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Young’s Modulus and Poisson’s Ratio Changes inJapanese Radish and Carrot Root Tissues During BoilingYukiharu Ogawaa, Motoki Matsuurabc & Nami Yamamotod

a Graduate School of Horticulture, Chiba University, 648, Matsudo, Matsudo 271-8510, Japanb Aichi Prefectural Government, 1-2-3, Sannomaru, Naka, Nagoya 460-8501, Japanc (Formerly Faculty of Horticulture, Chiba University)d Faculty of Education, Wakayama University, 930, Sakaedani, Wakayama 640-8510Accepted author version posted online: 21 Jul 2014.

To cite this article: Yukiharu Ogawa, Motoki Matsuura & Nami Yamamoto (2014): Young’s Modulus and Poisson’s RatioChanges in Japanese Radish and Carrot Root Tissues During Boiling, International Journal of Food Properties, DOI:10.1080/10942912.2013.879388

To link to this article: http://dx.doi.org/10.1080/10942912.2013.879388

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YOUNG’S MODULUS AND POISSON’S RATIO CHANGES IN JAPANESE RADISH AND CARROT ROOT TISSUES DURING BOILING ELASTIC PROPERTIES OF BOILED VEGETABLE

Yukiharu Ogawa1,*, Motoki Matsuura2 and Nami Yamamoto3

1Graduate School of Horticulture, Chiba University, 648, Matsudo, Matsudo 271-8510, Japan

2Aichi Prefectural Government, 1-2-3, Sannomaru, Naka, Nagoya 460-8501, Japan

(Formerly Faculty of Horticulture, Chiba University)

3Faculty of Education, Wakayama University, 930, Sakaedani, Wakayama 640-8510

*Address Correspondence to Yukiharu Ogawa, Graduate School of Horticulture, Chiba University 271-8510, Japan. E-mail: ogwy@faculty.chiba-u.jp

Abstract

Young’s modulus and Poisson’s ratio changes in Japanese radish and carrot during boiling were

examined. Young’s modulus decreased rapidly within 2 min, then the decrease moderated. Carrot

(3.0 to 0.5 MPa) exhibited increased modulus values relative to radish (1.8 to 0.3 MPa) during the

same boiling period. Poisson’s ratio decreased slightly during boiling, carrot Poisson's ratio (0.40

to 0.33) was smaller than radish (0.35 to 0.23) during the same boiling period. Boiling in saline

solutions increased moduli reductions under the same treatment conditions. These results

indicated that carrot maintained hardness, but reduced volume relative to radish during boiling.

Keywords: Vegetable tissue, Boiling, Hardness, Salt, Compression, Imaging

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INTRODUCTION

Dietary fiber has traditionally been defined as the indigestible portions of plant derived foods,

including fruits and vegetables.[1] These plant sources can be consumed in raw and cooked forms.

The cooked fruit and vegetable texture is typically softened, and quite different from the raw

material. The elastic properties of fruits and vegetables are a primary trait used to evaluate the

product’s textural attributes.[2,3] Young's modulus is a measure of the elastic property of a material,

and is evaluated based on its stress-strain curve.[2,3] Poisson's ratio is also a measure of a material’s

elastic properties, and is defined as the strain ratio in the direction perpendicular to the applied

force, to the strain in the direction of the applied force.[2,3] These elastic properties are often used as

a parameter to assess food quality.[4,5,6]

Young's modulus can be measured using precious testing devices.[2] Poisson’s ratio can be

measured using mechanical equipment.[7,8] However, mechanical methods are difficult to apply to

Poisson's ratio measurements for boiled food products due to the uncertain state of the contact

point between the pinching instrument, and the sample object. Therefore, a non-contact ultrasonic

technique method was developed and used,[9,10] although the method remains complex, and still

difficult to apply to softened materials.

Anazodo and Chikwendu[11] conducted an evaluation of corn cob samples under a compressive

loading between two parallel steel plates using photographic measurements, which is a

non-contact method to evaluate Poisson's ratio. Pallottino et al.[12] measured compressive

deformation of Tarocco orange fruit to assess its mechanical properties using digital imaging

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devices. Recently, high quality digital cameras for commercial use have become available, which

can capture high-resolution digital images and analyze material deformations using a commercial

personal computer with graphic software.

In the present study, changes in Young’s modulus and Poisson’s ratio for cylindrical root tissue

samples of Japanese radish and carrot at different boiling times in distilled water, and 1, 2, and 4%

saline solution concentrations were examined using a precious testing device, and captured digital

images of individual samples were compared before and after deformation.

MATERIALS AND METHODS

Materials

Fresh Japanese radish (Raphanus sativus L. cv. Daikon) and carrot (Daucus carota L. cv.

US-Harumakigosun), harvested in 2008 in Hokkaido, Japan were purchased at a local supermarket

in Matsudo, Japan. Samples were stored in a refrigerator at 8 °C, and laboratory tests were

conducted the day following purchase. Refined salt (over 99% NaCl, manufactured by the salt

industry center of Japan) was purchased, and used to prepare the saline solution.

Sample Preparation

The surface of boiled vegetable tissues collapsed or distorted, rendering Poisson’s ratio

measurements is challenging. Therefore, we developed a method to maintain sample shape pre-

(pre-formed), and post- (post-formed) boiling (Fig. 1). A 25 mm diameter cylindrical piece of

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tissue was excised from the root vegetable center along the growth axis as a pre-formed sample in

preparation for boiling (Fig. 1). The cylinder height was 50 mm, and the base faced horizontally.

Samples were excised using a precious cutting apparatus with a sharp cylindrical knife (NS-3M,

Hirano, Chiba, Japan). Following removal, pre-formed individual cylinders were placed in a pot

containing 1L of boiling distilled water or saline solution heated by a 600W electric cooking stove

(SK-65, Ishizaki Electric, Tokyo, Japan). The boiling time was up to 30 min in distilled water, and

10 min in saline solution, adding boiling water as necessary to maintain approximately 1L of

water. Saline solution concentrations were 1, 2, and 4% (w/v). Tissue cylinder temperature was

measured in the root center by a fiber optic thermometer (FL-2000, Anritsu, Tokyo, Japan). After

boiling, the pre-formed cylindrical samples were placed in a refrigerator at 8 °C, and cooled

approximately 30 min to equalize the thermal conditions similar to raw samples. A second formed

cylinder was carefully excised from the center of cooled samples to measure Young’s modulus and

Poisson’s ratio (Fig. 1). A precious slice cutter (SK-4N, Hirano) was used to remove a formed

cylinder sample of 15 mm in diameter and 30 mm in height; and a circular level (ED-CI, Ebisu,

Niigata, Japan) verified the cylindrical form. Verified cylinders were rapidly measured at room

temperature, and averaged for the reduplications.

Measurement Procedures

A creep meter (RE2-3305S, Yamaden, Tokyo, Japan) with a planar plunger (Φ30 mm) as the

compression utensil was applied to compress the formed cylindrical sample from the base. The

creep meter also measured normal stress against compression, calculated from the load divided by

the base area, and compressive strain, calculated as a percentage of compressed length divided by

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initial sample length (height). Compression rate was set to 1 mm/s, and the apparatus trigger force

was set at 0.2 N. The initial contact point between sample and plunger, which is regarded as the

initial sample length, was set at 0% compression level (zero compressive strain). Young’s modulus

(E) was calculated from normal stress (σ) values and compressive strain (ε) as follows:

εσ=E (Eq. 1)

Poisson’s ratio (μ) is defined as the ratio of width change (ΔW) amount per initial width (W), and

length change (ΔL) amount per initial length (L) as follows:

L/LW/W

∆∆=µ (Eq. 2)

The widths of cylindrical samples were expanded, and lengths were shortened, because a

compression test was applied in this study. A digital camera (E-510, Olympus, Tokyo, Japan) with

a macro lens (35MM, Zuiko, Tokyo, Japan) was used to capture a digital image of each cylindrical

sample. The camera position was fixed during examination (Fig. 2). The image size was 3648 x

2736 pixels, and the image resolution was approximately 120 pixels/mm. Changes in cylinder

width and length were calculated from differences in pixel number between images before and

after compression using graphic software (Photoshop CS2, Adobe, San Jose, CA., U.S.A.).

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Statistical Analyses

Young's modulus and Poisson's ratio were expressed as means ± standard error (SE). One-way

Analysis of Variance (ANOVA) was applied to ascertain significant differences among means at P

< 0.05 level of significance using JMP 9 software (SAS Institute Inc., Cary, NC., U.S.A.).

RESULTS AND DISCUSSION

Attributes of Cylindrical Samples

Japanese radish sample temperature changes measured from pre-formed cylinder centers and

water content during boiling in distilled water, 1% and 4% saline solution concentrations are

shown respectively in Figure 3 (A) and (B). Radish internal temperature reached 100 °C in

approximately 10 min (Fig. 3A). Thus, cylindrical samples at each 1 min stage within the total 10

min boiling duration possessed different thermal conditions, which would influence the elastic

properties of vegetable tissues. Consequently, boiled samples at each boiling interval were rapidly

removed from the distilled or saline boiling water, and cooled in a refrigerator. Results showed the

sample water content remained constant at approximately 94% for up to 10 min of boiling (Fig.

3B). All Japanese radish samples exhibited these attributes under these conditions.

Stress-strain curves derived from formed cylinders of fresh and boiled Japanese radish samples

(cut from pre-formed cylinders), and preliminary Poisson’s ratio at each compressive strain are

provided in Figure 4 (A) and (B), respectively. Young’s modulus was strictly defined for an elastic

object, i.e. Hookean solid or the elastic region of compressive strain. The modulus is the elastic

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range slope value, and was depicted as a linear region in the stress-strain curve, as described above.

These results were determined as the apparent Young’s modulus.[2,3] Consequently, the sample

elastic range needs to be examined. Results showed the linear region of the stress-strain curve

ranged from 0 to approximately 0.03 of the compressive strain (Fig. 4A), and the apparent

Young’s modulus can be calculated from the slope (shown by dashed lines in Fig. 4A). Young’s

modulus for individual samples for each treatment condition was calculated as a slope value from

0 to 0.03 of the compressive strain, and subsequently averaged for the reduplication under the

same treatment conditions. Poisson’s ratio was also calculated from the amount of change in

cylindrical sample shape, measured as a change in pixel number captured in digital images from

before and after sample deformation. Poisson’s ratio standard errors at 0.01 or 0.02 compressive

strains exceeded 0.03 or 0.04 (Fig. 4B). Due to the linear region definition for Young’s modulus

calculation and Poisson’s ratio errors, 0.03 of the compressive strain was applied to Poisson's ratio

measurement in this study.

Changes in Young’s Modulus and Poisson’s Ratio during Boiling

Changes in Young’s modulus and Poisson’s ratio from formed cylindrical Japanese radish and

carrot samples during boiling in distilled water are depicted in Figure 5 (A) and (B), respectively.

Young’s modulus in Japanese radish decreased rapidly (within 2 min) from approximately 1.8 to

0.3 MPa. Following 10 min of boiling, no significant difference (P > 0.05) in Young’s modulus

was detected at approximately 0.1 MPa, which indicated the samples had reached a stable state.

Poisson’s ratio for Japanese radish decreased from approximately 0.40 to 0.33 within 8 min, and

reached stability after boiling for 8 min. Changes in Young’s modulus for carrot showed a sudden

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decrease from 3.0 to 0.5 MPa within 2 min, and the modulus stabilized at approximately 0.1 MPa

after boiling for 15 min. Carrot modulus values exhibited slight increases compared to Japanese

radish, although a consistent trend was not observed. Poisson’s ratio in carrot, which was less than

the Japanese radish ratio, exhibited a decreased tendency from approximately 0.35 to 0.23 during a

15 min boiling period. This result indicated the volume reduction in carrot tissue against

compression was greater than in Japanese radish.

The pre-formed cylinder center temperature increased to approximately 40 °C within 2 min of

boiling (Fig. 3A), however Young’s modulus exhibited a rapid decrease, which indicated the

tissues softened during treatment. Typically, vegetable tissue softening during boiling is

associated with elution and/or pectin degradation in the cell wall.[13] In contrast, Poisson’s ratio

changes showed degree level decreases up to an approximately 10 min boiling duration.

Tamura[14] concluded that physical tissue structure, including the xylem parenchyma primary cell

wall matrix was changed to a sponge-like structure by boiling, and a pectin elution from the cell

wall was increased during boiling. These observations suggested Poisson’s ratio was reduced

during boiling with decreased Young’s modulus, although the effect would be species-specific i.e.

varies among different taxa.

Changes in Elastic Properties during Boiling in Saline Solutions

Changes in Young’s modulus and Poisson’s ratio for cylindrical samples during boiling in distilled

water, and 1%, 2%, and 4% saline solution concentrations are depicted in Figure 6 (A-D). Young’s

modulus for Japanese radish (Fig. 6A) and carrot (Fig. 6B) boiled in saline solutions rapidly

decreased, and saline results were significantly less (P < 0.05) than distilled water values from

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each boiling interval. In particular, 1 min of boiling was approximately 0.1 MPa, which remained

at a stable level for over 10 min of boiling in distilled water. Tamura et al.[15] and Fuchigami et

al.[16] conducted sensory tests, and reported that boiling in less than 1% saline solution resulted in

softer vegetables. In the present study, the samples boiled in 2% and 4% saline solutions should

therefore show a rapid decrease in Young’s modulus values. Congruent with Young’s modulus,

saline effects on Poisson’s ratio (Fig. 6C, D) were significant (P < 0.05) following less than 4 min

of boiling. The ratios calculated based on boiling in saline solution were less than the ratios

derived from boiling in distilled water. In addition, consistent with Young’s modulus results,

differences among concentrations were not detected. These results showed increased tissue

reduction following boiling in a saline solution; however the samples treated in 1%, 2%, and 4%

salt concentrations exhibited no significant change in tissue volume.

CONCLUSIONS

Sample deformation from all directions, including plastic range against compression must

typically be considered. However, the present method exhibits utility in evaluating the elastic

properties of boiled and softened foods. The results of this study indicated Japanese radish was

softer than carrot under the same boiling conditions; however Japanese radish volume showed

decreased reduction against compression compared to carrot samples. In terms of the eating

attributes of these two root vegetables after boiling, carrots should be more easily swallowed than

Japanese radish under the same cooking conditions, if the root vegetables become fragments

following mastication. Future research will involve ascertaining temperature dependency by

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mathematical modeling for a complete assessment of the elastic properties of softened food

materials. Differences among varieties of the same vegetables will also be reported.

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Figure 1 Schematic diagram of the sample forms.

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Figure 2 Elastic sample deformations and digital image capturing.

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Figure 3 Changes in temperature (A), and water content (B), of cylindrical samples of Japanese radish during boiling in distilled water, and 1% and 4% saline concentration solutions.

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Figure 4 Stress-strain curves for raw and boiled Japanese radish samples (A), and Poisson’s ratio at each compressive strain for raw samples (B) (n = 6).

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Figure 5 Changes in Young’s modulus and Poisson’s ratio in Japanese radish and carrot during the boiling period (n = 6). n.s. Indicates no significant differences; P > 0.05.

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Figure 6 Changes in Young’s modulus (A, B), and Poisson’s ratio (C, D) in Japanese radish and carrot during boiling in distilled water, and 1%, 2%, and 4% saline concentration solutions (n = 6). * Indicates significant differences, P < 0.05.

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