Using photographic imaging and dye tracking experiments, we scrutinize
the dynamics
of a contact line when a finite volume of partially wetting fluid is driven
by gravity
to spread over a slightly inclined dry plane. Unlike spreading mechanisms
driven by
molecular forces, gravity-driven spreading over a dry plane is shown to
possess a
characteristic interfacial ‘nose’ that overhangs
the contact line when the film thickness
is in excess of the capillary length. A unique recirculating vortex exists
within the
nose front which spreads at speeds corresponding to capillary numbers in
excess
of 10−2. Our experiments show that fingering from a gravity-driven
straight front occurs when the above nose configuration cannot be sustained
across
the entire front as the film thins and the apparent contact angle θ
reaches
π/2. The fingers retain the nose configuration while
the remaining segments of the front evolve into a
wedge configuration and stop abruptly due to their large resistance to
fluid flow. This
fingering mechanism is insensitive to fluid wettability, noise or surface
heterogeneity.
Via matched asymptotics, we obtain accurate estimates of fingering position
and speed
at θ=π/2 that are in good agreement with measured values.
This new mechanism
is distinct from other instability and sensitivity fingering mechanisms
and can be in
play whenever θ of the straight front approaches
π/2 from above as the film thins.
Drops fall off a viscous pendent rivulet on the underside of a
plane when the
inclination angle θ, measured with respect to the horizontal, is below
a critical value
θc. We estimate this θc by
studying the existence of finite-amplitude drop solutions
to a long-wave lubrication equation. Through a partial matched asymptotic analysis,
we establish that fall-off occurs by two distinct mechanisms. For
θ>ϕ, where ϕ is
the static contact angle, a jet mechanism results when a mean-flow steepening effect
cannot provide sufficient axial curvature to counter gravity. This fall-off
mechanism
occurs if the rivulet width B, which is normalized with respect to
the capillary length
H=(σ/ρg cosθ)1/2, exceeds a critical
value defined by β=−cosB>1/4. For θ<ϕ,
the normal azimuthal curvature is the dominant force against fall-off and the
azimuthal capillary force. The corresponding critical condition is found to be
1.5β1/6>tanθ/tanϕ. Both criteria are in good
agreement with our experimental data.
We use MRI imaging to decipher the physical mechanism behind helical gel formation when a colloidal solution is evaporated from a small vertical or inclined capillary. A gel column, surrounded by the solvent, is observed to appear in the middle of a capillary. For nearly vertical capillaries, the denser gel column buckles under gravity to form a loose spiral. Further heating leads to the formation of a helical vapor pocket, surrounded by asymmetric liquid menisci. As the heating continues, this vapor pocket propagates downward and traces the buckled column. If gravity buckling occurs and if the maximum thickness of the annular solvent film is less than the solvent capillary length, significant nonuniform vapor pressure builds up within the vapor bubble because the vapor's escape is obstructed and because the evaporation is nonuniform. This upward air pressure spiral is amplified by asymmetric menisci of the vapor pocket to produce a high liquid pressure gradient along the liquid spiral next to the helical vapor pocket. Both pressures are inversely proportional to the internal capillary diameter d, and together, they twist the buckled column to a much higher pitch. The balance of this force to the elastic force of the buckled column, which opposes coiling, leads to a minimum distance between pitches L that scales as d. When all the fluid outside the column has evaporated, the slow vapor release by the drying gel cannot provide sufficient pressure for coiling. Hence, the "compressed spring" starts to rewind and lengthen. The dominant force balance with the opposing dry friction force leads to a lower final pitch with an L ∼ d 2 scaling. Both these scalings are consistent with our experimental data.
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