Science and Cooking: Problem Set 8

Due on Canvas by 11 PM on Thursday, November 6th

Please type or write your answers within this document or on a separate sheet of paper. Then save your work as either a Microsoft word document (.doc or .docx) or as a PDF file (.pdf) and upload to Canvas. If you write your answers by hand, you may scan your work and paste the images into either of these file types, but submissions that are NOT either of these file types will not upload properly. 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. YOU WILL NOT RECEIVE FULL CREDIT WITHOUT SHOWING YOUR WORK. Be sure to calculate all results fully (don’t leave numbers in fraction form, or in terms of pi, etc) and to provide answers in the requested units, if applicable.

Equations of the Week

휎 퐸 = (휑 − 휑 ) 푅 퐶

Concept Description Units E Elastic Modulus Pascals

σ Surface/Interfacial Tension N/m R Droplet Radius m φ Dispersed Phase Volume Fraction Unitless φC Critical Volume Fraction 0.64 (Unitless)

Problem 1 - Lab Follow up (20 pts)

In lab this week, you made an aioli according to a recipe like the one copied here:

Materials: Ingredients: Mortar & pestle 1 Egg Second bowl (for collecting the egg white) Olive oil (or any other type of oil) Salt & black pepper Procedure: 1. Separate the egg yolk from the egg white. This can be done by simply cracking the egg into your hand over a bowl and allowing the white to run through your fingers while carefully keeping the yolk from falling through or breaking. Set aside the egg white for Part II. 2. Before you start, weigh the egg yolk and calculate its volume using the density given on the worksheet. 3. Add the egg yolk to the mortar and mix with the pestle. 4. Measure out about 30 ml of oil. 5. Drizzle oil very, very slowly into the bowl or mortar while continuously whisking or grinding with the pestle. If you add oil too fast the emulsion will break and then it cannot be saved. If you are making the mayonnaise with someone else, this is best done with one person adding the oil slowly while the other person mixes. 6. Add salt and freshly ground black pepper to taste, and enjoy with bread or vegetables while continuing to the next step!

a. In the recipe above, the phospholipids in the egg yolk act as emulsifiers. If you assume that one egg yolk weighs 10g, that about 33% of this is fat, and that the majority of the fat is phospholipids, how many grams of emulsifier are there in an egg yolk? Give your answer in grams. (4 pts)

10·0.33 = 3.3g

b. If you take the average molecular weight of a phospholipid to be 800 g/mol. How many phospholipid molecules are there in one egg yolk? (2 pts)

3.3g/800g/mol = 0.004125mol 0.004125mol·6.022x1023molecules/mol = 2.48x1021molecules

c. If you managed to break the oil into droplets with a diameter of 0.1 mm by whisking very hard, what would the surface area of each droplet be? Give your answer in m2. (2 pts)

SA = 4πr2 SA = 4π(0.00005m)2 = 3.1x10-8m2 or 0.031mm2

d. Assuming that the “head” of each phospholipid molecule (i.e. the part of the molecule that would project from the surface of the oil droplets and protect it from the water phase) has an area of 10 x 10 Ångstroms (1 Ångstrom = 10−10m), how many phospholipid molecules do you need to cover the entire surface area of one oil droplet? (4 pts)

-10 2 -18 2 Aphospholipid = (10x10 ) = 10 m 2 -8 2 Adroplet = 0.031mm = 3.1x10 m 3.1x10-8/10-18 = 3.1x1010phospholipids/droplet

e. How many droplets can you cover with the number of phospholipid molecules you have in one egg yolk? (4 pts)

2.48x1021phospholipids from part b 2.48x1021phospholipids/3.1x1010phospholipids/droplet = 8x1010 droplets

f. What is the total volume of the oil droplets you were able to cover with phospholipids in the question above? This is the theoretical volume of mayonnaise you could make from one egg yolk. Give your answer in liters. (4 pts)

3 Vdrplet = 4/3πr 3 -13 3 Vdrplet = 4/3π(0.00005m) = 5.24x10 m total volume covered = 5.24x10-13m3/droplet·8x1010droplets = 4.19x10-2m3 4.19x10-2m3·1000L/m3 = 41.9L

Problem 2 - Christina Tosi - MilkBar Chocolate Chip cake (40 pts)

Here is a link with a recipe for one of Milk Bar’s famous desserts: http://www.hummingbirdhigh.com/2013/06/momofuku-milk-bar-chocolate-chip- cake.html

a. Go to the coffee frosting portion of the recipe. What is the volume fraction of water in this recipe? Assume that butter is roughly 15% water and milk is roughly 97% water. (4 pts)

volume water in butter = 0.5C·0.15 = 0.075C volume water in milk = 0.25C·0.97 = 0.2425C φ = (0.075C + 0.2425C)/(1C) = 0.318

Also: φ = (0.075C + 0.2425C)/(0.75) = 0.4243

b. Based on your answer to (a), is this frosting an elastic solid? Why or why not? (2 pts)

This is less than the critical volume fraction, so no. c. What other components of this recipe – ingredients or procedures - could be adding to the volume fraction in part (a)? Assume moving forward that the total volume fraction for this frosting is 0.65. (6 pts)

BEST ANSWER: Sugar will dissolve in the water (like starch would) but doesn’t swell, so it is likely not causing the added volume. However, creaming butter with sugar adds air, which can add to the volume fraction. Coffee powder can also help, although there’s not that much.

But this is tricky: The other dry ingredients could add to the volume fraction, mostly the sugar. c. You want your frosting to be able to withstand the weight of one of your cake layers without squishing too much. Assume that your cake layer has a radius of c8cm and weighs about 40g. What should the elasticity of this frosting be if you can’t let your 1cm layer of frosting depress by more than 0.5cm? (5 pts)

E = (F/A)/(dL/L0) F = .04kg·9.8m/s2 = .392N A = πr2 = π(.08m)2 = 0.02m2 E = (0.392N)/(0.02m2)/(.5cm/1cm) = 39.2Pa

d. Assume that the surface tension between the fat and water in your frosting is about 25mN/m. To achieve the elasticity in c, what should the radius of your emulsion droplets be? (5 pts)

휎 퐸 = (휑 − 휑 ) 푅 퐶 R = σ(φ- φc)/E R = ((25*10-3)(.65-.64)/39.2) = 6.38 * 10-6m = 6.4um

f. The instructions in step 3 say: “DO NOT ADD MORE COFFEE MILK INTO THE BUTTER MIXTURE UNTIL THE PREVIOUS ADDITION IS FULLY INCORPORATED.” What will happen if you add the milk too quickly? Give the term and explain what happens. (4 pts)

The emulsion could invert. This means that the water would become the continuous phase instead of the dispersed phase.

g. The final instruction for this recipe is to use the frosting immediately. What processes might happen if you let the frosting sit too long before using? Explain how each process works and state their technical terms. (8 pts)

Creaming/sedimentation – two liquids separate based on density Coalescence– droplets combine to lower surface energy Ostwald Ripening– smaller bubbles feed into larger ones even without touching

h. You have to cancel your party last-minute but have already made your cake components and are worried about your frosting. Assuming that you haven’t assembled the cake, what type of molecule could you add to your frosting to improve its emulsion stability? What properties of this type of molecule contribute to making the emulsion more stable? (4 pts)

Some sort of surfactant would decrease the surface energy of the emulsion. These molecules have a hydrophobic part and a hydrophilic part. This allows them to sit between the interface of the droplets acting like a shield and preventing them from merging with other or changing in size.

i. What other part of this full cake recipe contains an emulsion similar to the coffee cream? (2 pts)

Chocolate Cake

passionfruit curd (uses gelatin, not really an emulsion)

Problem 3 - ATK Angel Food cake (20 pts)

This week, Dan Souza from America’s Test Kitchen talks about foams in his video on angel food cake. Please watch this video here: http://cm.dce.harvard.edu/cs50player/youtube.html?title=&youtube_id=eLuyXvTKEM0 &srt_url=srts/eLuyXvTKEM0.srt

a. What component of egg whites allows them to foam? (2 pts)

proteins in the egg whites

b. What does adding cream of tartar do to the foam? Describe what happens in terms of the molecules involved. (8 pts)

Cream of tartar is an acid. When you add it to egg whites, it changes their electrical charge which reduces the interactions between the protein molecules, slowing protein bonding. This decrease in protein interaction allows the foam to be more stable because the proteins will be holding the air bubbles in place instead of interaction with eachother.

c. What other ingredients could you use instead of cream of tartar to achieve this same effect? (4 pts)

Other acids or things that interrupt the electrical charge

d. This video shows gravity playing a role in the angel food cake process at two points: one before baking and one after baking. For the part before baking, Dan shows two funnels filled with whipped egg whites. What part of the foam is being pulled down by gravity? Why is this bad? (6 pts)

The water is being pulled away. In this foam, water is the dispersed phase. If you remove the dispersed phase, there will be nothing holding the air bubbles there and the foam will disappear.

Problem 4 - Final project proposal (20 points)

Over the week, you should have met with your final project group and talked to your TF or one of the course heads about what you will be doing your final project on. Please fill out the proposal form online under week 10. Only one form needs to be submitted per team.