Temperature modeling simulation
Temperature rise due to sonication is modelled using the ‘Heat transfer
in solid and fluid interface’ module in COMSOL Multiphysics v5.4 as a
time dependent study. The simulated model has three domains (Fig 7c): 1)
sonication tube domain, 2) polypropylene tube wall domain, and 3) ice
bath domain. The thermal and physical properties of each of the domains
is listed in supplement (Supplement Table 13).
The time dependent heat transfer equation is:
\(\rho\)s Cp\(\frac{\partial T}{\partial t}\) =\(\kappa\)s\(\nabla\)2 T +\(\rho_{s}C_{\text{p\ }}\overrightarrow{u}\ \nabla.T+\ \)Qg\(\ +\ \)Qloss[Eq. 10]
Where \(\rho_{s},\) Cp , T ,ks , \(\overrightarrow{u}\), Qgand Qs are domain material density, specific heat,
temperature, thermal conductivity, velocity vector, heat generation term
and heat loss term, respectively.
Returning to the velocity field solution above, the assumption of
laminar flow should not be used for this calculation, only for
generalization of fluid volume affected by the tip (Fig 2). Rather, in
an extremely turbulent environment with nonlinear cavitation constrained
to a small cavity it is difficult to determine the time dependent
velocity field coupled with heat transfer. Due to turbulence, there is a
time-dependent change in thermal properties such as the thermal
conductivity ‘k’. Due to high conductivity, small scale and assumed
complete turbulent mixing, the cell suspension domain is considered
isothermal and the velocity term can be neglected. This simplifies the
heat transfer in the tube to the following equation –
\(\rho\)s Cp\(\frac{\partial T}{\partial t}\) =\(\kappa\)s\(\nabla\)2 T\(+\ \)Qg [Eq. 11]
The ice-bath is considered large enough so that it can effectively act
as a heat sink without much temperature rise. The material and thermal
property of ice bath is assumed similar to ice. The total outside domain
can be considered insulated (no heat flow in or out) as outside
temperature has negligible effect in temperature of the domains.
The heat generation term Qg is active only inside the sonication tube
domain as a volumetric heat source in W/m3. The power
delivered is measured empirically from the sonicator and multiplied with
a tip conversion factor to account for realistic loss of power of 0.85
from literature (Pasumarthi, 2016) and divided by the sample volume to
get the volumetric heat source term. The volumetric heat source is
multiplied by a piecewise time function to incorporate pulsing. The
function value is 1 while the pulse is on and 0 when pulse is off.
Temperature value is stored for each second.