Measurement Methods and Coefficient Determinations for Porosity, Bulk Density, and Volume Reduction During Drying

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Porosity, Bulk Density, and Volume Reduction During Drying: Review of Measurement Methods and Coefﬁcient Determinations

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Porosity, Bulk Density, and Volume Reduction During Drying: Review of Measurement Methods and Coefficient Determinations

Jun Qiu, Seddik Khalloufi, Alex Martynenko, Gerard Van Dalen, Maarten Schutyser & Cristhian Almeida-Rivera

To cite this article: Jun Qiu, Seddik Khalloufi, Alex Martynenko, Gerard Van Dalen, Maarten Schutyser & Cristhian Almeida-Rivera (2015) Porosity, Bulk Density, and Volume Reduction During Drying: Review of Measurement Methods and Coefficient Determinations, Drying Technology, 33:14, 1681-1699, DOI: 10.1080/07373937.2015.1036289

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Review Article

Porosity, Bulk Density, and Volume Reduction During Drying: Review of Measurement Methods and Coefficient Determinations

Jun Qiu,

^1,2

Seddik Khallouﬁ,

¹

Alex Martynenko,

³

Gerard Van Dalen,

¹

Maarten Schutyser,

²

and Cristhian Almeida-Rivera

¹

1Unilever R&D, Vlaardingen, The Netherlands

2Agrotechnology & Food Sciences, Wageningen University, Wageningen, The Netherlands

3Dalhousie University, Halifax, Nova Scotia, Canada

Several experimental methods for measuring porosity, bulk density, and volume reduction during drying of foodstuffs are available. These methods include, among others, geometric dimension, volume displacement, mercury porosimeter, micro-CT, and NMR.

However, data on their accuracy, sensitivity, and appropriateness are scarce. This article reviews these experimental methods, areas of applications, and limits. In addition, the concept of porosity, bulk density, and volume reduction and their evolution as a function of moisture content during drying are presented. In this study, values of initial porosity (e0) and density ratio (b) of some food products are summarized. It has been found that e₀is highly dependent on the type of food products, whilebranges from 1.1 to 1.6. The possibility of calculating solid density based on food compositions has also been validated. The inter-predictions between porosity, bulk density, and volume density have been made mathematically evident.

Keywords Collapse; Density; Modeling; Porosity; Shrinkage;

Volume reduction

INTRODUCTION

Drying is one of the oldest food processing technologies used to preserve food products and increase their shelf-life by reducing the moisture content and microbiological activity.^[1,2] During drying processes, food products undergo various structural and morphologic changes.

These later changes can be depicted by shrinkage and collapse phenomena as shown in Fig.1.^[3]The composition of food matrixes can be divided into three parts: (1) water; (2) dry material; and (3) air. During the drying process, the volume of the food may change due to the shrinkage and=or collapse phenomena. It is possible that all the

volume of the removed water is replaced by air and the initial air, represented by initial porosity, does not disap- pear. In this case, neither shrinkage nor collapse occurs and the volume of the food keeps constant. However, whenever shrinkage and=or collapse phenomenon occurs, the food volume will decrease.

The shrinkage and=or collapse phenomena of food matrixes, experienced during drying, have direct impact on volume reduction, bulk density, and porosity of food products. These modifications of the material structures can sig- nificantly influence the process performance; e.g., drying rate and mass and heat transfers.^[4]They are also of impor- tance to food quality and therefore have significant impact on the consumer’s choice.^[2,3] For example, volume reduction of the dried samples can negatively impact the per- ception of dried products. Indeed, products with low bulk density are characterized by: (1) high volume and therefore the impression of a large amount for the same mass; and (2) floating on the water surface, which makes the product visible to the consumer. With respect to porosity, there is a correlation between high porous products and good rehydration kinetics. Furthermore, porosity has a significant effect on mechanical, textural, and quality characteristics of dried products.^[5] Therefore, optimization of these parameters is required for drying technologies.

Different experimental methods are applied to measure porosity, bulk density, and=or volume reduction.^[6]

Mercury porosimeter, gas penetration methods, and pycnometer are the most commonly used methods to measure porosity.^[7–11]Density and volume reduction can be determined by gas, liquid, or solid pycnometers. These technologies have limitations of low accuracy and=or low sensitivity.^[5,7,12] To overcome these drawbacks, modern imaging technologies (i.e., Scanned Electronic Microscopy (SEM), Confocal Scanning Laser Microscope (CSLM), Correspondence: Seddik Khallouﬁ, Unilever R&D, Olivier van

Noortlaan 120, 3133 AT Vlaardingen, The Netherlands; E-mail:

seddik.khallouﬁ@unilever.com

Color versions of one or more of the ﬁgures in the article can be found online atwww.tandfonline.com/ldrt.

Drying Technology, 33: 1681–1699, 2015 Copyright#2015 Taylor & Francis Group, LLC ISSN: 0737-3937 print=1532-2300 online DOI:10.1080/07373937.2015.1036289

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and X-ray micro tomography (micro-CT)) were developed.

However, these methods are expensive and require special equipment and skills.^[5,13–16]

Another alternative is using models to predict porosity, bulk density, and=or volume reduction as a function of moisture content.^[2,17–22] Several empirical models have been reported by Lozano et al.,^[23]which resulted in good ﬁtting of the experimental data. However, the limitation of empirical models is that they are highly dependent on products, drying technologies, and drying conditions and the ﬁtting parameters do not have physical meanings.[3,4,24,25]

Therefore, it was suggested to build theoretical models, based on the understanding of the fundamental phenomena and mechanisms involved during drying. An important difference between theoretical and empirical models is that the ﬁtting parameters from theoretical models have physical meaning. Some theoretical models have been reported by Zogzas et al.^[22] and Rahman.^[24] However, these models are not in agreement with the experiment, where porosity has inversion points.^[1]

Recently, improved models of porosity, bulk density, and volume reduction, as well as their internal relationships, were developed.^[1,3,17] It is suggested that relationships can be expressed by initial porosity and density ratio, shrinkage, and collapse functions. To reduce the number of ﬁtting parameters, initial porosity and density ratio can be obtained from the open literature.

The purpose of this article is threefold: (1) to summarize different methods of measuring porosity, density, and=

or volume reduction; (2) to present the mathematical relationships between porosity, bulk density, and volume reduction; (3) to gather the values of initial porosity e0

and density ratio b of some food products available in the open literature.

LITERATURE REVIEW Density

Deﬁnition

The density of a substance is the ratio between the mass (kg) divided by the volume (m³) of the same mass. Some- times, this density is also called the volumetric mass density. As shown in Fig. 1, the food matrix consists of water, dry material, and air.^[3] The dry material includes proteins, fats, carbohydrates, and ash. Depending on the structure and the composition of the material, three types of densities can be used to characterize the food matrixes:

bulk, particle, and solid density.^[26]

Bulk Density

The bulk density, also known as the apparent density, is deﬁned as the ratio between the total mass and the total volume of material, including air and water:

q_b ¼m_wþm_sþm_a VwþVsþVa

ð1Þ wheremw,ms, and maare mass of water, dried solid, and air respectively.Vw,Vs, andVaare volume of water, solid, and air within food matrix, respectively. As the mass of air can be neglected in comparison to solid and water fraction, Eq. (1) can be simpliﬁed:

q_b¼ m_wþm_s VwþVsþVa

ð2Þ Depending on the number of particles involved in the calculation (Eq. (1)), bulk density can be classiﬁed into two types: bulk density of a single particle and bulk density of several particles. For the former, only one particle is involved and the total volume includes the solid volume, water volume, and internal pore volume of a particle (Fig. 2(A)). Therefore, in the case of a single particle, the bulk density is an intrinsic property of the material. In calculation of bulk density of several particles, the total volume includes the volume of solid, water, and internal pores of all particles, and the inter-particle void volume (Fig.2(B)). In the case of several particles, the bulk density is not an intrinsic property of the material since it depends on the size and shape of the container. In this article, only the bulk density of a single particle will be considered.

Particle Density

The particle density is deﬁned as the ratio of the matrix mass to its volume excluding the volume of air ﬁlling the open pores. The particle density can be expressed as:

q_p ¼ mwþms

VwþVsþVclosedpores

ð3Þ

FIG. 1. Explanatory chart of shrinkage and collapse phenomena of food matrixes during drying processes (adapted from Khallouﬁ et al.^[3]).

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Solid or True Density

The solid density, also known as true density, is the ratio of matrix mass to its volume, excluding both the volume of water and air. When measuring the volume of solids, matrixes should be ground small enough to guarantee that no open and closed pores of air remain.^[1,22,27] The expression of dried solid density is:

q_s¼ms

V_s ð4Þ

Methods of Measuring Density

The density can be determined by measuring both mass and volume of the samples. Mass is the weight of a sample and can be determined by an analytic balance. Volume can be determined by various experimental methods, depending on the kind of density needs to be measured.

Table1summarizes commonly used methods of measuring volumes and densities of food products. The challenge of density measurement is how accurate the volume is determined. In the following, we will present the main techniques of volume measurements.

Geometric Dimensions

Bulk density can be determined by measuring the volume of sample including water and air (Eq. (1)). The easiest and cheapest method is the geometric dimension method with digital micrometer (calliper). If the sample has a regular geometric shape, its characteristic dimensions can be measured to calculate the volume (Fig. 3). In the case of foods, this method is not accurate enough due to the irregular shape of the samples. Some food products (e.g., cherry tomatoes) can be represented by geometric shapes (i.e., spheres), but their shapes are not always

regular (Fig. 4). Indeed, although some food products could have a regular shape when they are fresh, during drying processes the volume reduction is most likely to be non-homogeneous (Fig. 5). One reason for the non- homogeneous shrinkage could be the tissue and air distribution within the food matrixes (Fig.6).

Volumetric Displacement

Another method for measuring bulk density is the volumetric displacement method.^[5] Two options can be discussed. In the ﬁrst option, the volume of the sample can be determined by quantifying the volume of solid or liquid displaced by samples^[12] (Fig. 7(A)). In the second option, Archimedes principles are applied to calculate the density when sample weight is measured sequentially in the air and liquid (Fig. 7(B)). The bulk density can be calculated as a function of the sample weight in air and in liquid by using the density of the liquid (Eq. (5), Table 1). This method is easy, fast, and cost-effective.

However, its disadvantage is that the immersion liquid, usually toluene, heptane, or mercury, is toxic. Further- more, there is a possibility of extracting substrates of the sample, which could result in ampliﬁcation of the error.^[5]

It is noted that if the liquid is applied, measurements should be made as quickly as possible to avoid liquid uptake by samples. The samples can also be covered by wax to prevent liquid absorption.^[7] However, in certain cases the shape of the sample is not easy to cover (e.g., food products) and the thickness of the wax can affect the measurement.

The volumetric displacement method is also commonly used to measure particle density. In contrast, the sample should not be waxed to account for the space occupied by open pores. The presence of air bubbles in the sample or the immersion liquid during measurement can lead to errors.

FIG. 2. Difference between two kinds of bulk density: (A) bulk density of a single particle, (B) bulk density of several particles.

POROSITY, BULK DENSITY, AND VOLUME REDUCTION 1683

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TABLE1 Methodsofmeasuringvolumes(usedfordensityand=orvolumedeterminations) MethodsPrincipleAdvantagesLimitsCommentsReference Geometric dimensionIfthesamplehasaregulargeometricshape,its characteristicdimensionscanbemeasuredto calculatebulkvolumeandbulkdensity.

Easytooperate; minimalcost;fastNotvalidforsampleswith irregularshapesandporesNotapplicablefor majorityoffood products(irregular formsand non-homogeneous shrinkagesduring dryingprocesses)

[7] Archimedeslaw (Buoyantforce)Sampleweightsaremeasuredinairandliquid, respectively.Buoyantforcecanbedeterminedby Archimedeslawandtheparticledensityis calculatedfrom qparticle¼qliquidminair minairminliquid

Easytooperate; minimalcost;fast1.Measurementshouldbe madeasquickaspossible topreventthepossible exchangebetweensamples andliquid. 2.Liquidwithalowerdensity thansamplesisneededto preventpartialﬂoating, usuallytolueneorheptane, whicharetoxic. 3.Bulkdensitymeasurements requiresurfacewaxing.

Formeasurementsofbulk andparticlevolume= density

[5,7,12,42] Liquidpycnometer (liquid displacement)

Samplevolumesequalstothevolumeofliquid displaced.Easytooperate; minimalcost;fast1.Measurementshouldbe madeasquickaspossible topreventthepossible exchangebetweensamples andliquid. 2.Liquidwithalowerdensity thansamplesisneededto preventpartialﬂoating, usuallytolueneorheptane, whicharetoxic. 3.Bulkdensitymeasurements requiresurfacewaxing.

Formeasurementsofbulk andparticlevolume= density

[5,7,12]

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SoliddisplacementAvialfullwithglassbeads: qbead¼mvialþbeadmvial Vvial Thenthesamevialfullwithsampleandglassbeads: Vsample¼mvialþbeadmvialþsampleþbeadmsample qbead

Preventthepossible exchange betweensamples andmeasuring mediums

.Formeasurementsofbulk volume=density[12] GaspycnometerByusingtheperfectgaslaw,thevolumeofthe sampleisdeterminedby: Vsample¼VVP1P2 P2 Visthevolumeofthetank. P1isthegaspressureoftheemptytank. P2isthegaspressureofthetankwithsamples.

Accurate measurement1.Forsolidvolume measurements,samplesare neededtobegroundsmall enoughtoremoveallclosed pores. 2.Ittakestimetoreach equilibriumpressure. 3.Itneedsprecisecalibration.

Formeasurementsof particleandsolid volume=density.Helium isappliedduetoits smallmolecular diameters,whichallows accesstoporeswith smallsizes

[5,7,29] ImagingUseacameratorecordtheimagesofthesampleand applyimageanalysistoestimatethevolumeofthe sample. Someassumptionaremade: 1.Theshapeofthesamplesisregular. 2.Theshrinkageofthesamplesisregular.

1.Monitoringbulk shrinkageprocess duringdrying. 2.Observingthe immediate shrinkage Imagesofthesampleare2D, whichcannotshowthe3D shapeofthesample.

Notapplicablefor majorityoffood products(irregular formsand non-homogeneous shrinkagesduring dryingprocesses)

[20]

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Digital Camera

The camera monitoring method is a relatively new method to measure the volume of the sample and then calculate the bulk density.^[28]One beneﬁt is that it can record the volume reduction of the sample in real time and show details of its morphology change. Because the image taken by a camera is 2D rather than 3D, some assumptions should be made before obtaining the sample volume:

(1) the shape of the samples is regular; (2) the shrinkage of the samples is homogenous.^[16,20] However, the shape of food products cannot be that regular and non- homogeneous shrinkage is likely to occur because of the irregular distribution of air and tissue within the food product towards the end of drying (Figs. 5 and 6).

If samples cannot fulﬁll the two requirements, the errors could be high.

Gas Pycnometer

Gas pycnometer is another option for measuring particle density or, more accurately, the particle volume (Fig. 8). The tested sample is placed in Tank 2 and a transducer is used to measure the pressure. Air is supplied into Tank 1 when Valve 2 is closed. Then Valve 1 is closed, and the pressure P1 is read by transducer.

After that, Valve 3 is closed and Valve 2 is open, and pressure P2 is read. The volume of the sample can be calculated by Eq. (6), shown in Table1. Usually, helium is applied due to its small molecular diameters, which allow access to the pores with small sizes.^[5] However, it requires very precise calibration. Another drawback is that it needs time to reach the equilibrium pressure.

Not allowing sufﬁcient time for the sample to reach equilibrium will result in errors.^[5,7,29]

Solid density can be obtained by the same methods as measuring particle density. It should be noted that the sample has to be totally dried and ground small enough to guarantee that no open and closed pores of air remain.^[22,27]

FIG. 3. Measuring geometric dimensions of food by digital micrometer (calliper).

FIG. 4. Example of irregular shape of fresh product: cherry tomatoes and soy beans.

FIG. 5. Example of non-homogeneous volume reduction during drying.

Photos and micro-CT images of fresh and air-dried cylinders of carrot with a diameter and length of about 10 mm.

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Mercury Porosimeter

This is the only method to measure particle density of wet and semi-dried samples, because mercury is a non-wetting liquid. Due to its high surface tension, mercury is not able to penetrate pores smaller than six micrometers in diameter, which requires additional pressure. The porosity and pore size are determined from applied pressure and Washburn equation in the assumption that pores are cylindrical.^[30–32]

Estimation of Solid Density

Based on the composition of food matrixes, it has been reported that the solid density can be estimated by using the following expression:[1,5,21,27,33]

1

q_s¼X^Yi_q

i ð7Þ

FIG. 6. Tissue and air distribution within fresh courgette (zucchini) imaged using micro-CT showing the volume rendering of air in blue (box¼5mm5mm5 mm) and a gray level image of a radial cross-section of the tissue from skin to skin (length: 51 mm; width: 14 mm).

FIG. 7. Explanatory chart using volumetric displacement method to measure volume and density.

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in whichqiis the density of theithcomponent in the matrix andYiis the mass fraction of theithcomponent on the dry basis. This equation was ﬁrst used to predict the density of liquid at a constant pressure. Therefore, one fundamental assumption behind Eq. (7) is that the intracellular pressure does not vary with concentration of components and permeability of cell membranes.^[5] According to the published data, most food products have dried solid density between 1 400 kg=m³and 1 500 kg=m³, as the solid constituents are fairly similar.^[33]

Table 2 summarizes the density of the main dried food constituents, which were reported in the open literature. In this study, in order to simplify the calculations, the average values of the densities of protein, fat, carbohydrate, and ash were applied and the calculated results are shown in Table3.

It can be seen that, for most food products, their dried solid densities lie between 1,390 kg=m³ and 1,550 kg=m³, which is in agreement with the statement of Lewis.^[33]

Table 3 also shows the composition of different fresh food products and their solid densities reported in the open literature. By comparing calculated densities (Eq. (7)) and the reported data for carrots and apples,[2,22,23,34]

signiﬁ- cant differences could be noted. The following reasons could explain this discrepancy:

1. The model used to estimate the solid density does not consider the intracellular pressure, which varies as a function of the component concentration and the permeability of the cell membranes. This may make the calculated density a little different from the real value.

2. The reported data, although for the same products (e.g., carrots, apples), do not consider possible effect of the variety, ripeness, and heterogeneity of the product.

Furthermore, experimental errors can also be related to the research methodology (e.g., sample selection, part of the samples, etc.).

Hence, the deviation of the density within 10% could be considered acceptable. If this is the case, Eq. (7) could be

suggested as a fast and reliable tool for estimating dried solid density of different food products.

Porosity

Porosity is an important parameter, which signiﬁcantly impacts both heat and mass transfers during the drying process and rehydration. It is deﬁned as the ratio of the volume of air (void) to the total volume of the food matrix.

Porosity can be calculated from bulk and particle density:

e¼1q_b

q_p ð8Þ

Non-Imaging Methods of Measuring Porosity

There are several methods of measuring porosity, which can be classiﬁed as direct or indirect.^[35]Considering direct methods, the porosity can be measured directly by certain devices; i.e., a mercury porosimeter. In terms of indirect methods, the information of the geometry and=or size distribution of the pores is obtained and used to calculate

TABLE 2

Density of the main dried food constituents

Constituents Source

Density

(kg=m³) Reference

Protein – 1,300 [63]

b-Lactoglobulin 1,247 [64]

– 1,400 [33, 58]

– 1,320 [65]

Fat Soybean oil 891– 919.3 [66, 67]

Castor oil 906 [67]

Canola=rapeseed oil

914–917 [68]

Olive oil 910 [33, 58]

Palm oil 889.9 [68]

Meat (tallow) 900 [33, 58]

– 900–950 [58]

– 930 [63]

– 917 [65]

Carbohydrate Cellulose 1,270–1,610 [33, 69]

Starch 1,550 [70]

Sucrose 1,590 [33, 69]

Glucose 1,560 [58]

Hemicellulose 1,520 [71]

Fructose 1,694 (1)

Lactose 1,525 (2)

– 1,350 [63]

– 1,593 [65]

Ash – 970 [63]

– 2,418 [65]

FIG. 8. Explanatory chart using gas pycnometer to measure volume and density.

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porosity; i.e., 3D images from X-ray micro tomography.^[35]

The majority of the methods are summarized in Table4.

Pycnometer

According to the data available in the open literature, it is found that pycnometer is the most commonly used device to

measure food porosity (Table5). Bulk and particle volume measured by a pycnometer are used to calculate bulk and particle density, respectively. Equation (8) is applied to calculate the porosity.^[35] Compared to the gas penetration method or X-ray microtomography, the pycnometer is fas- ter, cheaper, and easier to operate without special skills.

TABLE 3

Solid density of some food products Composition (wet basis %) qs(kg=m³)

Reference Protein

Yp

Lipid Yl

Carbohydrate Yc

Ash Ya

Estimated values (Eq. 7)

Published values

Product Reported Experimental

Meats Beef

Sirloin, lean 20.64 4.54 0.71 0 1 295.8 1 100–1 117 1 100.9 (1) [27, 72, 73]

Brisket 15.6 25.9 0.6 0 1 085.2 – – [74]

Chicken 18.6 15.06 0 0.79 1 103 – 1 220 (1) [75, 76]

Fishes

Squid 15.46 0.18 0.8 1.06 1 356.4 1 451 – [27, 77]

Tuna 23.33 4.9 0 1.18 1 391.3 1 319 – [27, 76]

Fruits

Apple 0.19 0.36 15.25 0.27 1 544.4 1 650 () – [2, 22, 23, 34, 76]

– 1 540 (2)

– 1 510 (1)

Banana 1.03 0.48 23.4 0.83 1 528.3 – 1 497 (1) [19, 78]

– 1 920 (3]

Pear 0.7 0.4 15.3 0.4 1 513.7 – 1 473 (1) [2, 23, 27, 78]

1 460 –

Quince 0.4 0.4 15.3 0.4 1 552.9 – – [76]

Vegetables

Carrot 1.03 0.19 10.14 0.85 1 488.9 – 1 750 (1) [2, 19, 22, 23, 76]

– 1 530 (1)

– 1 610 (1)

Potato 1.6 0.1 22.6 1 1 533.5 – 1 316 (1) [22, 23]

– 1 540 (1)

– 1 617 (1)

Garlic 6.3 0.1 29.8 1.8 1 507.4 – 1 383 (1) [2, 23, 78]

Pumpkin 1 0.1 6.5 0.5 1 547.3 1 533 – [27, 76]

Grains

Wheat kernel 16 3 70 2 1 314 1 453 () – [33, 63, 79]

1 423.5–1 454.9 –

Rice 9.09 1.2 80.2 0.07 1 520.3 1 400–1 438.2 () – [33, 80, 81]

– 1 504 (1)

Beans

Pea 6.3 0.4 14.4 0.9 1 473.7 1 284.57 () – [27, 82, 83]

1 368– 1 427 –

(1): Gas pycnometer.

(2) Archimedes law (Buoyancy force method).

(3) Liquid pycnometer.

(): Extracted from model.

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TABLE4 Methodsofmeasuringporosity MethodsPrincipleAdvantagesLimitsCommentsReference MercuryporosimeterThepressure,whichisrequiredto forcemercuryintopores,andthe poresizesfollowstherelationship: p¼2ccosh r p:imposedpressure(MPa) c:surfacetension h:contactangle r:radiusofthepore(nm). Knowingpressure,surfacetension andcontactangle,theradiuscan becalculated

1.Poresizedistributioncanbe obtained. 2.Simpleexperimentalprotocol andstraightforwardmethod 3.Widerangeofporessizes (0.04–100mm).

1.Notaccurate 2.Anempiricalmodelisrequired torepresentporousmediums. 3.Poresareassumedtobe cylindrical(veryfewreal materialsfulﬁllsuch requirements). 4.Samplescannotbeusedfor furthertestaftermeasurement. 5.Highpressuremaydestroy samples. 6.Thecostofmeasurementis relativehigh. 7.Mercury(Hg)istoxic.

Mercuryporosimeter isthemost commonlyused methodtomeasure porosities.

[7–11] GaspenetrationmethodSimilarasmercuryporosimeter.1.Thismethodisreproducible. 2.Thelowoperationpressure allowsprobingverysmall poreswithoutsigniﬁcant structuraldestructive.

1.Ittakestimetoreach equilibriumpressure. 2.Itneedsveryprecisecalibration.

[35] Isotonicsolution penetrationThesampleisimmersedinisotonic solutionundervacuumpressure P1andthenunderatmospheric pressureP2.Porositycanbe calculatedfromthemodel: e(k1)¼(XU)kþU1 X:m3 impregnatedsolution=m3 initialsample k:compressionrate(P2þPc)=P1 U:Volumedeformationduringthe experiment(m3=m3initialsample) U1:Volumedeformationduringthe vacuumstage(m3 =m3 initial sample)

Masstransfercanbeavoidedby usingisotonicsolution.Closedporescannotbedetected.[36,37]

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Pycnometer=Apparent densitymethodThebulkvolumeandparticle volumeofthesampleare measuredbypycnometeras discussedinTable1.Theparticle densityandbulkdensityofthe samplearecalculatedrespectively. Theporositycanbecalculated fromEq.(8).

Fast Cheap Easytooperate 1.Notaccurate. Errorsexistsinmeasuringboth bulkandparticledensities. 2.Notsensitivetolowporosities.

Whenmeasuringbulk densityofthe sample,waterproof treatmentis required.

[35] ScannedElectronic Microscopy(SEM)Theelectronsinteractwithatomsin thesample,producingvarious signalsthatcanbedetectedand thatcontaininformationabout thesamplesurfacetopography andcomposition. Thesizeoftheporescanbe measuredfromthe2Dimages

Itiseasytoobtainthesurface porosity.1.Expensiveequipment. 2.Noinformationaboutthethird direction(only2D). 3.Becausethestructureofthe sampleissigniﬁcantlydifferent, itsbulkporosityisquite differenttoobtained. 4.Qualitativemethod. 5.SEMisavacuumtechniqueand requiresextensivedryingofthe samples.

[35] X-raymicrotomography (micro-CT)Thistechniqueisbasedonthe attenuationofX-rayswhen travellingthroughasample.The sampleisscannedbyX-raybeam. Alargeamountof2DCTslice imagesareperformedwhilethe sampleisrotatedfrom0to 180.Theskeletonofthesampleis extractedbyreconstructionsof thesamplefrom2Dimagesanda 3Dimageisgenerated. Informationofporespace;i.e., volume,shape,distribution,can bedetectedfromthesample skeleton.Thetotalvolumeofthe sampleisalsoshowninthe3D image.Theporositycanbe calculatedby: e¼Vair Vtotal

1.Non-destructivemethod Afterscanningbymicro-CT,the sampleisintactandcanbe usedforfurthertest. 2.Micro-CTprovidesa 3-dimensionimageofthe sample,whichismuchcloser totherealsituation.

1.Aspecialexpensiveinstrument isrequired. 2.Specialsoftwareskillsare requiredforanalyzing.

[5,13–16]

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TABLE 5

Initial porosity of some food products

Product Initial porosity % Measuring method Reference

Meat

Beef 1.28 Pycnometer [84]

Fish

Tuna 0 Pycnometer [27, 85]

Fruit

Apple 25 Pycnometer [21]

11.6 Gas pycnometer [19]

21.7–28.6 X-ray microtomography [15]

Pear 2.92 Pycnometer [86]

8.9 Pycnometer [23]

3.4 Isotonic solution penetration [27, 36]

Quince 6.9 Pycnometer [18]

Banana 7.4 Gas penetration [19]

Apricot 2.2 Isotonic solution penetration [36]

Mango 5.9 Isotonic solution penetration [36]

Kiki 0.7 Isotonic solution penetration [36]

Peach 4.7–9.1 Isotonic solution penetration [36]

Plum 3.7 Isotonic solution penetration [36]

Strawberry 6.4 Isotonic solution penetration [36]

Cranberry 35–40 Gas pycnometer (Martynenko, in press)

Vegetable

Carrot 0.3 Pycnometer [87]

2.8 Gas penetration [19]

15.2 Pycnometer [23]

11.7–15.7 Isotonic solution penetration [36]

Potato 3.5–6.5 Pycnometer [88]

3.1 Gas penetration [19]

4.9 Pycnometer [23]

Pumpkin 14.7 Pycnometer [89]

Beetroot 6 Pycnometer [87]

3–5.6 Gas penetration [36]

Eggplant 59.6 Pycnometer [87]

Mushroom 37 Pycnometer [87]

34–37.8 Isotonic solution penetration [36]

Zucchini 18 Pycnometer [87]

Garlic 12–14.7 Pycnometer [23]

Grain

Rice 45–49 Pycnometer [27, 90]

Wheat 41–65 Pycnometer [27, 63]

Bean

Chick pea 44–45.9 Pycnometer [27, 91]

Lentil 27.5 Pycnometer [92]

Herb

Ginseng 3.3 Calculated from Eq. (17) [20]

1692 QIU ET AL.

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Compared to the mercury porosimeter, the pycnometer allows the food sample to be reused for further drying, which can provide information about porosity as a function of moisture content for the same sample. However, the unavoidable experimental errors during measuring of both bulk and particle densities make this method inaccurate and not sensitive enough to capture low porosity values.

Isotonic Solution Penetration

Another alternative method is isotonic solution penetration. The sample is weighted in the air and then immersed into isotonic solution under vacuum. After that, atmospheric pressure is restored and the sample is kept immersed for a while. During the impregnation, volume change of the sample is recorded. After the experiment, the sample is weighted. Porosity is calculated by Eq. 10 (Table 4). This method can avoid mass transfer between the sample and liquid by using isotonic solution.^[36,37]

Mercury Porosimeter

The mercury porosimeter is also very popular (Table5).

In addition to measuring porosity, the mercury porosimeter permits direct assessment of the product pore size distribution.^[10]It is relatively sensitive to probe pores with small sizes. However, an empirical model (Eq. (9), Table4) is required to represent the porous medium, which makes the measurement not very accurate since not all pores of the sample fulﬁll the assumption. Also, because it needs to be operated under high pressure, it is not suitable for some food products with soft textures which might be destroyed during measurement.^[10]

Imaging Methods of Measuring Porosity

Some imaging techniques, such as SEM and micro-CT, can provide images of the samples, which are much closer to the real situation.^[16]However, their drawback is that a special expensive instrument=equipment and special software skills are required for analyzing.^[5] In the case of SEM, another disadvantage is that having 2D images is not sufﬁcient to extrapolate for the third dimension. In this section, different imaging methods will be discussed.

Scanning Electron Microscopy (SEM)

This method is widely used for porosity determination.^[20,38–42] Visser and Bogemann^[43] determined porosity by cross-section analysis with a hand microtome, which could be expressed as:

e¼100 area of air spaces total cross section area

Error of measurements could be diminished with pretreat- ment of samples and capturing multiple images from inde- pendent samples.^[44] Danaldson et al.^[45] compared SEM

and ﬁeld emission scanning electron microscopy (FESEM), combined with serial sectioning and 3D reconstruction.

As compared to SEM microscopy, FESEM had a greater and wider ﬁeld with high resolution. However, only a combination of SEM and FESEM, combined with advanced image processing, is able to demonstrate both external and internal structure at the nanometer scale, which is suitable for porosity determination.

Confocal Scanning Laser Microscopy (CSLM)

Confocal scanning laser microscopy is a new, non-invasive technology for 3D high-resolution imaging.

It captures in-focus images at the selected depth through a process called optical sectioning. The 3D capabilities of CSLM are limited by the laser penetration depth considering the assay conditions, the sample, and the dye used. For dried apple,^[46] a maximum depth of about 270mm was obtained and an image size of (1.51.5 mm). Fo¨ldes-Papp et al.^[47] found that confocal images add additional z-dimension (optically dissected) to the two-dimensional pictures. As image depth increases, laser attenuation and resolution decrease. However, it is compensated for by con- trolling the illumination frequency.^[48]The epi-ﬂuorescence and the epi-reﬂection modes (surface and topography) are commonly used for imaging.^[49] A computer program makes it easy to analyze and process the images and to reconstruct the sample microstructure, including true morphology and pore distribution.^[50] Du¨rrenberger et al.^[49]

found that CSLM also works with samples in a hydrated state, which makes it possible to determine microstructure changes during drying.

Nuclear Magnetic Resonance (NMR)

Nuclear magnetic resonance is widely used for the measurements of porosity and pore size distribution in multi- scale porous media, like rocks^[51] and coal.^[52] The advantage of NMR is high sensitivity to both inter-particle and intra-particle pores.^[53] The NMR relaxation distribution is scaled by the surface relaxivity parameter, which incorporates a surface area to volume ratio (S0=V0) term to yield a corresponding pore size distribution. As compared to mercury porosimeter and computer tomography, low-ﬁeld NMR allows nondestructive quantiﬁcation of pore size distribution.^[51]Due to the ability to work a wide range of moisture content, NMR was successfully used for biomaterials; i.e., for determination of bone porosity^[54]

and porosity changes during dehydration and rehydration of food biomaterials.^[55] Unfortunately, the high cost of the equipment and specialized software is a limiting factor for the application of NMR in food drying.

X-Ray Microtomography (Micro-CT)

Micro-CT has proven to be a very useful technique for the 3D visualization and measurement of the internal

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microstructure of cellular food products.^[56,57] It can be used for the determination of the shrinkage, porosity, pore and wall size distribution and pore connectivity.

Micro-CT can probe the microstructure of samples non-invasively up to a few millimeters across with an axial and lateral resolution down to a few micrometers.

The contrast in micro-CT images is based on the difference in absorption of X-rays by the constituents of the sample (e.g., water and air). Micro-CT allows observa- tions under environmental conditions without sample- disturbing preparations that are normally used in SEM.

Micro-CT is better suited for quantitative image analysis due to its ability to generate 3D images (e.g., connectivity cannot be analyzed from 2D images) and the better contrast between pores and solid matrix. Also, the physical cutting needed for SEM may lead to damage to the thin walls or induce cracks. The high vacuum may also induce cracks.

Volume Reduction During Drying

In general, during conventional drying, food products undergo volume reduction. When the volume reduction equals the water removed, the shrinkage is total.^[3] On the other hand, there is pore formation if the volume reduction is less than the volume of the water removed.^[2,17,20]The mathematical expression of volume reduction or shrinkage coefﬁcient (Sv) is deﬁned as the following:

Sv¼ V

V₀ ð11Þ

V and V0 are the sample volume during drying and the initial volume, respectively. The volume measurements are performed as described in Table 1.

Mathematical Relationship Between Porosity, Bulk Density, and Volume Reduction

Models to predict porosity, bulk density, or volume reduction as a function of moisture content were reported in the open literature.[2,17,18,21,22,58]

In order to express the possible relationships between porosity, density, and=

or volume reduction, only fundamental models will be discussed in the following sections.

The ﬁrst fundamental model was derived by Madamba et al.^[59] to describe the bulk density as a function of moisture content on the wet basis (W):

q_bðWÞ ¼ q_s

1þðb1ÞW ð14Þ

However, this model was developed in the assumption of negligible close pores and did not account for volume reduction of biomaterials, which signiﬁcantly limited the range of practical applications. Independently, Zogzas et al.^[22]developed a more universal relationship

between particle density and moisture content on the dry basis (X):

q_pðWÞ ¼q_sð1þXÞ

1þbW ð15Þ

This model is applicable for both shrinkable and non- shrinkable biomaterials. It predicts consistent increase of particle density with moisture removal, approaching value of true density (qs) at X¼0. Veriﬁcation of this model was done by Krokida et al.^[19]for apples, potatoes, bananas and carrots and by Boukouvalas et al.^[27]for garlic and onions.

It should be noted that closed pore development at low moisture content could result in deviation of particle density from the theoretical model (Eq. (15)). However, the difference between measured particle density and model prediction could be used to quantify contribution of closed pores to bulk density. Since open and closed pores play sig- niﬁcantly different roles in rehydration of dried material, this information is of great interest to food technologists.

Madiouli et al.^[4]were the ﬁrst to describe the theoretical relationship between porosity and volume reduction. Their model was derived in the assumption of negligibly small closed pore volume.

Expression of volume reduction as a function of porosity:

S_vð Þ ¼X ð1e0Þ 1eð ÞX

ð Þ 1þbX 1þbX₀

ð16Þ

Expression of porosity as a function of volume reduction:

eð Þ ¼X 1ð1e0Þ

S_vð ÞX 1þbX 1þbX₀

ð17Þ This set of equations, ﬁrst established by Katekawa and Silva,^[60] shows a linear relationship between porosity ratio(1e)=(1e0), volume reduction (Sv), and moisture content (X). The governing parameters of the volume reduction are the initial porosity (e0) and the density ratio (b).

Further development of the model of Madiouli et al.^[4]

allowed the establishment of correlations between porosity, density, and volume reduction.^[61] For these relationships, the following expression of the initial porosity was used:

e0 ¼1q₀

q_s 1þbX₀ 1þbX0

ð18Þ Porosity as a function of volume reduction is expressed as Moisture-Shrinkage-Porosity (MSP) correlation^[61]:

eð Þ ¼X 1q₀ q_s

1þbX 1þbX0

1

Svð ÞX ð19Þ

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Porosity also could be expressed as Moisture-Shrinkage- Density (MSD) correlation^[61]:

eð Þ ¼X 1bq_bð ÞX q_s

þq₀ q_s

b1 1þX0

1

Svð ÞX ð20Þ Porosity as a function of moisture and density (MDP- correlation) is derived by excluding volume reduction from Eq. (19)^[61]:

eð Þ ¼X 1q_bð ÞX q_s

1þbX 1þX

ð21Þ This correlation was ﬁrst derived by Katekawa and Silva.^[60]Equations (18)–(21) require only two experimental parameters (e0 and) to calculate porosity or bulk density as a function of moisture content and volume reduction.

Indeed, the density ratio (b) is obtained by knowing the solid density (Tables5and7).

The main limitation of these theoretical models is that none of them takes into consideration the evolution of the initial porosity (initial air) as a function of moisture content. However, some food products, such as eggplant, have very high initial porosity (up to 66%, Table 5).

Neglecting the evolution of this signiﬁcant volume portion during drying would negatively impact the accuracy of the models and limit their use in explaining the mechanism behind the volume reduction and=or the pore formation.

In 2009, the ﬁrst theoretical model taking into account the evolution of this initial air was suggested.^[3] In this model, the relationships between porosity, bulk density, and volume reduction are established, involving initial porosity (e0), density ratio (b), shrinkage function (u(X)), and collapse function (d(X)) (Table6).

The shrinkage function (u(X)) is used to describe the volumetric fraction of water, which is removed during drying and replaced by air. The collapse function (d(X)) is applied to account for the variation of the initial air (e0) within the food matrix during drying. To minimize the number of ﬁtting parameters, onlyu(X) and are considered as ﬁtting functions. Indeed, initial porosity (e0) and density ratio (b) could be taken from available experimental data or calculated from published data, as will be shown in the next sections.

Determination of Initial Porosity of Some Food Products Table 5 summarizes the initial porosities of some food products reported in the open literature. From Table5, it follows that the initial porosity varies in the wide range from 0% to 66%. Some food products (i.e., eggplants) have a high porosity (larger than 50%), and some (i.e., carrots) have a low porosity (lower than 5%). It should be noted that the initial porosities of rice, wheat, and chick pea

are, in fact, bulk porosities, which include porosity between kernels. The porosity of a single kernel is lower than the value showed in Table 5 (data are not presented in this article).

As can be seen from Table 5, the values of initial porosity of the same product can signiﬁcantly differ from one publication to another. This difference may be due to the variety of the samples and=or the variety of measurement methods used in each study. In some cases (for example, for carrots), the difference is large enough even within the same measurement method. This could provide the evidence either that the commonly used porosity measurement methods are not reliable and accurate enough or that the variety and=or ripeness of the crop are critical. Therefore, there is a need for more investiga- tions to understand the reason for the discrepancy in porosity measurements.

Calculation of Density Ratio (b) of Some Food Products Density ratio (b) is another parameter that can be determined before ﬁtting models to experimental data (Table6).

bis a ratio between solid density of a sample and the water density (Tables5and7). It has been reported that the water density varies as a function of temperature^[62]as in the following:

q_w¼

999:83952þ16:945176T7:7987040110³T² 46:17046110⁶T³þ105:5630210⁹T⁴ 280:5425310¹²T⁵

0

@

1 A 1þ16:8798510³T

ð22Þ The water density varies with the temperature, as shown in Fig.9. Although it seems from Fig.9that the temperature has a signiﬁcant effect on water density, the variation is less than 5% within a range of 0 to 100C. In general, initial porosity should be calculated, using value of water density at ambient temperature (1000 kg=m³), while porosity during drying should be calculated, using values of water density, corresponding to the variation of drying temperature.

Dried solid density can be obtained either by experimental measurements or by model predictions. The main components of dried food matrixes are protein, fat, carbohydrate, and ash. If the fraction of each component is known, the solid density can be calculated from Eq. (7).

The results of the calculationbby using the two extremes values of 965 and 1000 kg=m³are shown in Table 7. As can be seen from Table7, the differences between calculated and reportedbare within acceptable ranges, which suggests that the model could be an appropriate tool to calculate solid density and therefore to predict b. For food products, it seems that the values of b lie between 1.1 and 1.6.

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TABLE 6

Mathematical expressions of porosity, bulk density, and volume reduction as a function of moisture content ^[1,3,17]

Model Mathematical expression Comments

Porosity (e)

eð Þ ¼X A Xð Þ þB Xð ÞX C Xð Þ þD Xð ÞX Where:

A(X)¼e0d(X)þX0b[u(X)(1e0)þe0d(X)]

B(X)¼bu(X)[e₀1]

C Xð Þ ¼1e0þe0dð ÞX

þX₀b u½ ð ÞX ð1e₀Þ þe₀dð ÞX D(X)¼b[1e0][1u(X)]

e0is the initial porosity. This parameter can be measured before starting drying

X0is the initial moisture content. This parameter can be measured at the beginning of a drying