## Comment Notes from Excel File 'Desiccants and Moisteners.xls'

### From Sheet1:

**Desiccants and Moisteners.xls** (In cell A1)

**>>Model Assumptions<<** (In cell A3)

**Model Assumptions:** This Microsoft Excel workbook file takes an entered equilibrium water activity value, '**New (final or target) Aw**', of a dry multicomponent food or pharmaceutical mixture stored in a hermetically sealed container and computes the water activity decrease or increase from the initial Aw including the addition of a single desiccant or moistener component to the mixture. It is assumed that the ingredients do not interact chemically, that the temperature is constant and that the amount of moisture absorbed by or released to the atmosphere trapped in the container is negligible. The model uses from 2 (minimum) to 15 (maximum) ingredients' moisture sorption isotherm equations, each one of which may or may not be the same as the equation of another ingredient. Input moisture values should be entered on a wet basis and will be converted to a dry basis for calculation and plotting.

***** Instructions ***** (In cell A4)

**Instructions:** This Excel workbook applies to dry mixtures of from 2 to 15 food or pharmaceutical ingredients. User input is required on Sheet1 in the block of multi-colored cells in columns C through G, rows 4-18 and in the Light Turquoise colored cells of columns C, D and G as described in Steps 1-13 below. The last step, clicking the '**Update Workbook**' button to run a VBA macro, is only needed if some aspect of the Moisture Sorption Isotherms chart on Sheet1 needs updating or a change has been made to one or more of the equations in column G. The macro updates this Excel workbook to use the currently entered equations. **The new mixture must conatin at least two (2) ingredients for the update to occur.** Data and some user entries for the chart are located on Sheet2.

**Step 1** (In cell A5)

**Step 1:** When a water activity value between 0.00 and 0.99 is entered into Sheet1 cell C1, '**Aw (in equations)**', the percent moisture of each ingredient of the mixture at that Aw value is computed with each ingredient's equation and displayed in cells 4-18 of Sheet1 column G. The same applies to desiccants and moisteners.

**Step 2** (In cell A6)

**Step 2:** Enter into Sheet1 cell C2, '**New (final or target) Aw**', the water activity value (a real number > 0.00 and <= 0.99) of the equilibrated mixture.

**Step 3** (In cell A7)

**Step 3:** Enter the initial water activity value (a real number from 0.00 to 0.99, inclusive) of each ingredient of the mixture in rows 4-18 of Sheet1 column C, '**Initial Aw**'. If all ingredients' initial Aw entries are the same value it indicates that the initial mixure has been equilibrated. Leave unused ingredients' cells blank. To **omit** an ingredient, desiccant or moistener from the mixture enter a value of 0.00 as its '**Intial Aw**' value in column C and also as its '**Initial Wet Mass (g)**' value in column E. To **delete** an ingredient, desiccant or moistener from the workbook enter a **negative** value (e.g., -1) as its '**Intial Aw**' value in column C. When the '**Update Workbook**' button is clicked all entries for any ingredient, desiccant or moistener having a negative '**Initial Aw**' value will be cleared on Sheet1 and Sheet2, it will be removed from the model and it's curve and legend entry will be deleted from the chart. If an **Inital Aw** cell of an active ingredient, desiccant or moistener is is left blank, Excel interprets it as an entry of 0.00.

**Step 4** (In cell A8)

**Step 4:** For each of the up to 15 ingredients, enter an ingredient's name in place of a color name in rows 4-18 of Sheet1 column D, '**Ingredient Name**'. The color will be used for that ingredient's line on the Moisture Sorption Isotherms chart on Sheet1. Enter the non-blank name for each desiccant or moistener in rows 22-27 of column D. The names will also be used as the text for the legend of each curve on the chart.

**Step 5** (In cell A9)

**Step 5:** Enter the initial wet mass (in grams and >=0) of each ingredient of the mixture in rows 4-18 of Sheet1 column E, '**Initial Wet Mass (g)**'. Leave unused ingredients' cells blank.

**Step 6** (In cell A10)

**Step 6:** Enter the percent moisture (on a wet basis; >=0 and <=100) of each ingredient of the mixture in rows 4-18 of Sheet1 column F, '**% Moisture (wb)**'. Leave unused ingredients' cells blank.

**Step 7** (In cell A11)

**Step 7:** Enter the moisture sorption isotherm equation of each ingredient of the model in rows 4-18 of Sheet1 column G, '**Equation**', as an Excel formula (i.e., starting with an '=') by entering one ingredient's equation per cell. Use 'Aw' as the independent (x) variable for all equations. Leave unused ingredients' cells blank. If you copy a formula from another colored cell, use 'Paste Special: Formulas' from the Edit menu rather than 'Paste' to avoid also pasting the copied cell's background color into the new cell. In any case, the original color will be restored when '**Update Workbook**' is clicked.

**Step 8** (In cell A12)

**Step 8:** If a desiccant addition is considered, enter the equation for each one in Sheet1 column G rows 22 to 24. Up to 3 desiccants may be entered but each is considered to be added **alone** to the mixture and not combined with any other desiccant or moistener.

**Step 9** (In cell A13)

**Step 9:** Enter each desiccant's initial water activity value (>=0 and <=0.99) in Sheet1 column C, '**Initial Aw**', in rows 22 to 24. These should typically be values of 0.00.

**Step 10** (In cell A14)

**Step 10:** If a moistener addition is considered, enter the equation for each one in Sheet1 column G rows 25 to 27. Up to 3 moisteners may be entered but each is considered to be added **alone** to the mixture and not combined with any other moistener or desiccant.

**Step 11** (In cell A15)

**Step 11:** Enter each moistener's initial water activity value (>=0 and <=0.99) in Sheet1 column C, '**Initial Aw**', in rows 25 to 27. These values should be greater than the '**New (final or target) Aw**' value of the mixture located in cell C2.

**Step 12** (In cell A16)

**Step 12:** If a desiccant is used to lower the water activity of the initial mixture, the value in cell E20, '**Delta Water**', will be **negative** and the amount (in grams) of needed initial desiccant of each type will be shown in cells E22 to E24. If a moistener ingredient is used to raise the water activity of the initial mixture, the value of '**Delta Water**' in cell E20 will be **positive** and the amount (in grams) of needed initial moistener of each type will be shown in cells E25 to E27.

**Step 13** (In cell A17)

**Step 13:** Click the '**Update Workbook**' button to run a VBA macro that copies equations of all active ingredients, desiccants and moisteners into relevant cells of Sheets 1 & 2 then updates the Moisture Sorption Isothems chart on Sheet1 to include a curve for all ingredients, desiccants and moisteners in the equilibrated mixture, a curve for the combined % Moisture of the mixture and shows a vertical dashed line at the new (final or target) equilibrated mixture's Aw value. Data and some user entries for the chart are located on Sheet2. **'Update Workbook' only needs to be clicked if a change has been made to one or more of the equations in column G of Sheet1 or some aspect of the chart needs to be updated.**

**References** (In cell A19)

**References:**

Iglesias, H.A. and Chirife, J. 1982. Handbook of Food Isotherms: Water sorption parameters for food and food components. Academic Press. New York.

Peleg, M. and Normand N.D. 1992. Estimation of the water activity of multicomponent dry mixtures. Trends in Food Science and Technology, 3:157-160.

Peleg, M. 1993. Assessment of a four parameter general model for sigmoid moisture sorption isotherms. Journal of Food Process Engineering, 16:21-37.

Wolf, W., Spiess, W. E. L. and Jung, G. 1985. Sorption Isotherms and Water Activity of Food Materials. Elsevier, New York.

**Authors** (In cell A20)

**Authors:**

Model by: Micha Peleg
Professor
Tel: 413-545-5852
Fax: 413-545-1262
E-mail: micha.peleg@foodsci.umass.edu
Worksheet by: Mark D. Normand
EDP Programmer II
Tel: 413-545-2365
Fax: 413-545-1262
E-mail: mnormand@foodsci.umass.edu
Postal address: Department of Food Science
Chenoweth Lab.
100 Holdsworth Way
University of Massachusetts
Amherst, MA 01003
Web site URL: http://www.umass.edu/foodsci/

(In cells A23:A25)

Click 'Update Workbook' below

if an equation has been changed

or to update the chart.

(In cells B4:B28)

User entries in: Sheet1!C1:C2, C4:G18,

C22:D27, G22:G27 & in Sheet2 column A.

Values in column G, Equations, are

the %Moisture of each ingredient,

desiccant or moistener at the value

entered in C1, Aw (in equations).

Enter the New (final or target) Aw

value of the mixture in cell C2.

Enter a positive (> 0.00 and <=0.99)

Initial Aw value in column C for

each ingredient, desiccant or

moistener to include in the mixture.

Enter an Initial Aw and Initial Wet

Mass of 0.00 to omit an ingredient

from the mixture.

Enter a negative (<0) Initial Aw value

to delete (completely erase) an

ingredient, desiccant or moistener

from this workbook file when the

'Update Workbook' button is clicked.

**Aw (in equations)** (In cell B1)

**Aw (in equations):** Enter a water activity (Aw) value >= 0.00 and <= 0.99 in cell C1 to use as the independent variable for the equations in column G. The percent moisture value of each ingredient, desiccant or moistener at the entered Aw value will be shown in the cell of column G that contains each equation.

**New (final or target) Aw** (In cell B2)

**New (final or target) Aw:** Enter a water activity (Aw) value > 0.0 and <= 0.99 in cell C2 that will be the new (final or target) value of the equilibrated mixture of ingredients and a desiccant or moistener. This value is shown on the Moisture Sorption Isotherms chart on Sheet1 as a 40%-Gray dashed vertical line.

**Initial Aw** (In cell C3)

**Initial Aw:** Enter in the background-colored cells of rows 4-18 and 22-27 of column C below a **positive** (> 0.00 and <= 0.99) initial water activity (**Initial Aw**) value for each ingredient (in cells C4 to C18), desiccant (in cells C22 to C24) and moistener (in cells C25 to C27) to be **included** in the mixture. Enter an **Initial Aw** value of 0.00 and an **Initial Wet Mass** value of 0.00 to **omit** that component from the mixture. Enter a **negative** (<0) Initial Aw value to **delete** (**completely erase**) that component from the mixture, the chart and both sheets of this Excel workbook file.

**Ingredient Name** (In cell D3)

**Ingredient Name:** Enter into the background-colored cells of rows 4-18 and 22-27 of column D below the non-blank name of each ingredient, desiccant or moistener included in this workbook's model. Its curve will be shown on the chart and the entered name included in the chart's legend text for the curve.

**Initial Wet Mass (g)** (In cell E3)

**Ingredient Name:** Enter into the background-colored cells of rows 4 to 18 of column E below the **Initial Wet Mass** (in grams and >=0) of each ingredient in this workbook's model. Enter a value of 0.00 here and as the **Initial Aw** value in column C to **omit** that ingredient from the model.

**% Moisture (wb)** (In cell F3)

**% Moisture (wb):** Enter into the background-colored cells of rows 4 to 18 of column F below the percent moisture on a wet basis (i.e., including the water; >=0 and <=100) of each ingredient included in this workbook's model.

**Equation** (In cell G3)

**Equation:** Enter an Excel formula (i.e., starting with an '=') into the background-colored cells of rows 4-18 and 22-27 of column G, '**Equation**', the moisture sorption isotherm equation of each ingredient, desiccant and moistener included in this workbook's model. All equations should use 'Aw' as the independent (x) variable. The result of substituting the Aw value found in cell C1, '**Aw (in equations)**', will be displayed in each equation's column G cell. Appropriate modifications of column G's equations will be pasted into columns H, I and J of Sheet 1 and columns C through X of Sheet2 by a VBA macro that is run when the '**Update Workbook**' button on Sheet1 is clicked. This should be done whenever a change is made to any equation in column G or if some aspect of the chart needs updating.

### From Sheet2:

**Chart Data** (In cell A1)

**Chart Data:** This sheet, Sheet2, contains the data used to draw the Moisture Sorption Isothems chart on Sheet1. Items in the following cells may be changed by the user: A4, A7, A10, A13, A16, A19, A22, A25, A28 and A31.

**User entries: A4,7,10,13,16,19,22,25,28 & 31** (In cell A2)

**Number of Points (5-200)** (In cell A3)

**Number of Points:** The cell below contains the number (5 to 200, default=100) of points used to draw the curve for each ingredient, desiccant or moistener on the Moisture Sorption Isotherms chart on Sheet1.

**X-Axis Minimum** (In cell A6)

**X-Axis Minimum:** The cell below contains the minimum value (>= 0. and < x-axis max., default=0.) of the x-axis (Aw) of the Moisture Sorption Isotherms chart on Sheet1.

**X-Axis Maximum** (In cell A9)

**X-Axis Maximum:** The cell below contains the maximum value (> x-axis min. and <= 1., default=0.8) of the x-axis (Aw) of the Moisture Sorption Isotherms chart on Sheet1.

**Y-Axis Minimum** (In cell A12)

**Y-Axis Minimum:** The cell below contains the minimum value (>= 0. and < y-axis min., default=0) of the y-axis (Moisture (%db)) of the Moisture Sorption Isotherms chart on Sheet1.

**Y-Axis Maximum** (In cell A15)

**Y-Axis Maximum:** The cell below contains the maximum value (> y-axis min. and <= 100., default=30.) of the y-axis (Moisture (%db)) of the Moisture Sorption Isotherms chart on Sheet1.

**Main Title** (In cell A18)

**Main Title:** The cell below contains the text used for the Main Title of the Moisture Sorption Isotherms chart on Sheet1 (default is 'Moisture Sorption Isotherms').

**X-Axis Title** (In cell A21)

**X-Axis Title:** The cell below contains the text used for the x-axis title of the Moisture Sorption Isotherms chart on Sheet1 (default is 'Aw').

**Y-Axis Title** (In cell A24)

**Y-Axis Title:** The cell below contains the text used for the y-axis title of the Moisture Sorption Isotherms chart on Sheet1 (default is 'Moisture (%db)').

**NewAw Series Name** (In cell A27)

**NewAw Series Name:** The cell below contains the non-blank text used in the legend to label the dashed gray vertical New Aw line on the Moisture Sorption Isothems chart on Sheet1 (default is 'New Aw').

**Mixture Series Name** (In cell A30)

**Mixture Series Name:** The cell below contains the non-blank text used in the legend to label the dotted dark gray Mixture curve on the Moisture Sorption Isothems chart on Sheet1 (default is 'Mixture').

**dAw (In cell A33)**
**dAw:** The cell below contains a formula to compute delta Aw, the value used as the increment between the x-coordinates of the points of each curve on the Moisture Sorption Isotherms chart on Sheet1.

**Chart's New Aw** (In cell A36)

**Chart's New Aw:** The two cells below are the x-coordinates of the upper and lower points of the dashed gray vertical New Aw line on the Moisture Sorption Isotherms chart on Sheet1.

**Chart's New Aw Moisture Limits** (In cell A40)

**Chart's New Aw:** TThe two cells below are the y-coordinates of the upper and lower points of the dashed gray vertical New Aw line on the Moisture Sorption Isotherms chart on Sheet1.

**AwC** (In cell B1)

**AwC:** The cells below in column B are the x-coordinates(Aw Chart) used for all the points of the curves for all ingredients, desiccants and moisteners drawn on the Moisture Sorption Isothems chart on Sheet1.

**Mixture % Moisture** (In cell C1)

**Mixture % Moisture:** The cells below in column C contain the y-coordinate values for all the points of the curve of the mixture of all ingredients drawn on the Moisture Sorption Isotherms chart on Sheet1. They are computed from formulas in each cell that use the equations for all currently active ingredients.

**Ingr. 1 % Moisture** (In cell D1)

**Ingr. 1 % Moisture:** The cells below in column D contain the y-coordinate values for all the points of the curve of ingredient 1 drawn on the Moisture Sorption Isotherms chart on Sheet1. They are computed from the formulas in each cell that use the equation for ingredient 1. The same applies to the cells of Sheet2 columns E to R for ingredients 2 to 15, respectively.

**Des. A % Moisture** (In cell S1)

**Des. A % Moisture:** The cells below in column S contain the y-coordinate values for all the points of the curve of desiccant A drawn on the Moisture Sorption Isotherms chart on Sheet1. They are computed from the formulas in each cell that use the equation for desiccant A. The same applies to the cells of Sheet2 columns T & U for desiccants B & C, respectively.

**Moi. A % Moisture** (In cell V1)

**Moi. A % Moisture:** The cells below in column V contain the y-coordinate values for all the points of the curve of moistener A drawn on the Moisture Sorption Isotherms chart on Sheet1. They are computed from the formulas in each cell that use the equation for moistener A. The same applies to the cells of Sheet2 columns W & X for moisteners B & C, respectively.

Content last updated: April 27, 2012