therefore, Fig. 6 shows a

diagram where the position of fixation and the time to

fixation are presented for the different roller speeds and

cooling temperatures.

The general trend is that the fixation position is shifted

towards the end with increasing speed. The differences in

position found between the lower speed-rates are larger than

those between the higher rates. The fixation positions seem

to reflect the shape classes found in Figs. 4 and 5. The

fixation for class I positioned first around 46 mm and class

III later around 60 mm. The similarities between position

and shape for classes III and I are in agreement with

previous results. The same agreement could not be

concluded for class II, because the two bars representing

10 rpm could not be interpreted in terms of classes as

10 rpm includes drops from all three classes.

Inverse dependence for different roller speeds is found

for the time to fixation. The plain bars show that even if the

drops in class III are fixed at later positions, they still

become fixed earlier than the drops from class I. A higher

roller speed moves the drop more quickly to the end of the

outflow area with the low forces. Furthermore, it is possible

that more elongated drops at the higher speeds could cool

faster due to a larger surface area.

There is no obvious cooling temperature effect found in

the fixation time data. Either the temperature difference is

too small, or competing phenomena could be affecting the

fixation time. A lower cooling temperature results in a

slightly higher cooling rate, which should mean that the

temperature drops sooner to below Tgel for drops cooled at

Fig. 6. Time to fixation, plain, and position of fixation, netted, for different speeds and cooling temperatures: (grey) 10 8C and (white) 20 8C.


10 8C. Nevertheless, the cooling rate is also known to alter

the measured Tgel; (Hermansson et al., 1991) and shift it

towards lower values, resulting in a later decrease to

temperature below Tgel: On time scales corresponding to the

ones in the experiments, and for the complex system that the

small moving drop represents, proper measurements to

establish the superior phenomena are difficult.

3.4. Shaping-process measurements

To explain and conclude in what way the process

parameters results in the different shapes in Figs. 4 and 5, it

is necessary to study more than the pre-set parameters and

the final result. Therefore, measurements of the shaping

process were made in terms of image analysis of the

macrographs from the process with the different parameters.

This makes it possible to interpret the mechanisms involved

in shaping, by following the development of the shape of the

drop systematically, by plotting characteristic features

(Fig. 1).

3.4.1. Position

The shaping shown in Fig. 2 could also be represented as

in Fig. 7, where some characteristic parameters of the drop

are plotted against the position. The parameters shown in the

graph are: area, perimeter, Feret’s X and Y with the

definitions according to Fig. 1. Note that perimeter is scaled

down by a factor of two, and all units are in millimetre

except that the unit for area is mm2. The position refers to

the distance along the centre line, between the centre of the

4-RM and the centre of gravity of the drop.

The perimeter and the Feret’s X curve have the same

characteristics, and they start with a steep increase in the

beginning until around the narrowest gap located at

27.5 mm. In the divergent outflow, the two parameters

decrease until they both flatten out. The two curves level off

at different positions—first, the perimeter around 45 mm,

and later Feret’s X; at approximately 55 mm. There could be

a dual reason for this. First, as the drop is cooled from the

surrounding fluid, a skin could be developed around

the drop, fixing the perimeter. The second and probably

the main reason is revealed in combination with Fig. 2, in

macrograph 6 and onwards. There the bow limb appears to

be flexible, allowing Feret’s X to continue to change after

fixation. Therefore, the levelling of the perimeter indicates

the fixation of the drop shape. However, the levelling of

Feret’s X not only indicates that the fixation of a shape has

passed, but also that rotating movements and flexibility have

ended.

The curve for Feret’s Y ; the projection perpendicular to

the centre line, shows no significant changes before the

narrowest gap. In the divergent outflow, the curve rises as

the drop stretches in the Y-direction, until it flattens just

before the position of 50 mm.

The measured projected area is also shown in Fig. 7. The

changes in this graph are a result of movements

in the z-direction. A larger area results in a ‘thinner’ object.

The increase in area is present up to a stage later than

the maximum length, and the final decrease seems to be at the

same time and position as for the development of the solid

body (Fig. 2). Therefore, the body should have the largest

extension in the z-direction.

3.4.2. Time

The data in Fig. 8 come from the same drop as in Figs. 2

and 7. The graph shows how the shape develops with time

instead of position, and it presents the same characteristic

parameters as above. By plotting the data against time, it is

Fig. 7. Shape curve showing the progress of (-·-) Area, (—) Perimeter/2,

(–-) Feret’s X and (· · ·) Feret’s Y as a function of position. Conditions of

15 rpm, 10 8C and 109 mM Naþ.

Fig. 8. Shape curve showing the progress of (-·-) Area, (—) Perimeter/2,

(---) Feret’s X and (· · ·) Feret’s Y as a function of time. Conditions of

15 rpm, 10 8C and 109 mM Naþ.


not only easier to relate the graphs to the macrograph

sequence in Fig. 2, but it also reveals the time scales for the

different parts of the process better. The time scales

involved in the development of the different characteristics

can be hard to decide from Fig. 7 as the drop moves at

different speeds at different positions.

The shaping in Fig. 8 was divided into four zones and

was interpreted in terms of external and internal forces. The

external forces are forces from the flow field acting on and

deforming the drop. The internal forces are the surface

forces that keep the drop spherical and the forces from the

internal plastic and elastic response in terms of drop

viscosity and gel strength.

In the first zone, from time 0 to 2.2 s, the external forces

are superior to the internal forces. The accelerating increase

in drop length is expected, since the acceleration at the

centre line in a hyperbolic flow should be constant in this

zone.

In the second zone, from 2.2 to 3.6, where the drop has its

highest elongation, an unexpected symmetry exists for

perimeter and Feret’s X: This symmetry is surprising,

although an ideal hyperbolic flow field should generate

symmetric external forces. The internal properties of the

drop are neither symmetrical with time, nor should one

expect the result from the surface forces to be symmetrical.

As the drop in the process is chilled down from 90 to 10 8C,

the drop viscosity changes, and the change in the viscosity

ratio should therefore result in unsymmetrical forces. The

surface forces should counteract with the elongation of the

drop before the narrowest gap. However, in the contraction

behind the gap, the surface forces should contribute to, and

instead increase the contraction of the drop and thereby

result in an unsymmetrical graph. From this, it is possible to

conclude that flow has a greater effect on the change of

shape than internal forces.

In the third zone, from 3.6 to 4.5 s, the superior force

goes from being external in the beginning to internal at the

end. This is where the fixation occurs. The total hold-up

time is ,1 s, and the forces that are involved are gel

formation, viscosity increase, and lowering of the external

forces. The first two involve the temperature and the heat

transfer out from the drop. One could only speculate about

the temperature, since the temperature gradient is high as it

decreases with an overall gradient higher than 10 8C/s, and

is therefore hard to measure. The fact that the perimeter

reached its final value half a second earlier could point to an

uneven temperature profile in the drop. Hence, the earlier

fixation of the perimeter could be interpreted as a skin

formation. The equal time to a steady value for area and

Feret’s Y strengthen the assumption that the drop is fixed at

4.5 s, although the graph for Feret’s X has not reached its

final value.

In the final zone, from 4.5 s to the end of the

measurement, all graphs but the one for Feret’s X are

stable. Feret’s X indicates that there is still some flexibility

left in the drop until at least 5.6 s. In the end, the external

forces acting on the drop could be so small that they do not

even show or indicate the flexibility of the drop.

3.4.3. Speed

Fig. 9 presents Feret’s X; the projection length of the drop

along the centre line versus its centre position, for different

roller speed rates from 5 to 25 rpm. The curves are taken

from experiments with a drop Naþ salt concentration of

109 mM and a cooling temperature of 10 8C. They therefore

correspond to the final drop shapes in the middle row in

Fig. 4. For all speed rates, the curves show that the drop

elongates until a position fore the centre of the drop around

29 mm. Hence, the centre has already passed the narrowest

gap at 27.5 mm when the drop has its maximum elongation.

In the outflow, all drops contract and the curves drop and

flatten out in the end indicating a fixation of the drop.

The trends seen in Fig. 9 are expected; an increase in

speed results in a higher maximum length during the first

stages of the process. In addition, the slope in the increasing

part follows the trend of higher values at higher speed; this

is also found in the descending part. The slopes and the

outline of the graphs again seem rather symmetrical around

the narrowest gap. See discussion earlier.

The interpretations of the later stages of the curves are

hazardous because the drop could start to rotate and some of

the limbs are flexible after their fixation. However, the

tendency for the higher speed-rates is that, although the

differences are large at the narrowest gap, the differences

subside and are small at the end of the process. This leads to

the conclusion that high deformation does not alter the

cooling substantially.

3.4.4. Temperature

Temperature is an important factor in the shaping process

when using a cold set biopolymer for preserving the shape.

It is not only by the direct affect of determining when and

Fig. 9. Effect of different roller speeds on Feret’s X: 109 mM Naþ and

10 8C. (þþ ) 5 rpm, (· · ·) 10 rpm, (-·-) 15 rpm, (---) 20 rpm, (—) 25 rpm.


where the gel formation in the drop should occur in the

process, but also by changing other important parameters

like viscosity/viscosity ratio and surface tension. Therefore,

a close monitoring of the drop-temperature distribution

inside the drop during the shaping would be of great

relevance and help when trying to control and analyse the

process. Unfortunately in this investigation it was not

possible to follow the temperature development in the drop

by measurements as the process was on a timescale of

seconds.

The different cooling temperatures influence the system

in different ways. First, a lower temperature increases the

cooling rate of the drop, and therefore the drop cooled at

10 8C should be fixed earlier due to an earlier passing of Tgel

than for a drop cooled at 20 8C. Second, the faster cooling of

the drop should also lead to a lower temperature of the k-

carrageenan-solution inside the drop, at a certain position. A

lower temperature corresponds to a higher drop viscosity,

Table 2, and therefore a different viscosity ratio. Finally, the

different cooling temperatures could also affect the viscosity

of the continuous phase.

Effects of temperature on Feret’s X and Y for the process

are shown in Fig. 10, where the solid and dotted graphs

represent a cooling temperature of 10 and 20 8C, respect-

ively. The graphs for Feret’s X start together, but during the

increase in the inlet between the rollers, the graph with a

cooling temperature of 10 8C increases more and reach a

higher maximum value. The graphs keep approximately this

difference towards the end during the decrease and finish at

a higher value than the graph with a cooling temperature of

20 8C. For Feret’s Y ; the curves have approximately the

same value and profile until the final stages, where the lower

cooling temperature curve flattens out earlier at a position

below 50 mm and the other does not flatten until around

55 mm.

The temperature effect on drop and oil viscosity oppose

each other in terms of shaping, and it is clear from the

graphs of Feret’s X that the last effect is more dominant in

the beginning. The higher viscosity in the continuous phase,

and thereby lower viscosity ratio, elongates the drop more at

the beginning of the process. It is also reasonable to believe

that the drop viscosity changes due to different temperatures

are less at higher temperatures far from Tgel; than for

temperatures in Tgel surroundings. This increase in tem-

perature dependence near Tgel could explain the behaviour

of the 10 and 20 8C Feret’s X-curves shown in Fig. 10. In the

figure, the graphs do not end at the same level, as the

viscosity-ratio-change increases at the end of the process.

The effect of the viscosity increase of the continuous

phase should also be notable for Feret’s Y and lead to a

similar difference between these curves. No such effect is

visible but instead the first effect, earlier passing of Tgel;

results in a shorter drop in the Y-direction. Hence, a

decrease in cooling temperature leads to an increase in the

X-direction but a decrease in Y-direction.

3.4.5. Viscosity

LBG was added to the solutions for some samples to

investigate the effect of the viscosity ratio, as the change in

drop viscosity was shown to have a complex effect when the

viscosity change was temperature-induced. Tgel for k-

carrageenan blended with LBG is known not to differ

much from Tgel for pure k-carrageenan (Stading &

Hermansson, 1993). The effective difference in viscosity

was found to be ,7 at 60 8C and ,10 times higher at 35 8C

than the original pure k-carrageenan solution for the

solution with LBG (Table 1). The rheological characteris-

ation also showed that Tgel for the blended solution was also

only slightly affected (Table 1).

The different curves shown in Fig. 11 are the progress of

Feret’s X and Y plotted as a function of the centre position.

Fig. 10. Effect of different cooling temperatures: (---) Feret’s X-10 8C, (—)

Feret’s X-20 8C, (· · ·) Feret’s Y-10 8C, (-·-) Feret’s Y-20 8C. Conditions of

109 mM Naþ and 15 rpm.

Fig. 11. Effect of different viscosities on Feret’s X and Y : 109 mM Naþ and

15 rpm: (—) Pure k-carrageenan and (· · ·) k-carrageenan mixed with LBG.


All curves are from drop conditions of 109 mM Naþ salt

concentration, 10 8C as cooling temperature and a roller

speed of 15 rpm. The curves are two replicas for pure k-

carrageenan and k-carrageenan with LBG, respectively.

The two Feret’s X curves with pure k-carrageenan are

superior to the k-carrageenan/LBG curves for positions

around the narrowest gap in the 4-RM. Close to the start and

at the end, there are no large differences. All curves in Fig.

11 have a similar pattern except for the altitude of the

maximum and show similarity to the difference among the

speed graphs in Fig. 9. Hence, it could be reasonable to

believe that the viscosity ratio and speed effects could be

exchangeable at the same temperature.

This type of viscosity change shows a different pattern

from the temperature-induced change. The differences are

found in the later stages of the process, where the

differences between the curves decrease in Fig. 11 instead

of being nearly constant in Fig. 10. The most likely reason is

that the differences in the viscosity ratio are similar both at

the start and at the end in Fig. 11.

Perpendicular to the centre line, Feret’s Y shows no

changes until the outflow, after the narrowest gap around

30 mm. There, a steady increase become visible and

continues until the curves reach a stable plateau at the

end, just before the 50 mm position. Again, as for Feret’s X;

the curves with the lowest viscosity reach the highest values

for Feret’s Y :

The multiple Feret’s X and Y curves also show the

differences within a group of curves created under the same

conditions. The differences shown for pure k-carrageenan

are among the highest ones found in the measurements,

while the differences for the blended solution are among the

smallest. The individual differences within samples with the

same conditions also tend to be larger for a cooling

temperature of 10 8C than for 20 8C and for samples with

higher Naþ concentrations. This could be explained that a

more rapid cooling, in combination with the thin limbs

created from drops with higher gel strength, makes the

individual drop more sensitive to the differences that could

be found in k-carrageenan solutions.

The shape reproducibility in Figs. 4 and 5 was

surprisingly high, and even under the most shaped

conditions the differences due to changes in the process

parameters were larger than the differences within the

replicates.

3.4.6. Drop size

The influence of different drop sizes is an important issue

for the shaping that has been omitted in this study. A change

in size will not only affect the deformation but also fixation

of the drop, since the cooling time is influenced by the drop

size. In this investigation, the drops have an initial diameter

of 2.7 mm, and therefore too large for many applications.

Nevertheless, the questions addressed concerning shaping in

the small sub-millimetre range have proved to be hard to

answer due to limited observability (Hamberg et al., 2002).

The limitations in observability on the time scales noted

here are even bigger on the smaller scale. One could expect

that some of the observations and conclusions could be

applied to the downscaled systems as well.

Although the drop sizes are in the millimetre range,

surface phenomena are expected to play a role in the general

shaping mechanisms. Here, as the effect of differences in

surface tension was believed to be minor between all

different investigation set-ups and since the surface tension

was difficult to measure on the time scales involved in this

process, surface measurements were omitted in this

investigation. Characterisation will be difficult, as the

surface measurements would have featured problems

when the biopolymer solution in the drops changes from a

viscous solution to a visco-elastic gel through gel formation.

Another unsatisfactory circumstance is that no steady state

is believed to occur at the surface on the short time scale of

the shaping process. Nevertheless, the surface properties

and function must be investigated to fully master the

shaping. Therefore, the role of surfactants in shaping and

surface tension will be studied further as a challenging task

for the future.

4. Conclusions

The measurements of the shaping process, in terms of

image analysis of the different parameters on the

macrographs from the process, was found to be a good

new tool for investigating how the process parameters

determined the different shapes. By plotting the charac-

teristic features of the drop with position and time, it was

possible to interpret the mechanisms and time scales

involved in shaping. The fixation occurs on a time scale

of ,1 s, and the mechanisms involved are gel formation,

viscosity increase, and lowering of the external forces.

With the same hyperbolic flow, very different shapes

could be achieved with small process changes and with

high reproducibility. The final shape of all the drops

produced could be graded into three classes. The first

class contained all drops with just a solid body. The

second class contained the drops with a body and one

bow limb. In the last shape-class, the drops had a solid

body with one bow limb and one aft limb. The class to

which the drop belonged seemed to be correlated to the

position in the flow where the drop was fixed. Earlier

position gives the simpler shape. Time to fixation and

fixation position had an inverse behaviour. However, the

differences between the characteristic features inside a

class did not correlate with position or time.

The fixation of the characteristic features, perimeter,

area, Feret’s X and Y ; does not occur at the same time

and position. The first feature to be fixed is the

perimeter, and this is believed to be due to skin

formation of the drop. Then comes the synchronous

fixation of area and Feret’s Y : This fixation point has


been used as the end of the shaping. Under some

conditions, the fixation of Feret’s X is separated from the

others due to flexibility of the drop. Flexibility has not

been included as a part of the shaping.

For the different process-parameters investigated, a

change in speed and viscosity ratio affect the process in

the same straight way as if the viscosity ratio is changed at a

constant temperature. If the change in viscosity ratio is

temperature-induced, the effect is complex. Various

additions of Naþ ions to alter the drop flexibility do not

change the process or the shapes much.

The set-up and technique have proven to be a good new

tool for studying and producing differently shaped drops.

This tool could be applied in the future to study the

rheological impact of drop shape and drop flexibility on

smaller drops suitable for real food products.

Acknowledgements

This work has been carried out with financial support

from the Swedish LiFT program (Future Technologies for

Food Production) and the EU project Structure engineering

of emulsions by micro-machined elongation flow proces-

sing (QLK-CT-2000-01543) within the RTD programme

Quality of Life and Management of Living Resources.

Special thanks to Bernhard Walther, SIK.

References

Djalili-Moghaddam, M. (2001). Rheological measurements on fibre

suspensions. Goteborg: Chalmers University of Technology.

Erwin, L. (1991). Principles of laminar fluid/fluid mixing. In C.

Rauwendaal (Ed.), Mixing in polymer processing (pp. 1–16). New

York: Marcel Dekker.

Feng, J., & Leal, L. G. (1997). Numerical simulations of the flow of dilute

polymer solutions in a four-roll mill. Journal of Non-Newtonian Fluid

Mechanics, 72, 187–218.

Hamberg, L., Walkenstrom, P., & Hermansson, A.-M. (2002). Shaping of

gelling biopolymer drops in an elongation flow. Journal of Colloid and

Interface Science, 252, 297–308.

Hamberg, L., Walkenstrom, P., Stading, M., & Hermansson, A.-M.

(2001). Aggregation, viscosity measurements and direct observation of

protein coated latex particles under shear. Food Hydrocolloids, 15,

139–151.

Hermansson, A.-M., Eriksson, E., & Jordansson, E. (1991). Effects of

potassium, sodium and calcium on the microstructure and rheological

behaviour of k-carrageenan gels. Carbohydrate Polymers, 16,

297–320.

Joung, C. G., Phan-Thien, N., & Fan, X. J. (2001). Direct simulation of

flexible fibers. Journal of Non-Newtonian Fluid Mechanics, 99, 1–36.

Joung, C. G., Phan-Thien, N., & Fan, X. J. (2002). Viscosity of curved

fibres in suspension. Journal of Non-Newtonian Fluid Mechanics, 102,

1–17.

Petrie, C. J. S. (1999). The rheology of fibre suspensions. Journal of Non-

Newtonian Fluid Mechanics, 87, 369–402.

Rallison, J. M. (1984). The deformation of small viscous drops and bubbles

in shear flows. Annual Review of Fluid Mechanics, 16, 45–66.

Rochas, C., & Rinaudo, M. (1980). Activity coefficients of counterions and

conformation in k-carrageenan systems. Biopolymers, 19, 1675–1687.

Rochas, C., & Rinaudo, M. (1984). Mechanism of gel formation in k-

carrageenan. Biopolymers, 23, 735–745.

Rochas, C., Rinaudo, M., & Landry, S. (1989). Relation between the

molecular structure and mechanical properties of carrageenan gels.

Carbohydrate Polymers, 10, 115–127.

Stading, M., & Hermansson, A.-M. (1993). Rheological behaviour of

mixed gels of k-carrageenan-locust bean gum. Carbohydrate Polymers,

22, 49–56.

Stokes, J. R., Wolf, B., & Frith, W. J. (2001). Phase-separated biopolymer

mixture rheology: prediction using a viscoelastic emulsion model.

Journal of Rheology, 45(5), 1173–1191.

Stone, H. (1994). Dynamics of drop deformation and breakup in viscous

fluids. Annual Review of Fluid Mechanics, 26, 65–102.

Taylor, G. I. (1934). The formation of emulsions in definable fields of flow.

Proceedings of the Royal Society of London, A146, 501–523.

Walther, B. (2001). Deformation and break-up of drops and filaments in

laminar flow—A literature review. SIK-report 2001 No. 682, Goteborg:

SIK.

Walther, B., Walkenstrom, P., Hermansson, A.-M., Fischer, P., & Windhab,

E. (2002). Flow processing and gel formation—a promising combi-

nation for the design of the shape of gelatine drops. Food

Hydrocolloids, 16, 633–643.

Wolf, B., Frith, W. J., Singeleton, S., Tassieri, M., & Norton, I. T. (2001).

Shear behaviour of biopolymer suspensions with spheroidal and

cylindrical particles. Rheologica Acta, 40, 238–247.

Wolf, B., Scirocco, R., Frith, W. J., & Norton, I. T. (2000). Shear-induced

anisotropic microstructure in phase-separated biopolymer mixtures.

Food Hydrocolloids, 14, 217–225.


Shapes and shaping of biopolymer drops in a hyperbolic flow

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