Some things do not stay mixed. 
Sometimes, things do not stay mixed. 
Sometimes, things do not stay mixed. 
Have you ever noticed how oil and vinegar do not stay mixed? 
Phase separation works based on something called Gibbs free energy. This energy decides if things stay mixed or separate. The energy has two main parts: enthalpy and entropy. Entropy is often the main driver for mixing. Entropy increases when particles have more space to move around. In a mixture, particles can share a larger volume to increase entropy. However, if the temperature is low, the enthalpy can cause separation. This happens when the increase in entropy is not enough to lower the energy.
Scientists use special charts to study these changes. These charts are called phase diagrams. They show where a mixture is stable or unstable. There are two important boundary lines on these charts. One is called the binodal coexistence curve. The other is called the spinodal curve. Between these two curves, a mixture is called metastable. This means it might stay mixed unless something disturbs it. Beyond the spinodal curve, the mixture is absolutely unstable and will separate on its own.
Temperature is a very important factor in how things mix. There are two special heat levels called critical temperatures. One is the upper critical solution temperature, or UCST. The other is the lower critical solution temperature, or LCST. Above or below these levels, things will mix in all amounts. For example, nicotine and water have a special relationship. They mix well below 61 degrees Celsius. They also mix at high pressures above 210 degrees Celsius. Between those two temperatures, they only mix partially.
We can even see this happening in very cold gases. For instance, two types of helium can separate. These are called helium-3 and helium-4 isotopes. When they are mixed, they spontaneously separate into different regions. One region becomes rich in helium-4. The other region becomes rich in helium-3.
Phase separation is a physical process where a single, uniform mixture splits into two distinct parts. This phenomenon is known as the creation of different phases from a homogeneous mixture.

Entropy is a measure related to the space available for particles to explore. Generally, entropy increases when atoms or molecules have a larger common volume to share. Because a higher entropy usually lowers the Gibbs free energy, mixing is often favored. However, phase separation occurs when the energy balance shifts. If the enthalpy of mixing is positive and the temperature is low, the increase in entropy cannot lower the free energy enough to keep the mixture stable. In rare cases, the entropy of mixing is actually unfavorable, meaning it is negative. This leads to the concept of the lower critical solution temperature (LCST).
Beyond the spinodal curve, the mixture enters a state of absolute instability. If a mixture starts in a mixed state within this region, it will undergo spontaneous phase separation. This specific type of spontaneous separation is called spinodal decomposition. The Cahn–Hilliard equation is used to describe this process. Temperature also plays a vital role through critical temperatures. The upper critical solution temperature (UCST) and the lower critical solution temperature (LCST) are key markers. Above the UCST or below the LCST, components are miscible, meaning they can mix in all proportions.
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