solvation - the action of surrounding a molecule with solvent.
dynamics - time dependent nature
Hence, solvation dynamics is the study of how a solvent interacts with molecules as a function of time. One can imagine that this is a complex issue. A single solute molecule, depending on its size, can be surrounded by tens to thousands of liquid molecules, each one tumbling and interacting with other solvents molecules and the solute.
theoretical modelling
Despite this molecular complexity, reasonable attempts have been made to make simple predictions about the time dependent behavior of solvents. Many of these are based on ingnoring the molecular nature of the solvent and instead treating it as a bulk dielectric which react response to changes in the solute (continuum models). This is much the same as describing a particular liquid by its bulk viscosity, which ignores the molecular friction that gives a liquid its consistency on the atomic scale. For those who are not comfortable with the myriad of assumptions that go into creating continuum models, explicit, all atom models are available. These fall mostly into the realm of molecular dynamics. Each solvent molecule is treated individually and its behavior at any given instant is determined by the sum of all interactions impinging upon it. These approaches, while potentially more accurate than continuum models, are computationally expensive.
experimental techniques
Solvation dynamics can also be measured experimentally by looking for solvent interactions with spectroscopic probes. Much work has been done using time-resolved fluorescence to this effect. The advantage of fluorescence is the ability to introduce an instantaneous change (see the Franck-Condon Principle) to the solute, which then perturbs the solvent in a time dependent manner. That is to say, exciting a molecule with a photon causes its electrons to rearrange, changing its physical and chemical nature. The solvent, which was accustomed to seeing a ground state molecule, are now confronted with a transient excited state species. They start to move and rearrange to accomodate this change. Now, looking back at the molecule - if the excited state molecule is sensitive to its environment, it will sense the motion of the solvent. This will affect the light it emits. The molecule serves both as the trigger which starts the solvent change, and the camera which can view the dynamics.
The simplest behavior is the time-dependant red shift that occurs in the instantaneous emission spectrum at any given instant after excitation. After excitation, the solvent molecules 'relax' around the excited state species. This relaxation often results in an increased electric field across the molecule. As the electric field increases, the gap between the first singlet excited state and the ground state decreases in energy, causing the photons that are emitted to be redder and redder in color as time goes on. Superimposing emission spectra at various times after emission show a spectrum whose center of mass keeps shifting to the red until a new equilibrium is reached.
applications
Solvation dynamics are interesting in the field of protein structure. Polarization of water molecules due to electrostatic forces of the protein are implicated in the activity of many enzymes. The study of unusual media such as glasses and supercritical fluids are also new frontiers in solvation dynamics. By comparing emperical observations with theoretical models, it is hoped we will soon understand how solvent interactions affect chemical processes in solution. | 
