The thermocapillary flow in liquid bridges is investigated numerically. In the limit
of large mean surface tension the free-surface shape is independent of the flow
and temperature fields and depends only on the volume of liquid and the hydrostatic
pressure difference. When gravity acts parallel to the axis of the liquid bridge the shape
is axisymmetric. A differential heating of the bounding circular disks then causes a
steady two-dimensional thermocapillary flow which is calculated by a finite-difference
method on body-fitted coordinates. The linear-stability problem for the basic flow is
solved using azimuthal normal modes computed with the same discretization method.
The dependence of the critical Reynolds number on the volume fraction, gravity level,
Prandtl number, and aspect ratio is explained by analysing the energy budgets of the
neutral modes. For small Prandtl numbers (Pr = 0.02) the critical Reynolds number
exhibits a smooth minimum near volume fractions which approximately correspond
to the volume of a cylindrical bridge. When the Prandtl number is large (Pr = 4)
the intersection of two neutral curves results in a sharp peak of the critical Reynolds
number. Since the instabilities for low and high Prandtl numbers are markedly
different, the influence of gravity leads to a distinctly different behaviour. While
the hydrostatic shape of the bridge is the most important effect of gravity on the
critical point for low-Prandtl-number flows, buoyancy is the dominating factor for
the stability of the flow in a gravity field when the Prandtl number is high.
Modelling fluid injection-induced fracture activation, damage growth, seismicity occurrence and connectivity change in naturally fractured rocks
