# SPU 27

Topics: Milk, Ball bearing, Processed cheese Pages: 6 (1262 words) Published: November 2, 2013
SPU 27 Problem Set 7
Due in TF’s homework box before class on Thursday, October 31st You are encouraged to work in groups, but all submitted work must be your own. If you work with others, please note who they are.
Please type or write your answers on a separate sheet of paper. Your work must be organized and legible – if your TF can′ t understand what you wrote, they won′ t give you credit.
Show your work for derivations and calculations. Be sure to calculate all results fully (don′ t leave numbers in fraction form, or in terms of pi, &c.) and to provide answers in the requested units, if applicable.

Equation of the Week:
ϕ=

ϕ
Vdispersed
Vtotal
t

Vdispersed
Vtotal

Description
Units
Volume fraction
Unitless
Dispersed phase (particles and droplets) volume
L
Total volume of the mixture
L
Time
s

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SPU 27

Problem Set 7

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Problem 1: Macaroni and Cheese (45 points)
This week we studied a few recipes for Macaroni and Cheese, suggested by Erika Chan, Bianca Bamgade, Margaret Crane, and Sebastian Chiu. The secret to making a good Macaroni and Cheese is to achieve the correct consistency of the sauce, the theme for the week. These different recipes achieve a good Mac and Cheese in different ways.

Mouse’s Macaroni and Cheese
1/4 cup butter
2 tsp (6 g) all purpose flour
1 tsp mustard powder
1 tsp ground black pepper
2 cups milk
1 cup (230 g) American cheese, cubed
1 cup (230 g) Velveeta, cubed
1 1/2 cups macaroni

From Allrecipes

1. Melt the butter over medium heat.
2. Blend in the flour, mustard powder, and pepper until smooth. 3. Slowly stir in the milk, beating out any lumps.
4. Add the American and processed cheeses, and stir constantly until the sauce is thick and smooth.

We will contrast this recipe with the simplest macaroni and cheese recipe imaginable – Kraft Dinner. This recipe was developed in 1916 when James Kraft won a patent for inventing processed cheese, which he later marketed together with macaroni in 1937. The core of the product is a mixture of emulsifying salts and powdered cheese.

The directions on a box of Kraft Mac and Cheese call for a cheese sauce made with 1/4 cup margarine, 1/4 cup milk, and one 39-gram packet of powdered cheese mixture. According to the label, the cheese sauce mix contains whey, milk fat, milk protein concentrate, salt, and sodium tripolyphosphate, as well as minor ingredients.

Our goal is to compare the viscosity between these two recipes and understand how the ingredients lead to this difference in viscosity, as outlined below. Questions 1-3 pertain to Mouse’s Macaroni and Cheese specifically.

1. (4 points) What is the volume fraction of cheese in the cheese sauce? Is this fraction large enough to contribute substantially to the viscosity of the cheese sauce? 2. (8 points) A typical dry starch granule swells to double 30x its original volume during hydration.1 What is the volume of hydrated starch granules in the finished cheese sauce? 3. (3 points) Is the combined volume fraction of hydrated starch granules and cheese large enough to contribute significantly to the sauce’s viscosity? Explain. 4. (6 points) Which ingredients are likely to increase the viscosity of the Kraft Mac and Cheese sauce? Explain.

5. (8 points) Which of Nathan Myhrvold’s four major classes of viscosifiers occur in these recipes? Explain.
6. (8 points) Sketch what you see when viewing Mouse’s Mac and Cheese sauce under a microscope, including a scale bar (for reference, Daniel mentioned that the entire field of view was 1

Recall from Week 1 that starch makes up roughly 75% of flour by weight and that ρflour = 0.59 g/mL.

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SPU 27

Problem Set 7

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roughly 2 mm across). What features are visible at this magnification? 7. (2 points) How will the cheese sauce viscosity change as it cools? 8. (4 points) Describe a method for testing the relative viscosities of the cheese sauces. How would you interpret...