A mineral dust grain presents a flat wall to supercooled water

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Nucleation and the lifetime of a metastable phase

Problem

A mineral dust grain presents a flat wall to supercooled water, with a contact angle θc=45∘\theta_c = 45^\circ measured through the ice, the new phase (Young's equation). At the relevant supercooling the homogeneous nucleation barrier is ΔFhomo∗=150 kBT\Delta F^*_{\rm homo} = 150\,k_BT. Using fhet(θc)=14(2+cos⁡θc)(1−cos⁡θc)2f_{\rm het}(\theta_c) = \tfrac14(2+\cos\theta_c)(1-\cos\theta_c)^2, find: ((a)) the heterogeneous factor fhetf_{\rm het}; ((b)) the barrier ΔFhet∗\Delta F^*_{\rm het} for nucleation on the dust grain.

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