(343c) Long-Time Dynamics of Thin Leaky Dielectric Films: Sliding and Cascading Structures

The long-time dynamics
of an interface between two leaky dielectrics subject to normal electric field
is investigated under the long-wavelength assumption. A reduced-order nonlinear
model for interface evolution is developed based on the method of weighted
residual integral boundary layer technique. For the two limiting cases of a
perfect conductor-perfect dielectric fluid pair as well as a pair of perfect dielectrics,
it is shown that the interface exhibits spontaneous sliding as it approaches
the wall, wherein the interface translates parallel to the wall (cf. Fig. 1(a)).
Under these limits, only the normal component of Maxwell stress at the
interface is significant and the interface dynamics resembles that of a
Rayleigh-Taylor unstable interface. For a general pair of leaky dielectrics, the
presence of interfacial charge results in an additional tangential stress at
the interface, which prevents the onset of sliding. For leaky dielectrics with fast
relaxation times, a single evolution equation governing the interface position
is derived. In this case, only for dielectric pairs with conductivity ratio (σ)
equal to the permittivity ratio (ϵ), it is shown that the interface exhibits
sliding dynamics. This is because σ=ϵ
corresponds to the case of zero interfacial charge and the interface dynamics
is governed by the normal Maxwell stress alone. It is further shown that for
dielectric pairs with σ²=ϵ,
the normal stress component vanishes, and the
interface dynamics is governed solely by the tangential component of Maxwell
stress. The interface, in this case, then exhibits cascading structures (cf. Fig
1(b)) similar to those reported in long-wave Marangoni instability. The fate of
the interface for dielectric pairs with sigma and permittivity values other than
those discussed above is governed by a combined effect of tangential and normal
stress, with the tangential stress predominating as the interface approaches
the wall.

Fig. 1. (a) Evolution
of the interface between thin leaky dielectric films exhibiting spontaneous
sliding; t=0.001x10⁷ (dotted), 2 x10⁷
(dot-dashed), 4.7 x10⁷ (dashed) 6.7 x10⁷ (solid). The arrow indicates the direction of horizontal
translation (b) Cascading structures exhibited by the interface between thin
leaky dielectrics. The insets depict magnified view of the interface inside the
boxed regions near the wall.

We are grateful to NASA
via NNX17AL27G for financial support.