A Phase is a portion  of matter that has a rheological behavior and physical properties in a macroscopic sense, that is, it behaves as a fluid e.g. portion of dust or sand can flow as fluid. Gases and liquids are easily seen as fluids.

Hence, a multiphase system have more than one fluid  e.g. water and oil,  air and water, dust and air, etc. Flowing at same time. Each phase will has a density and a viscosity ( constant or not, it doesn't matter) as well as other physical properties as diffusivities of mass and heat .

A Specie is a type of matter,  a chemical substance as O2, N2, or CO2. The air is a fluid formed by chemical species as aforementioned  substances.  One fluid can be seen as a unique substance with its physical properties or as a mixture of other substances that can change its proportions due to mass transfer process, or chemical reactions. e.g.  combustion.

When a fluid is formed by other components, is common to refer to it as a multicomponent fluid.

A phase in a multiphase flow can be formed by Species also, e.g. water and  air bubbles. There are a diffusion of species among the fluids (or phases) as well chemical reactions. O2 can diffuse from air to water in aeration process. Dangerous gases can be extracted from air stream  through a bubble column, etc. 

I hope that help you!

the species model is based on eulerian-lagrangian view.It is used when the void fraction of species phase is significantly smaller than the fluid.In this view for each species diffrential equation is solved individually.

multiphase models which consist of VOF,Mixture and Eulerian, are based on Eulerian-Eulerian view. In this model governing equations of species models the same as fluid, and define in a Eulerian coordinate.

therefore, For modeling multiphase flow it is important to know about the volume fraction of phases.

Multiphase flow is a flow in which more than one fluid is present. In general, the fluids consist of different chemical species, such as air-water. In some applications, they may represent different thermodynamic phases of the same species, such as steam-water.

The fluids in a multiphase flow are assumed to be mixed at macroscopic length scales. In this case, it is necessary to solve for different velocity and temperature fields, etc., for each fluid. These may interact with each other by means of interfacial forces and heat and mass transfer across the phase interfaces.

A multicomponent fluid is assumed to consist of a mixture of chemical species which are mixed at the molecular level. In this case, single mean velocity and temperature fields, etc., are solved for the fluid.

A species is a chemical substance which diffuses within a phase containing generally more species: this phase has a barycentric velocity and the difference between the velocity of the species and the barycentric velocity is expressed through a diffusion term. An example could be dry air and vapour within the gaseous phase or water vapour and capillary water within the water phase. If you sum the mass balance equations of the species of a phase, the diffusion term cancels out.

Phases express the state of a substance: solid, liquid, gas, plasma;

So in general species feature diffusion terms, phases not. Phases have their own velocity.

There is a typing error in the second example: capillary water and bound water may form the water phase, e.g. in concrete.

So can I say, a liquid_water-air fluid mixture is a multi_species problem, but if that water starts boiling, then it becomes a multi_specie—multi_phase problem?

Soumitra Vadnerkar a water(liq) + air is a two-phase system such in aquarium with rising bubbles. The state change of water from liquid to steam - to water can another phase if there is a lot of steam and you can see the bubbles of steam rising. But the modeling is not so simple:

In this case we have liquid phase1(mixture liq. water + steam) + phase 2(mixture of dry air and steam). Two phases ( liq + gas) with two components each one Initially phase 1 and 2 has 0% of steam . Due to some process - boiling, cavitation, etc - steam is created due to some source. And simultaneously, to be transfer to phase 2 ( dry air and steam) due to saturation, vapour pressure, etc - the mass transfer is part of the problem-, but inside water there is 0% of air, therefore, bubbles of steam starting to grow and the phase 2 starts to be seen in the phase 1 and growing and rising. A model of bubbles formation PBM for example)is need because we need each diameter and interfacial area. Once the bubles reach the interface, the steam is released into the dry air and the composition is changed.

We have 2 phases and 3 species. This modeling is one example.

Yeah, thank Ricardo Vicente de Paula Rezende , I understood the answer as,

So basically it’s a multi_phase problem. Because, there is phase change between liquid and gas. But at the same time, there is presence of air- which makes it multi_species problem as well.

finally, it becomes multi_phase + multi_species problem.

Yes, Soumitra Vadnerkar , you 're right,a multiphase flow with more that one single chemical specie. It is a hard problem to solve due to fast time scales related to phase change and bubble formation. and there is the energy balance to be solved together.