Why doesn\'t milk separate out in the fridge? Here we will idealize the milk as

Question

Why doesn't milk separate out in the fridge? Here we will idealize the milk as a suspension of fat droplets (spheres of diameter up to about a micron) in water. The Handbook of Physics and Chemistry lists the mass density of butterfat as milk fat = 0.91 g/cm3 (the density of water is 1 g/cm3 ). Hint: because you repeat similar calculations a few times, it is helpful to keep your work in symbols, not numbers, until the very last step. That way, it is easy to see how changing the radius or the temp affect everything, and you won’t have to re-do the calculation.

a. Consider one of the fat droplets, and calculate the net force on the droplet, considering both gravity and buoyancy.

b. Use Stokes law that v = F/, for for small spheres to:

Estimate how long it takes for fat globules in homogenized milk to drift a distance equal the size of a milk carton (about 25 cm) if the carton is refrigerated.

Then find the time to drift this distance for raw milk (which has fat droplets up to 5 µm in diameter).

c. Repeat part b), but for milk that is kept at room temperature.

Explanation / Answer

A) Net force= weight-buoyant force

                                =[V*density milk fat*g]-[V*density water*g]

                                =V*g*[density milk fat- density water]

                                =4/3*pi*r3 *g*[density milk fat- density water]

As given, taking v=F/viscosity

{though for constant velocity we should ist equate

6*pi*r*viscosity*v=4/3*pi*r3 *g*[density milk fat- density water]

and get v =(2/9)*r2*g*[density milk fat- density water]/viscosity }

but as this line in statement is not clear, will proceed according to

v=F/viscosity

v=4/3*pi*r3 *g*[density milk fat- density water]/viscosity

viscosity for refrigerated case(5C)=0.015182cm2/s

viscosity at room temperature(25C)=0.0089 cm2/s

b) refrigerated case

b1) homogenized

r=0.5*10^-4 cm=5*10-5 cm

v=4/3*pi*(5*10-5)3 *g*[.91 -1]/0.015182

=3.04*10-11cm/s

t=25/v=8.21*1011s

b2)raw

r=2.5*10^-4 cm

v=4/3*pi*(2.5*10-4)3 *g*[.91 -1]/0.015182

=3.8*10-9cm/s

t=25/v=6.56*109s

b) nonrefrigerated case

b1) homogenized

r=0.5*10^-4 cm=5*10-5 cm

v=4/3*pi*(5*10-5)3 *g*[.91 -1]/0.0089

=5.185*10-11cm/s

t=25/v=4.82*1011s

b2)raw

r=2.5*10^-4 cm

v=4/3*pi*(2.5*10-4)3 *g*[.91 -1]/ 0.0089

=6.28*10-9cm/s

t=25/v=3.85*109s

values don't seem legit

kinldy clear this line in statement

Use Stokes law that v = F/, for for small spheres to

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