Scientific and Technical Aerospace Reports Volume 39 April 6, 2001

The hydrodynamics near steadily moving contact lines have been examined for a variety of material systems for low Capillary
number, Cais much less than1, and negligible Reynolds number, Re = approximately 0. However, in nature and in technological
applications, contact lines move under conditions of moderate Re and are often accelerating or decelerating. In both of these cases,
the role of inertia in the hydrodynamics controlling spreading must be considered. In this paper, we will discuss these hydrodynamics
in both the case of steady state motion of contact lines at moderate Re and the case of unsteady motion as the contact line accelerates
or decelerates to a final steady state after a perturbation from another, initial, steady state. In our experiments we test models
which incorporate inertia at steady state, and unsteady effects at essentially Re = 0. We first examine the steady state spreading
of four (-CH3)-terminated silicone oils on dry pyrex surfaces in the presence of significant inertia. Our measurements of the apparent
dynamic contact angle, omega(sub o), agree qualitatively with Cox’s predictions for this macroscopic contact angle and for
the interface curvature when inertia is important. However, quantitative comparisons of the hydrodynamics cannot be made
because of the lack of a uniformly valid asymptotic solution for the interface shape and the ambiguities arising from the variation
in inner physics with contact line speed. We observe that the presence of inertia reduces the dynamic curvature in the interface
shape and thus lowers omega(sub o). This is consistent with a simple picture of the effects of viscous forces and inertia. When
inertia becomes non-negligible with respect to viscous forces, the dynamic pressure gradient near the fluid-vapor interface
decreases. This is due to the fact that, when inertia becomes important, and all else being equal, the solid drags less fluid away
from the contact line region. by mass conservation, less fluid must be brought into the contact line by flow along the liquid/vapor
interface. This, in turn, implies that a smaller pressure gradient would be required along the interface to drive this smaller flow
rate into the contact line region. by the dynamic boundary condition, this decreased dynamic pressure leads to a reduced local
interface curvature compared to the purely viscous case as found in our experiments. In qualitative agreement with models incorporating
inertia, the integrated effect of this reduced curvature at each point along the interface causes the reduction in omega(sub
o) compared to the purely viscous case. We can contrast the successes and failures in comparing data to theory for the dependence
of omega(sub o) versus Ca, for four methyl-terminated oils. The quantitative success of the purely viscous model in predicting
omega(sub o) versus Ca for the three higher viscosity oils (3.0x10(exp -2) is less than Gamma(= Re/Ca) is less than 2.6x10(exp
2)) is consistent with the success of the model in describing the interface shapes for these cases. We see that the inner scale parameters
of these oils are velocity independent within our detectability limit. For our lowest viscosity oil (G=3.3x10(exp 4)), no model
quantitatively describes the observed dependence of omega(sub o) versus Ca. Since we do not know if the inner scale physics for
this oil has a significant velocity dependence, we cannot draw a firm conclusion on the moderate Re model. However, we note
that the lowest viscosity oil evaporates and this could have an effect on inner scale mechanisms that results in a velocity dependence
very different than higher viscosity oils with the same methyl termination. We have also studied the relaxation of contact
line motion and dynamic contact angles after an abrupt change in the relative velocity of the solid surface and the fluid body. In
these experiments, Ca remains small and Re = approximately 0 throughout the acceleration or deceleration of the contact line.
We used a model of the relaxation of the dynamic contact line by assuming that the interface shape is quasi-static, with an apparent
contact angle equal to the steady value at the instataneous contact line speed relative to the solid. Inertial effects are visible in our
data for short times after the abrupt change in surface velocity. At these short times, we find that the viscous bending of the interface
differs from that of a steadily moving contact line. Thus, we detect a deviation from Stokes flow in the intermediate region near
the contact line at early times. At very short times (i.e., less than 1 s for the lesser viscous fluid, 1000 cPoise) the contact angle
relaxation also disagrees with our quasi-static model. Later on after the abrupt change in surface velocity, the interface shape
agrees with the predictions of the steady state model, indicating that the flow near the contact line has returned to Stokes flow,
and the quasi-static model describes the contact line relaxation well. At long times, near the final steady state, the relaxation
becomes exponential as expected near the final point. Our models work equally well for both accelerating and decelerating contact
lines. The time scales both for the early time inertial regime and for the later quasi-static regime vary linearly with viscosity. However,
these times scales do not differ for -OH and -CH3 terminated oils of the same viscosity even though these oils show very
different steady state inner scale physics. Thus, the contact line relaxation we observe is likely due to viscous reorientation of the
fluid motion in the intermediate and outer regions and not controlled by relaxation of inner scale hydrodynamic mechanisms.
Author (revised)
Inertia; Hydrodynamics; Steady State; Viscosity; Spreading
20010024939 Washington State Univ., Dept. of Physics, Pullman, WA USA
Liquid Bridge Stabilization with Acoustic Radiation and Maxwell Stress
Marston, Phillip L., Washington State Univ., USA; Thiessen, David B., Washington State Univ., USA; Marr-Lyon, Mark J., Washington
State Univ., USA; Proceedings of the Fifth Microgravity Fluid Physics and Transport Phenomena Conference; December
2000, pp. 1079-1098; In English; See also 20010024890; No Copyright; Avail: CASI; A03, Hardcopy; A10, Microfiche
The stability of a liquid cylinder which bridges two solid cylinders has implications for the management of fluids in low-gravity.
It is well known that a cylindrical liquid bridge in zero gravity becomes unstable and breaks when the length of the cylinder
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