Physical meaning of tm The definition of dead time ($t_\mathrm m$) is mentioned as the time taken for elution of an unretained species. It is also mentioned that the retention time ($t_\mathrm r$) is sum of the time analyte spends in mobile ($t_\mathrm m$) and stationary phases ($t_\mathrm s$). But how can time spent by analyte in mobile phase be equal to the time required for an unretained species to pass through (dead time, $t_\mathrm m$)?

Both seems independent of each other. An analyte's time in the different phases is dependent on its affinity while the unretained species takes the same amount of time no matter what.

Please explain how they are same.
The analyte spends the same time in the mobile phase as it tooks for the mobile phase to pass through the column.


  An analyte's time in the different phases is dependent on it's affinity.


The time $t_\mathrm{m}$ is given.

The ratio of an analyte's time in the different phases is dependent on it's affinity and is equal:

$$\frac{t_\mathrm{s}}{t_\mathrm{m}}=K_\mathrm{D} \cdot \frac{V_\mathrm{s}}{ V_\mathrm{m}} $$.

where


$t_\mathrm{s}, t_\mathrm{m}$ are time is stationary and mobile phase
$K_\mathrm{D}$ is the phase distribution constant
$V_\mathrm{s}, V_\mathrm{m}$ are volumes of stationary and mobile phase.