Week 6 Module: Colloids and Emulsions

Research question#

A long-simmered pork or fish bone broth (奶汤, “milky soup”) turns opaque white and stays that way for hours, while a quickly-simmered clear stock made from the same bones does not. Both contain fat. Why does one separate into a clear stock with fat floating on top, and the other stay a stable, uniform milky emulsion?

Specimen 奶汤, milky bone broth, fat-in-water emulsion

Where this sits#

Closing module of Stage 2, Structures and Networks. Modules 4 and 5 built continuous solid networks from starch and protein; this module covers the other structural outcome available to a food system — a stable dispersion of one phase (fat droplets) in another (water), which never becomes a single network but can still be kinetically stable for a long time. It sets up Module 7’s transport framing directly: a milky broth is literally the product of vigorous simmering breaking fat into small droplets and dispersing them by turbulent mass transport.

The model: Stokes’ law and creaming#

An isolated spherical fat droplet in a broth rises (creams) or falls (sediments) under gravity at a terminal velocity given by Stokes’ law:

v (creaming velocity, m·s⁻¹)

how fast the droplet moves relative to the surrounding liquid.

Δρ (density difference, kg·m⁻³)

fat is less dense than water, so fat droplets rise; the larger this gap, the faster the separation.

g (gravitational acceleration, m·s⁻²)

fixed.

r (droplet radius, m)

the dominant lever: v scales with r², so halving droplet size cuts creaming velocity by a factor of four.

η (continuous-phase viscosity, Pa·s)

a more viscous water phase (from dissolved gelatin — Module 3's collagen-to-gelatin transition, held in solution) slows creaming.

A quickly-made clear stock is simmered gently, so fat stays in large droplets (or an unbroken layer) that cream out fast — the r² term dominates. A long-simmered milky broth is boiled hard enough that turbulence mechanically breaks fat into much smaller droplets, and the same long simmer dissolves collagen into gelatin, raising the continuous phase’s viscosity η. Both effects push in the same direction: smaller r and higher η both reduce v, so the emulsion resists separating even without any added emulsifier — though naturally-occurring phospholipids and proteins at the droplet surface also play a stabilising role that Stokes’ law, on its own, does not capture (see limitations below).

v scales as

r²

Two levers

droplet size, η

Stabiliser

smaller r + higher η

What you measure and analyse#

Using a supplied dataset of droplet-size distributions for broths simmered at three different intensities, you compute the Stokes’ law creaming velocity for the median droplet size in each case and rank the three broths by predicted visual stability over a 4-hour rest.

Activity#

A restaurant kitchen wants a broth that is milky (stable emulsion) but needs to be made faster than a multi-hour simmer allows. Using the two levers in Stokes’ law that a cook can actually influence during cooking (droplet size via mechanical agitation, continuous-phase viscosity via gelatin extraction), propose a process change and justify it from the equation rather than from taste alone.

References#

• McClements, D.J. (2015). Food Emulsions: Principles, Practices, and Techniques, 3rd ed. CRC Press.
• Walstra, P. (2003). Physical Chemistry of Foods. Marcel Dekker.