The Physics of Coal Liquid Slurry Atomization. Quarterly Technical Report, January 1995--March 1995 Page: 3 of 6
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The elongational stress, T, in the sample is related to the normal force, N, and the cross-sectional
area, A, by
T=N/A
The normal force can be determined from Newton's second law, whereby we have
-N- 2rRc-+ mg -Dr=ma (5)
where a is the surface tension, m is the mass of the suspended droplet, g is the gravitational
acceleration, a is the droplet acceleration and Dr is a correction for the aerodynamic drag on the
droplet. The mass of the suspended droplet is simply the flow rate (M) divided by the frequency
of formation of droplets (f). The normal force N is thus given by
N= M(g -a)-2rR- 24(1+ Re2/3))2 paV2 (6)
where the empirical drag law for a sphere of diameter d as a function of the Reynolds number (Re)
has been used. Re is defined as
Re = pa dV (7)
pa
The elongational stress (T) as a function of time (t) is given by
(g - a)-2rR-- 1+6Re2/3) d2 2 pav2
T =N_= -f Re 64(8)
A inR2
and the strain rate was given previously by Eq. (3).
In order to evaluate the transient elongational stresses (T) that are developed in the long
threads of liquid before breakup, the mass flow rate (M), the frequency of formation of droplets
(f), the acceleration of the droplet (a), the diameter of the ligament (2R), the diameter (d) and the
velocity of the suspended droplet (V) are required. In order to determine the strain rate (e) both the
instantaneous velocity of the droplet and the length of the ligament (L) are required. An
instantaneous elongational viscosity can be defined as
11E = T/
The mass flow rate (M) is measured by a simple catch and measure technique. The frequency of
formation of droplets (f) along with the instantaneous diameter of the ligament (2R) is measured by2
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The Physics of Coal Liquid Slurry Atomization. Quarterly Technical Report, January 1995--March 1995, report, September 1, 1995; [Pittsburgh, Pennsylvania]. (https://digital.library.unt.edu/ark:/67531/metadc792936/m1/3/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.