Status of Physics-Based Models in the Design of Food Products, Processes, and Equipment

Authors


Abstract

This article is part of a collection entitled “Models for Safety, Quality, and Competitiveness of the Food Processing Sector,” published in Comprehensive Reviews in Food Science and Food Safety. It has been peer-reviewed and was written as a follow-up of a pre-IFT workshop, partially funded by the USDA NRI grant 2005-35503-16208.

ABSTRACT:  Modeling, in particular physics-based modeling, can be an important tool to food product, process, and equipment designers by reducing the amount of experimentation (thus reducing the time and expenses involved) and by providing a level of insight that is often not possible experimentally. Food processes involve unique physics and challenges compared to other types of materials processing such as polymers and ceramics. These include complex multiphase transport and multiphysics that are difficult to implement in the available software, and often drastic changes in material properties during processing for which data are unavailable. Such unique and challenging features have made it difficult to embrace modeling as a tool in the food industry. This article discusses, in the context of design use of models, the nature and the state of modeling of food processes, emphasizing the more complex scenarios in both modeling and material properties needed for the models.

Introduction

A mathematical model is a mathematical analog of the physical reality, describing the properties and features of a real system in terms of mathematical variables and operations. Mathematical models can be classified somewhat loosely, depending on the starting point in making a model, into physics-based and observation-based models, as illustrated in Figure 1. In observation-based models, the starting point is the experimental data from which a model is built. They are primarily empirical in nature. In contrast, the starting point for physics-based models (Figure 2) is the universal physical laws that should describe the presumed physical phenomena. Physics-based models are also validated against experimental data, but in physics-based models the experimental data do not have to exist before the model. Most of the commonly used physics-based and observation-based models in food are discussed in Sablani and others (2007).

Figure 1—.

Examples of physics-based models contrasted with some observation-based models. Among the physics-based models, the continuum (macroscale) models are the most prevalent. Description of observation-based models can be seen in Sablani (2007).

Figure 2—.

Schematic showing the steps in the development and use of physics-based models in food processing.

The phenomenal growth in computing power and its associated user friendliness have allowed physics-based models to be highly realistic by including more and more of the detailed physics, and have fueled rapid growth in the use of models in product, process, and equipment design and research. Advantages of a physics-based model include (1) reduction of number of experiments, thus reducing time and expenses; (2) providing great insight into the process that may not even be possible with experimentation; (3) process optimization; (4) predictive capability, such as ways of performing “what if” scenarios; and (5) providing improved process automation and control capabilities. On the downside, physics-based models are more restricted to the food process itself rather than food quality or food safety because physics-based models require precise relationships between quality/safety and the process parameters, which are generally unavailable. Observation-based models can relate quality/safety to processing parameters more easily as they do not require detailed knowledge of the underlying physical process.

Physics-based models follow from fundamental physical laws such as conservation of mass and energy and the Newton's laws of motion. However, empirical (but fairly universal) rate laws are needed to apply the conservation laws at the macroscopic scale. For example, to obtain temperatures using a physics-based model, we would combine conservation of energy with Fourier's law (which is empirical) of heat conduction. The biggest advantages of physics-based models are that they provide insight into the physical process in a manner that is more precise and more trustable (because we start from universal conservation laws), and the parameters in such models are measurable, often using available techniques. Physics-based models today are less common in food and bioprocessing product, process, and equipment design than in some other manufacturing such as automobile and aerospace. This can be primarily attributed to variability in biomaterials and the complexities of transformations that food and biomaterials undergo during processing. Due to the advantages mentioned earlier, physics-based modeling is often the preferred way to go in the long run.

Like in other areas, physics-based modeling in food started with analytical approaches, with the work in sterilization (Ball and Olson 1957) and dehydration (Crank 1956). Numerical modeling also started with sterilization (Teixeira and others 1969). Until the late 1980s, the work was mostly analytical (for example, see Gekas 1992; Ozilgen 1998). As numerical methods improved together with computer technology, more complicated problems were dealt with. The biggest jump in the use of modeling in food processes came in the mid-1990s with the availability of user-friendly general-purpose computational fluid dynamics (CFD) software. The use of CFD in design is one of the areas in food process engineering that is now experiencing rapid growth (Welti-Chanes and others 2002; Sun 2007). Software to solve simple formulations of processes such as sterilization and drying has become commonplace. However, as we look at the processes in more detail and at less empirical ways, use of commercial software poses several major problems. First, the detailed 1st-principle-based and experimentally validated formulations of more complex processes such as baking are generally unavailable. Second, when the formulations can be made, there are unique aspects of food processes (see Discussion in the next section) that are often not implemented in typical commercial software. Third, when the formulation is available and the software can solve it, we often run into difficulties obtaining the appropriate material properties for specific condition of the food. This article discusses some of these issues as part of the general picture of the state of physics-based modeling of food processes and the development needs.

Characteristics of Food Processes

From the standpoint of modeling materials processing operations, food processing includes (1) complex multiphase heat and mass transfer such as evaporation and multiphase flow as in aseptic processing; (2) multiphysics such as combined microwave or microwave-infrared heating; (3) significant changes in material property during processing; (4) significant dimensional changes and associated physics; (5) considerable variation (batch to batch or within the same material) in material properties due to its biological origin; and (6) unavailability of kinetic data for final variables of interest (quality and safety) as they relate to temperature and moisture.

Characteristics of the User Base

The characteristics of the food-processing sector with regard to the use of models as part of manufacturing and distribution are also somewhat different from that of other industry sectors. It is the quality and microbiological safety issues that are of prime interest in food processing, and the food and biological scientists who are often in charge of these issues in an industrial setting have their training in chemistry and microbiology as opposed to physics-based mathematical modeling. By training, the technical people in the food industry are often more used to observation-based models. Also, food materials are complex and their quantitative studies are much less prevalent than other materials. Finally, modeling has to benefit in areas such as design of new products and processes. Food is generally not a high-value commodity (compared to semiconductors, for example), and the advantages that modeling can bring to other materials processing may not be so substantial in food processing. These factors influence in a significant way the development and use of models in food processing.

Types of Physics-Based Models That Have Been Used in Food

Physics-based models can be divided into 3 scales, molecular, macro, and meso (in between molecular and macro), as illustrated in Figure 1. An example of a physics-based model at the molecular scale is the molecular dynamics (MD) model (Rapaport 2004). Although applications of the MD model of relevance to food processing (such as protein functionality and solution properties of carbohydrates) have been reported (Ueda and others 1998; Schmidt and others 1994), there appears to be very little ongoing work in applying MD to systems of relevance to food processing. In the physics-based models at intermediate or mesoscale are models such as Lattice Boltzmann (LB) that is based on kinetic theory describing the dynamics of large system of particles. Such mesocscale models are also not very common in food processing, although being pursued in colloidal suspensions, polymer solutions, and flow-through porous media (see van der Sman 2007). A mesoscale model is one way to study properties at interface, as in food emulsions and suspensions (see Pugnaloni and others 2005). Macroscopic models are the most common among physics-based models in food. Examples of macroscopic models are the commonly used continuum models of fluid flow, heat transfer, and mass transfer. As we expand food and biological applications at micro- or nanoscale, such as in detection of microorganisms in a microfluidic biosensor, scales will be approached where these continuum models will break down (Tien and others 1998; Gad-el-Hak 2005). Similarly, at very short time scales, continuum assumption breaks down and mesoscale or molecular-scale models become necessary (Mitra and others 1995). It is fair to say that in the near future, macroscale or continuum-based modeling is the most developed in the food applications and has the greatest potential to be integrated into the design process. Table 1 shows a partial list of the food processes already implemented using macroscale or continuum-based models.

Table 1—.  Some food-processing operations and their physics-based model implementation possibilities in commercial software. This is an estimate based on the author's research group's experience with various software and anecdotal information. Capabilities in modeling newer processes improve continuously.
Food processEquations neededModel development using commercial software—current statusSpecial property needs
Mixing, fillingContinuity, momentumPossibleNon-Newtonian parameters
Sterilization of canned solidsEnergy, species (bacteria, nutrients)PossibleTransport property variation with temperature
Sterilization of canned fluids, stationary and rotatingContinuity, momentum, energy, speciesPossibleSame as above, including changes such as gelatinization
Sterilization of continuous flow systems (aseptic processing) with particulatesContinuity, momentum, energy, speciesGenerally not possible, except with major simplifying assumptionsSame as above
Drying and fryingEnergy, multiphase porous media transport equations, except semi-empirical when species equation will do for moisturePossible when simple species equation will do. Difficult or not possible when evaporation effect is significant.Transport property variation with structure and composition (moisture)
Conventional hot air oven designContinuity, momentum, energyPossible 
Microwave and microwave-conventional combination oven designMaxwell's equations, continuity, momentum, energy, radiative heat exchange (when radiative elements are present)Possible only when done separately, that is, Maxwell's equations are solved separate from the rest of the equations. Coupling of Maxwell's equation with others is available in very few software.Dielectric and transport properties
Conventional radiative oven designRadiative heat exchange equationPossibleReflection and absorption properties of food surfaces
Bulk cooling and storage of produceContinuity, momentum (or porous media equations), energyDifficult using existing software except when the bed is treated as a porous mediaPorous media transport properties of stacked produce
Microwave and radiofrequency pasteurization, sterilizationMaxwell's equations, energy, and possibly continuity and momentum equations (when fluid is involved)Possible to solve Maxwell's equations but not coupled with energy or momentum equations (only 1 software claims this capability)Dielectric and transport property variation with temperature
Equipment and processes for ohmic heatingVoltage equation, energy, also momentum and continuity equations when fluid is involved Electrical conductivity as a function of temperature, bulk properties of solid–liquid mixtures
Pulsed electric field processingVoltage equation, possibly energy equationPossible for voltage equation, but coupling with energy can be challengingDielectric and breakdown properties
Sheeting of doughEquation for stress and strain, energyPossibleRheological properties as a function of temperature and shear rates
High-pressure processingEquation for stress and strain, energyPossibleBulk modulus and heat generation from compression
ExtrusionContinuity, momentum, energy, speciesEasier in specialized software such as POLYFLOW due to the presence of complex geometryRheological properties as a function of temperature, shear rates, and compositional changes
Shrinkage/swelling effect in rapid freezing, drying, rehydrationEquations for stress and strain, energy equation, species equation, possibly porous media equationCoupled calculations of transport and solid mechanics are possible if the transport is treated in a simple way. Otherwise, difficult.Mechanical properties as a function of temperature, composition, structure and phase changes

Fluid mechanics

Modeling in fluid mechanics is based on the application of Newton's laws of motion to fluids, the most common form of the equation being the Navier-Stokes equations. Many fluid flow applications have been solved in food processing (for example, see Sun 2007). These include refrigerated display and transport systems, cooler, dryer, and baking oven designs, mixing, sterilization, and pasteurization systems, jet impingement heating and cooling, and extrusion. Although methodologies for modeling separation processes such as membrane processes have been well developed (Hughes and others 2007), their implementation may require specialized software due to the presence of partition coefficients. Foods are often non-Newtonian. Modeling capabilities in fluid flow are the most developed, and excellent commercial software are available that can solve most of the situations just mentioned. It appears the limitation in modeling fluid flow is primarily in the user expertise available as some of the flow situations can be quite complex and need to be formulated properly. However, there are food applications that cannot be implemented readily in a commercial software, for example, in the important area of multiphase (solid–liquid) flow modeling, as would be needed for aseptic processing of soups, further development is needed in the implementation of physics.

Heat transfer

Physics-based modeling in food processing started with the pioneering work by Teixeira and others (1969) on sterilization in canned foods. Today, heat transfer in an arbitrary-shaped solid food container is one of the simplest items to model using commercial software. Even batch sterilization of liquid food is an easy problem. Gel formation during heating of starch solution that results in large change of viscosity has also been included in batch sterilization (Tattiyakul and others 2002). Heat transfer in freezing and thawing is also routinely implemented. Radiative heating of foods in an oven or other heating situations have also been modeled and can be accomplished with a number of commercial software. It is fair to say that if the application involves primarily heat transfer and only simple mass transfer and fluid flow, it can be readily implemented.

Mass transfer

Modeling moisture transfer can be easy if evaporation is not present. For example, modeling of filtration processes can be readily implemented in commercial software. When evaporation is involved, however, as it would be in most drying, baking, and frying processes, modeling can become quite complex. Although the physics involved in such applications is also present in applications outside of food, such as in geology and ceramic processing, the equations involving mass transfer in a solid as a porous medium with multiple phases of liquid and vapor, and the associate pressure-driven flow from significant heating, are not implemented in most commercial software. Even specialized porous media software such as TOUGH2 (http://www-esd.lbl.gov/TOUGH2/) does not make it straightforward to implement such food processes. This makes it particularly difficult to simulate a large class of important food-processing problems. This will be further discussed under problem formulation in the following section.

Solid mechanics

Applications of solid mechanics in food processing can involve rheological behavior (that can relate to the physics of chewing, for example) of solid and semisolid foods. Most foods shrink or swell during processing, and this is another way solid mechanics is integrally involved in food processing. Such shrinkage and swelling during processing couples solid mechanics with other types of physics and will be further discussed under multiphysics below.

Electromagnetics

Radiofrequency (RF) heating and particularly microwave heating have become commonplace in the food industry (Datta and Anantheswaran 2001). Microwaves are important in food product development for the domestic microwave oven and also in commercial microwave and combination heating processes, including microwave pasteurization and sterilization. The physics of these heating processes involve electromagnetics, governed by the general Maxwell's equations. Microwave heating applications can be divided into plane waves and cavity heating. For the practical food-heating applications, plane wave is mostly an assumption that leads to a simple exponential decay of the microwave heat generation term. Cavity heating can be a single-mode cavity or a multimode cavity, such as the domestic microwave oven. Analysis of the electromagnetics in a cavity is complex, but major improvements have been made in the user friendliness of the software such that several commercial software items can solve these problems routinely. It is important to note that the complete electromagnetic modeling (as opposed to plane wave assumption) is the only way to obtain the often complex spatial variations of microwave heat deposition in the food heated in a microwave oven (Zhang and Datta 2001). The food community is definitely seeing more of these complete electromagnetic simulations (Schubert and Regier 2005). However, for the larger-size domestic ovens, full electromagnetic simulations are very computing intensive and can still be limited by computational resources available. RF heating is less common in food. Although RF can be modeled using the same equations of electromagnetics, very little work has been reported (for example, Yang and others 2003). Ohmic heating, which is typically at lower frequencies, is easily implemented in the software. Microwave heating is an example of a situation where modeling can provide details that are nearly impossible to obtain experimentally.

Multiphysics

Intended or unintended flow, temperature, and moisture changes can lead to other physical changes in food material such as swelling or shrinkage or changes in the thermophysical properties of the material. These changes, in turn, can affect the heat transfer, moisture transfer, microwave absorption, and so on. One way to visualize such coupling can be seen in Figure 3. Multiphysics models that couple more than 1 kind of physics (such as electromagnetics and heat transfer) are quite important in food processing.

Figure 3—.

Schematic showing coupling of different types of physics with heat transfer. The connecting solid lines stand for coupling due to temperature itself, whereas the dashed lines stand for additional coupling that can arise in a heating process such as moisture loss.

Heat transfer coupled with evaporation and moisture transport Heating of food almost always is accompanied by the evaporation of water in it. The more obvious examples are baking, drying, and frying processes. Evaporation changes the heat transfer process quite significantly and requires significant reformulation of the model such that it considers water and vapor transport coupled with heat transfer. Evaporation produces internal pressures that lead to Darcy flow of water and vapor, a mechanism separate from diffusion. As will be discussed further, commercial software generally does not implement the types of formulations needed in these problems. This class of problems is perhaps the most important one in food processing that also is the one that is currently the most difficult to implement in commercial software.

Heat and mass transfer combined with solid mechanics An example of multiphysics with solid mechanics and heat and mass transfer is in cracking during cooling of eggs, in drying, adsorption, baking, rapid freezing, and microwave heating. Temperature and moisture changes, and internal pressure development can lead to dimensional changes in the food and, therefore, mechanical stress. In some of these situations, large dimensional changes lead to cracking and are to be avoided. Although this type of coupling has been reported in research papers in freezing (Shi and others 1998), drying (Akiyama and others 1997), and baking (Zhang and others 2005), such analysis is not common. Commercial software in solid mechanics is highly well developed. The bottleneck in performing coupled thermo- and hygromechanics computations for food is often in the mechanics software's inability to model the transport processes accurately because these types of software typically have only the basic heat conduction or mass diffusion included. The solution here can be coupling 2 separate codes, 1 for transport and the other for mechanics.

Heat transfer in microwave combination heating Microwave heating described above involves multiphysics because the electromagnetics provides the rate of heat absorption that is used in heat transfer modeling to obtain the temperature. Dielectric properties can vary strongly with temperature, changing the electromagnetics as temperature increases during the heating process. This 2-way coupling causes additional difficulties in modeling and makes it even more computing intensive. Although many software items can compute the electromagnetics, fewer of them can solve the coupled electromagnetic-heat transfer process (Ansys Inc., Canonburg, Pa., U.S.A.) Another type of multiphysics problem in this context is where multiple modes of heating are combined, as in a domestic microwave combination oven, to obtain the desired temperature profile and rate of heating. Increasingly, combination of microwaves with other modes of heating is seen as a practical solution to improve the uniformity of microwave heating and provide more control on the moisture transport while simultaneously increasing the speed of heating. Two particular combinations that are being pursued most vigorously in the food industry are microwaves combined with infrared and microwaves combined with jet impingement heating, for which ovens are available in the market. Modeling of these combination heating processes has begun to appear (Datta and others 2005a). Today, persons having sufficient formal background in electromagnetics can develop coupled microwave-heat transfer models with some effort.

Status and Issues in Modeling Food Manufacturing

In foods, eventually our interest is either quality or safety or both. Thus, as shown in Figure 4, modeling can be divided into 2 stages, process model and quality/safety model. Process model here is meant to refer to the modeling of the physical process in product, process, or equipment design. Quality/safety model refers to quantitative description of quality/safety in terms of the process parameters obtained from the process model (for example, color or microbiological concentration as a function of temperature). Issues related to modeling of quality and safety are discussed in several of the companion papers (for example, Marks 2007; van Boekel 2007).

Figure 4—.

Overview of the modeling process showing the process model is combined with the model for quality and safety.

Some of the generic components of process model in the context of computer-aided engineering are (1) problem formulation (governing equations, boundary, and initial conditions); (2) computational software that is able to solve the formulated problem; (3) material properties; (4) ability to enter geometry and generate mesh; (5) visualization; (6) validation; and (7) sensitivity/uncertainty analysis. These are now discussed.

Problem formulation

Problem formulation is where the biggest uncertainty lies today in modeling food processes. Mathematical formulation often requires intelligent simplification of an otherwise complex problem. The goal is to keep as many details of the process as possible, without creating unnecessary computational complexity or time commitment. Said another way, the problem formulation needs to be “as simple as possible, but not simpler.” Many food processes have not been understood in nonempirical quantitative engineering terms, namely, in terms of 1st-principle-based models. In other words, the exact governing equations and the boundary conditions that apply to a particular process are far from clear. What we need is a knowledge base of various food processes and their accurate mathematical representations.

An example would illustrate the point. There have appeared many papers on modeling of frying processes, having varying formulations (governing equation and boundary conditions) of the process. In 1 formulation, a sharp boundary is assumed for evaporation. Here 2 separate sets of equations are written for the 2 zones—core and crust. A separate equation is written for the location of boundary (interface) between the 2 zones. In another formulation, evaporation is considered distributed throughout the porous material, with rates that are dependent on local temperature, saturation, and pressure. The governing equations for this formulation are quite different from the previous one. In yet another formulation, heat and water transports inside the material are considered to be simple diffusions, with all of the evaporation occurring at the surface. A still simpler formulation is empirical and provides a simple rate equation for water loss with the kinetic parameter for water loss estimated from the same experimental data.

There are 2 points to be made here. First, depending on the formulation, the governing equations and, therefore, the numerical methods used are quite different. Any given commercial software is unlikely to be able to accommodate all formulations of the problem in a satisfactory manner (which means it may not be able to solve the sets of equations in all possible formulations). Thus, depending on which formulation we choose to be the best one, we have to select software that can accommodate the formulation. The 2nd point here is a decision on the level of empiricism that is ideal. A more empirical formulation is less flexible. For example, as we change to different products and processes, new empirical parameters will be needed that would rely entirely on experimental data. This goes against the advantages of computer-aided engineering where we are trying to reduce our dependence on physical prototypes.

If the frying process is to be designed using a modeling software available commercially, we have to agree on either a formulation of the frying process or a number of equivalent formulations where the equivalence can be clearly demonstrated. Without such agreement on the framework, there will be disagreements on whether the mathematical model mimics the real physical process. This is perhaps the greatest need for development.

Implementation

Models in the past have often been custom developed in academic institutions or in-house in large, multinational corporations. Possibilities with commercial software were discussed previously in Section 4. Table 1 shows the implementation status of a list of food processes, based on the author's own experience and anecdotal information. It is important to know that the list of processes that can be implemented grows every day. As applied to the multiphase porous media model just discussed, its implementation in commercial software is either not possible or requires significant tweaking of the software (Halder and others 2007a) that would be difficult for most users. Transport in multiphase porous media with rapid evaporation from heating is an example of specialized physics that is critical to food processing but is not readily implementable in most available commercial software. Use of modeling food processes can increase significantly if such physics becomes easy to formulate in commercial software.

Properties and their variations during processing

Physics-based modeling is somewhat futile without having access to the material property data that are appropriate in ranges of process and product parameters. Some of the relevant properties are mechanical, rheological, thermal, mass transport, electrical, and kinetic (related to microbiological and chemical changes). During processing, food can undergo changes in temperature, moisture, composition, and structure. For example, we can easily see the major changes in structure during the processing when we consider the creation of bread from dough. The structure development would not be just a function of temperature or moisture, but would be a function of their history. The complex physical structure that develops changes the porosity and the transport properties. In general, properties need to be known as a function of these parameters to be able to model accurately. It is fair to say that for most properties such detailed information is not available, although, for some properties, more data are available than for others. Predictive models of properties as a function of parameters such as temperature (see next paragraph), pressure, moisture, and structure are one of the greatest needs in making modeling more useful in the design process.

Comments on selected properties data. Thermal conduction properties: Perhaps the most widely available data are on thermal conductivity, specific heat, and density of foods. Empirical correlations (Table 2) of these properties as a function of composition and temperature are available (Choi and Okos 1986) that are easily implementable for computer modeling. However, even these (Table 2) are valid in the range 0 to 90 ° C and, therefore, would not be useful when temperatures are near boiling at atmospheric pressure (for example, in case of sterilization).

Table 2—.  Thermal conductivity in W/mK of individual components, to be combined with composition to obtain thermal conductivity of food materials (Choi and Okos 1986).
ComponentConductivity equation
Water0.57109 + 1.762 × 10−3T− 6.703610−6T2
Ice2.21960 − 6.248910−3T+ 1.015410−4T2
Proteins0.17881 + 1.195810−3T− 2.717810−6T2
Fats0.18071 − 2.760410−3T− 1.774910−7T2
Carbohydrates0.20141 + 1.387410−3T− 4.331210−6T2
Fibers0.18331 + 1.249710−3T− 3.168310−6T2
Ash0.32961 + 1.401110−3T− 2.906910−6T2
Air0.025

Radiative properties: Radiative heat transfer is quite important in food processing, but radiative transport properties (emittance, reflectance, absorptance) are rarely available (Datta and Almeida 2005). Variation of radiative properties with moisture content and wavelength can be quite significant. Again, almost no data are available on such moisture content and wavelength dependence. Wavelength-dependent data are particularly useful for the newer technology of halogen light heating.

Mass transfer properties: Mass transfer properties include diffusivity, and Darcy permeability. For diffusivity, significant data are available (Saravacos and Maroulis 2001). However, the effective moisture diffusivity, which includes liquid capillary diffusivity and vapor molecular diffusivity, becomes a strong function of moisture content. Food process models almost always treat diffusivity as a constant value, which rarely holds. Such models generally end up using the “diffusivity” value as simply a parameter that fits the model to specific experimental data. Capillary diffusivity as a function of moisture content is needed for modeling multiphase transport in food as a porous media discussed earlier.

Like the transport modes of diffusion and capillarity, pressure-driven flow, also called Darcy flow, has major implications in moisture and other species transport during food processing. The source of such pressures can be significant internal evaporation, as in microwave heating, or it can be from shrinkage, as in roasting of meat. Property data needed to model pressure-driven flow, for example, permeability, are only beginning to be measured (Datta 2005).

Rheological properties: Rheological properties have also been very widely studied (Rao 1999). Here again one can see the tremendous influence of composition, temperature, flow rates, and so on. Although correlations with composition, temperature, and others are not available in a comprehensive manner, enough data are probably available that can be combined with well-known rheological models for simpler systems to obtain at least a reasonable estimate of data, perhaps sufficient for computer-aided engineering of processes.

Dielectric properties: Dielectric properties are available for a significant number of food products (Datta and others 2005b). Correlations, as in Table 1, are also available for some restricted situations. However, much of the literature data on dielectric properties have some inherent difficulties due to (1) the use of different measuring techniques, (2) the lack of sufficient composition data accompanying the measurement (dielectric property is particularly sensitive to salt, typically a minor component in food), and (3) most of the data reported do not provide sufficient explanations to elucidate the effect of composition and other factors on the data.

General comments on the state of food properties data Perhaps the following general conclusions can be made regarding the state of data (see, for example, Nelfood 2002):

Significant variability: Great variability exists in the data due to biological origins, recipe differences, and the rate at which new food products and processes are developed. Reported data often do not provide sufficient information to relate the data to composition, and so on, that could provide insight into the possible variability in the data.

Will stay incomplete: If one considers the historical rate at which new food property data are reported, it is unlikely that sufficient data will be available to cover most of the properties as a function of temperature, moisture, composition, and structure.

Hard to use in modeling: Data compilation in printed form and in databases are much less than needed and are not integrated in the context of computer-aided engineering. Even though some semi-empirical (unlike completely empirical formulas as in Table 2) prediction formulas are available, they are not very accurate beyond the particular range of parameters for which they were collected.

Have enough to get started: However, data compilation available today is likely to be sufficient in getting started, when the results can be combined with sensitivity analysis (discussed later) with respect to the data. For a complex material and process, as in food, sensitivity analysis is quite a reasonable way to get a model going.

Getting started with what is available Thus, if modeling has to wait for such data to become available, it will be a long time before modeling can contribute to design in a significant way. Fortunately, there is a workaround to this issue, some of which is mentioned below:

Start with approximate data: Simplified correlations such as Table 2 should give some estimate as the starting point. One can even start by simple interpolation of existing data (for foods of similar composition and structure) when no such correlations are available.

Perform sensitivity analysis with respect to the unavailable data: Because the idea of modeling is to try many “what if” scenarios anyway, it is only natural to examine the effect of property variations on the process. This way, we can see the effect of a range of properties on the process. If the outcome of the sensitivity analysis shows that the process is quite sensitive to property variations in the particular situation, it signals the need to obtain more accurate data for that particular property. Otherwise the rough estimate of the property available (such as from tissues of similar composition) can be considered sufficient for design purposes. Sensitivity analysis is one of the most important tools in computer aided engineering (CAE) and is not limited for use in the case of property variations, but can also be used in the case of other process parameter variations.

In the years ahead, we will have to put more effort in developing more comprehensive prediction equations (similar to Table 2) that relate to structural and other changes during processing, which would help us to better predict the changing transport properties and make modeling more realistic.

Mesh generation

Mesh generation for complex geometries is always a concern for any modeling project. Many major advances have been made in mesh generation (a web search with that keyword will show) and today most of the commercial software have good capabilities for complex mesh generation. Mesh generation can still consume a significant amount of time and effort. However, it is probably fair to say that the mesh generation process is not a bottleneck in food process modeling.

Visualization

Understanding and optimization, 2 primary goals of modeling, benefit critically from the visual representation of the data. Today visualization capabilities have improved remarkably in most software. For food applications, the bottleneck is more in computing the most appropriate quantity in the context of quality and safety rather than in the visual representation of the quantity. It is fair to say that required visualization tools are available.

Validation

Closely coupled with accurate formulation of the problem is the validation of the model computations. This can include mesh convergence study, checking for mistakes, checking if the results can be explained using common sense physics, and comparing the results with experimental data. Validation of model using direct experimental measurement is the best and some validation can often be done with relative ease. Sometimes detailed validation can be time consuming and expensive. We now have very sophisticated experimental measurement capabilities used in food applications. For example, in fluid flow, laser velocimetry has been used to find detailed flow patterns in jet impingement heating (Erdogdu and others 2007). In heat transfer, fiber optic and infrared temperature measurements have been used. For moisture transport, comprehensive validation can be done using magnetic resonance imaging (MRI), which is currently being attempted (for example, Rakesh and others 2006). Some of these detailed experimental validation methods can require more effort (and expenses) than the modeling itself.

Systematic validation of results using benchmark computations would provide increased confidence in results generated through CAE. It is also conceivable to build intelligence related to validation of the results in the code itself, somewhat like an expert system. Although such developments are already under way in some software (POLYFLOW 2002), they are generally unavailable.

Here a distinction needs to be made between validation in a research context in academia and validation in a design scenario in the food industry. The type of modeling we are talking about often provides trends (as opposed to exact numbers) that work very well in an industrial design scenario where modeling is often used as initial optimization followed by experimental work with actual prototype. Thus, requirements for validation are much less stringent for this situation. In fact, if every model were to be validated at the same rigorous way as in the food industry, modeling would no longer be an efficient tool for design.

Sensitivity/uncertainty analysis

Uncertainty (in input parameters such as food properties or kinetic data, process variables such as temperature) in food processing can be a great deal more than in other materials processing. For example, to design a sterilization process, one would like to know the initial load of bacteria, which can be extremely variable. Such uncertainty in model parameters is not implemented in most commercial software, although some software are beginning to include such analysis (ANSYS 2002). Specialized software for calculating uncertainty in computer calculation is available in research groups (for example, see Nicolai and others 2007), but these methodologies are often restricted to small changes in parameters. Also, at the research level, software to calculate derivatives are available that can be used to generate sensitivity data for any model (ADIFOR 2002). Such uncertainty calculations need to be included for the software to be useful for modeling in food processing. In the absence of built-in ways to calculate the uncertainty, Monte Carlo simulation (repeated simulation of a process for a range of parameter values chosen from a probability distribution) may be possible (Halder and others 2007b), provided the computation times are not prohibitive.

Status and Issues Related to Integration and Ease of Use

Status of customized software

For computer-aided food process engineering, it would be ideal to have a scenario where a technical person, with minimal knowledge of the physics of the process and computational aspects, can use a few clicks of a mouse to define a practical food process. For example, such a user could click and choose between various container types, food material, and heating systems, and ask the computer to provide the heating temperature needed for optimum quality in sterilization. The computer would need to formulate the physical problem (sterilization) into a mathematical one (equations), decide the best solution method, and finally do an optimization. For food-processing applications, this is still farfetched for most processes. Some efforts are under way to develop customized software (Torres 2003). To the best of the author's knowledge, these software items are still quite limited in terms of the physics they include. For example, they may include only diffusional heat and mass transfer.

Software companies would be the prime mover in developing customized software. However, there is a chicken-and-egg situation. Software companies are reluctant to make the investment as the user base is perceived by them to be too small to justify the added investment. Food processors, on the other hand, are reluctant to invest more in simulation capabilities because the existing software is not customized for food applications and too much time and resources would be involved in implementing many food processes in the existing software. Larger food companies that can invest more resources are doing this (Joussee 2007); however for companies other than the largest multinationals, modeling is often not seen as an efficient alternative. In this respect, consultants (for example, http://www.airflowsciences.com), including some of the software companies themselves, can play a critical role whereby the entire modeling process can be contracted out. Other factors that lower model use by the food industry include perhaps less investment in research and development compared to industries such as aerospace, automobile, and chemical processing. Yet another important characteristic of the food industry seems to be that issues relating to chemistry and microbiology have priorities over engineering issues. Trial and error approaches, the alternatives to modeling (also perhaps not as expensive), make modeling less attractive.

Human power development

In the immediate future, computer-aided engineering expertise can be brought to a small food manufacturer either by utilizing an outside consulting firm (which is increasingly becoming the software vendor itself) to perform the simulation or by getting the in-house engineers trained by the software vendors (together with adding the resources for hardware and software). In the long run, more food engineers with firm footing in modeling need to be developed. These engineers need to have a good grasp of the physical process, computational aspects, and an appreciation of working with food where quality is the final determinant of a successful process. In universities, computer-aided engineering has typically been a graduate course. At the undergraduate level, such courses are beginning to appear (Datta 2006) and will be more commonplace in the future, providing some of the human power needed in industrial food processing.

Summary: Status and the Future

Physics-based modeling of food processes has been around for over 30 y and has included all the common physical modeling approaches, particularly in the continuum approach. Most of the work is done in academia, with the largest of the corporations now being active to different degrees in their in-house modeling and, sometimes, in using outside consultants. The main ingredients needed for modeling (problem formulation, properties, and parameters) have been developed to some extent, but not in an organized and integrated manner. The bottlenecks appear to be (1) not enough knowledge of the process in engineering terms; (2) time and expenses due to lack of sufficient training in the modeling process; and (3) insufficient incentive for having a more complete knowledge of the process (cook and look may be sufficient in many cases). Although significant work is needed to organize the information and integrate it into a user-friendly package so that physics-based model can play a more significant role as design tools, enough information is available to use this tool now on a regular basis for many food processes.

Acknowledgments

The author gratefully acknowledges the partial financial support provided by the funds from the USDA Natl. Research Initiative award 2005–35503-16208 to develop the workshop that made possible a discussion on the big picture of modeling in food processes.

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