Local fluid and heat flow near contact lines

1998 ◽  
Vol 371 ◽  
pp. 377-378
Author(s):  
D. M. Anderson ◽  
S. H. Davis
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Heat Flow ◽  
Fluid Mechanics ◽  
Contact Line ◽  
Thermal Boundary Condition ◽  
The Other ◽  
Private Communication ◽  
Contact Lines ◽  
Rigid Plane

Journal of Fluid Mechanics, vol. 268 (1994), pp. 231–265It has recently come to our attention that our paper, which describes Marangoni-driven flow near a contact line, overlooks solutions involving a general thermal boundary condition on the free surface (private communication, S. J. Tavener 1997). These new solutions are applicable for non-isothermal flows in a corner region where one boundary is a rigid plane (and either perfectly insulating or perfectly conducting) and the other is a free surface upon which a general thermal boundary condition is applied. We describe these additional solutions below.

On identifying the appropriate boundary conditions at a moving contact line: an experimental investigation

1991 ◽  
Vol 230 ◽  
pp. 97-116 ◽  
Author(s):  
E. B. Dussan V. ◽  
Enrique Ramé ◽  
Stephen Garoff
Keyword(s):  
Boundary Condition ◽  
Experimental Investigation ◽  
Contact Line ◽  
Capillary Number ◽  
Silicone Oil ◽  
Outer Region ◽  
Contact Lines ◽  
Fluid Interface ◽  
Moving Contact ◽  
Inner Region

Over the past decade and a half, analyses of the dynamics of fluids containing moving contact lines have specified hydrodynamic models of the fluids in a rather small region surrounding the contact lines (referred to as the inner region) which necessarily differ from the usual model. If this were not done, a singularity would have arisen, making it impossible to satisfy the contact-angle boundary condition, a condition that can be important for determining the shape of the fluid interface of the entire body of fluid (the outer region). Unfortunately, the nature of the fluids within the inner region under dynamic conditions has not received appreciable experimental attention. Consequently, the validity of these novel models has yet to be tested.The objective of this experimental investigation is to determine the validity of the expression appearing in the literature for the slope of the fluid interface in the region of overlap between the inner and outer regions, for small capillary number. This in part involves the experimental determination of a constant traditionally evaluated by matching the solutions in the inner and outer regions. Establishing the correctness of this expression would justify its use as a boundary condition for the shape of the fluid interface in the outer region, thus eliminating the need to analyse the dynamics of the fluid in the inner region.Our experiments consisted of immersing a glass tube, tilted at an angle to the horizontal, at a constant speed, into a bath of silicone oil. The slope of the air–silicone oil interface was measured at distances from the contact line ranging between O.O13a. and O.17a, where a denotes the capillary length, the lengthscale of the outer region (1511 μm). Experiments were performed at speeds corresponding to capillary numbers ranging between 2.8 × 10-4 and 8.3 × 10-3. Good agreement is achieved between theory and experiment, with a systematic deviation appearing only at the highest speed. The latter may be a consequence of the inadequacy of the theory at that value of the capillary number.

scholarly journals An algorithm for the use of the Lagrangian specification in Newtonian fluid mechanics and applications to free-surface flow

1985 ◽  
Vol 152 ◽  
pp. 173-190 ◽  
Author(s):  
Poul Bach ◽  
Ole Hassager
Keyword(s):  
Contact Angle ◽  
Free Surface ◽  
Fluid Mechanics ◽  
Newtonian Fluid ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Contact Lines ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Plate Geometry

An algorithm is constructed for the use of the Lagrangian kinematic specification in Newtonian fluid mechanics. The algorithm is implemented with a finite-element method, and it is demonstrated that the method accurately describes free-surface flow, including the effects of surface tension, with the use of just bilinear isoparametric elements. Moving contact lines are modelled with a small amount of slip near the contact lines. The contact angle boundary condition is included in the form of a net interfacial force specified at the contact line. Simulations of measurements in a parallel-plate geometry show that the measured apparent contact angle is not the true angle, and that the true angle is always very close to the equilibrium value.

A note on the instabilities of a horizontal shear flow with a free surface

2000 ◽  
Vol 406 ◽  
pp. 337-346 ◽  
Author(s):  
L. ENGEVIK
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Shear Flow ◽  
Velocity Profile ◽  
Froude Number ◽  
The Other ◽  
Algebraic Equations ◽  
Horizontal Shear ◽  
Analytical Treatment ◽  
Unstable Region

The instabilities of a free surface shear flow are considered, with special emphasis on the shear flow with the velocity profile U* = U*0sech2 (by*). This velocity profile, which is found to model very well the shear flow in the wake of a hydrofoil, has been focused on in previous studies, for instance by Dimas & Triantyfallou who made a purely numerical investigation of this problem, and by Longuet-Higgins who simplified the problem by approximating the velocity profile with a piecewise-linear profile to make it amenable to an analytical treatment. However, none has so far recognized that this problem in fact has a very simple solution which can be found analytically; that is, the stability boundaries, i.e. the boundaries between the stable and the unstable regions in the wavenumber (k)–Froude number (F)-plane, are given by simple algebraic equations in k and F. This applies also when surface tension is included. With no surface tension present there exist two distinct regimes of unstable waves for all values of the Froude number F > 0. If 0 < F [Lt ] 1, then one of the regimes is given by 0 < k < (1 − F2/6), the other by F−2 < k < 9F−2, which is a very extended region on the k-axis. When F [Gt ] 1 there is one small unstable region close to k = 0, i.e. 0 < k < 9/(4F2), the other unstable region being (3/2)1/2F−1 < k < 2 + 27/(8F2). When surface tension is included there may be one, two or even three distinct regimes of unstable modes depending on the value of the Froude number. For small F there is only one instability region, for intermediate values of F there are two regimes of unstable modes, and when F is large enough there are three distinct instability regions.

scholarly journals Darcy-Brinkman free convection about a wedge and a cone subjected to a mixed thermal boundary condition

1992 ◽  
Vol 15 (4) ◽  
pp. 789-794 ◽  
Author(s):  
G. Ramanaiah ◽  
V. Kumaran
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Free Convection ◽  
Transformation Group ◽  
Darcy Number ◽  
Thermal Boundary Condition ◽  
High Porosity

The Darcy-Brinkman free convection near a wedge and a cone in a porous medium with high porosity has been considered. The surfaces are subjected to a mixed thermal boundary condition characterized by a parameterm;m=0,1,∞correspond to the cases of prescribed temperature, prescribed heat flux and prescribed heat transfer coefficient respectively. It is shown that the solutions for differentmare dependent and a transformation group has been found, through which one can get solution for anymprovided solution for a particular value ofmis known. The effects of Darcy number on skin friction and rate of heat transfer are analyzed.

scholarly journals Unsteady flow induced by a withdrawal point beneath a free surface

2005 ◽  
Vol 47 (2) ◽  
pp. 185-202 ◽  
Author(s):  
T. E. Stokes ◽  
G. C. Hocking ◽  
L. K. Forbes
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Unsteady Flow ◽  
Critical Values ◽  
The Other ◽  
Withdrawal Rate ◽  
Steady Solutions

AbstractThe unsteady axisymmetric withdrawal from a fluid with a free surface through a point sink is considered. Results both with and without surface tension are included and placed in context with previous work. The results indicate that there are two critical values of withdrawal rate at which the surface is drawn directly into the outlet, one after flow initiation and the other after the flow has been established. It is shown that the larger of these values corresponds to the point at which steady solutions no longer exist.

Part 2. The deeper structure of the Atlantic - Geological hypotheses and the earth's crust under the oceans

1954 ◽  
Vol 222 (1150) ◽  
pp. 341-348 ◽  
Keyword(s):  
Heat Flow ◽  
Recent Work ◽  
Sea Water ◽  
Volcanic Rocks ◽  
The Other ◽  
Ocean Floor ◽  
Peridotite Xenoliths ◽  
The Earth ◽  
Southern Rhodesia ◽  
Mohorovičić Discontinuity

Recent work has determined the depth of the Mohorovičić discontinuity at sea and has made it likely that peridotite xenoliths in basaltic volcanic rocks are samples of material from below the discontinuity. It is now possible to produce a hypothetical section showing the transition from a continent to an ocean. This section is consistent with both the seismic and gravity results. The possible reactions of the crust to changes in the total volume of sea water are dis­cussed. It seems possible that the oceans were shallower and the crust thinner in the Archean than they are now. If this were so, some features of the oldest rocks of Canada and Southern Rhodesia could be explained. Three processes are described that might lead to the formation of oceanic ridges; one of these involves tension, one compression and the other quiet tectonic conditions. It is likely that not all ridges are formed in the same way. It is possible that serpentization of olivine by water rising from the interior of the earth plays an important part in producing changes of level in the ocean floor and anomalies in heat flow. Finally, a method of reducing gravity observations at sea is discussed.

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