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# Stoke's law

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Stoke's Law calculates rate of destabilization of an emulsion by equating gravitational force with the opposing hydrodynamic force. Stoke's Law can be used to predict emulsion stability.

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### Stoke's law

1. 1. Stoke’s Law Photo  courtesy  of  Patrick  Willems  on  Flickr     Prof. Abd Karim Alias Universiti Sains Malaysia
2. 2. Stoke's Law calculates rate of destabilization of an emulsion by equating gravitational force with the opposing hydrodynamic force: where V = velocity of separation (or rate of creaming), cm/sec; g = acceleration of gravity (980 cm/sec); r = droplet radius (cm); d1 = density of disperse phase (g/cm3); d2 = density of continuous phase (g/cm3); µ = viscosity of the continuous phase (g/cm.sec) (µ = 0.01 at 20 °C) Stoke’s Law 2gr2 (d1 – d2) 9µ
3. 3. You are making orange soda from an orange flavor emulsion. The density of the orange oil is 0.85 g/cm3, the density of a 10% sugar solution is 1.04 g/cm3, the average particle radius is 3.0 micron, and µ = 0.01 g/ cm·sec. What is V? Will the emulsion remain stable? Stoke’s Law PROBLEM 1 2gr2 (d1 – d2) 9µ   Photo  courtesy  of  Brent  Moore  on  Flickr
4. 4. You homogenize the beverage mix so that the particle radius is decreased to 0.3 micron. What is V? Will the emulsion remain stable? Stoke’s Law PROBLEM 2 2gr2 (d1 – d2) 9µ   Photo  courtesy  of  Brent  Moore  on  Flickr
5. 5. You add brominated vegetable oil to the orange oil so the overall density is 0.95 g/ cm3 . What is V for particle radius 3.0 micron? For 0.3 micron? Will the emulsion remain stable? Stoke’s Law PROBLEM 3 2gr2 (d1 – d2) 9µ   Photo  courtesy  of  Brent  Moore  on  Flickr
6. 6. For the above problems, which approach stabilized the emulsion more -- decreasing particle size or increasing density of the dispersed phase? Stoke’s Law PROBLEM 4 2gr2 (d1 – d2) 9µ   Photo  courtesy  of  Brent  Moore  on  Flickr