  An erythrocytes sedimentation rate (ESR) measures how fast a blood sample
sediments along a test tube in one hour in a clinical laboratory. Since
elevated level of ESR is associated with inflammatory diseases, ESR is one of
the routine hematology test in a clinical laboratory. In this paper, the
physics of erythrocyte (RBC) sedimentation rate as well as the dynamics of the
RBC is explored by modeling the dynamics of the cells as the motion of Brownian
particle moving in a viscous medium. The viscous friction of blood $\gamma$ is
considered to decrease as the temperature of the medium increases \cite{aa1}.
The results obtained in this work show that the ESR increases as the number of
red blood cells (that bind together in the sedimentation process) steps up. The
room temperature also affects the sedimentation rate. As the room temperature
rises up, the ESR steps up. Furthermore the dynamics of the RBC along a
Westergren pipet that is held in an upright position is explored. The exact
analytic result depicts that the velocity of cells increases as the number of
cells that form rouleaux steps up. Since our study is performed by considering
real physical parameters, the results obtained in this work non only agree with
the experimental observations but also helps to understand most hematological
experiments that are conducted in vitro.
