Scientists have found a solution to a scientific problem in fluid mechanics: Why water doesn't soak into soil at an even rate, but instead forms what looks like fingers of fluid flowing downward.

MIT researchers call this effect "gravity fingers," The explanation for their formation - the surface tension where the water - or any liquid - meets the soil. Knowing how to account for this phenomenon mathematically will have wide-ranging impact on science problems and engineering applications, including the recovery of oil from reservoirs.

Co-authors Luis Cueto-Felgueroso and Ruben Juanes of the MIT Department of Civil and Environmental Engineering discovered the solution while studying the larger question of how water displaces oil in underground reservoirs. "Our paper addresses a long-standing issue in soil physics," said Cueto-Felgueroso. "Lab experiments of water infiltration into homogeneous, dry soil repeatedly show the presence of preferential flow in the form of fingers. Yet, after several decades, the scientific community has been unable to capture this phenomenon using mathematical models."

"This was the type of problem that required someone from a different research discipline to take a look at it and come up with the solution," said Juanes, the ARCO Assistant Professor in Energy Studies. "Luis applied his expertise to a fluid mechanics problem in another medium -- porous media flows -- and quickly figured out the solution."

Gravity fingers in soil (or clay or sand) look very similar to water flowing down a window pane, a fairly well-understood phenomenon.

The solution also describes one aspect of the water-flowing-down-a-windowpane phenomenon that previously was not understood by scientists, who actually refer to this as "the flow of thin films": why water builds up at the tips of the fingers. Again, the answer has to with the surface tension. Before the water can flow down the film, it must build up enough energy to overcome the tension holding it in place. The missing mathematical phrase describes the surface tension of the entire finger of water, which may be several centimeters in width, as opposed to the tension existing at the micron-scale of pores between soil particles.

 A team of Nizhyn Labs of Scanning Devices (NLSD), Ukrainian enterprise, develops the new molecular methods and systems for hydroaccumulation and electrical power production. One of these methods is related with the use of the energy of water molecules situated in the interface layer of liquid.

On the surface of section of two phases (liquid and its saturated pairs, two liquids, that are not fully mixed up, liquid and solid)  as a result of molecular interaction in contiguous tangent phases the resultant force is observed which is directed inward one of them and composed of the forces that act on 1 sm² superficial layer. In particular, on the surface of section liquid – steam this force is directed inward liquids.

For transfer of molecules from the volume phase into a superficial layer it is necessary to execute work which goes to the increase of superficial energy – creation of surplus of energy of particles in a superficial layer in comparison with their energy into the volume of phase.

For the isothermal increase of superficial layer of liquid due to molecules which are found in its volume, it is necessary to execute work, that goes to  the increase of surface energy of liquid

                             A = (F_s – F_v)N,                                                         (1)

where (Fs – Fv) – middle difference of free energy on a surface Fs and in a volume Fv on one molecule, N – number of molecules in the superficial layer of liquid.

Work of isothermal formation of a 1см² surface (specific free superficial energy) is named surface tension at the given liquid on a boundary with the second phase:

                        σ = A/S = (F_s – F_v)N/S = (F_s – F_v)n₁,                            (2)

where n₁ = N/S – amount of molecules in a 1см² surface layer. Surface tension is also expressed by a formula

                                     σ = ΔF/ΔS,                                                     ( 3)

where ΔF – change of free surface energy, ΔS – change of area of surface layer. On a boundary of liquid with it own steam at a room temperature σ =15…2000 еrg х sm^-2. At the increase of temperature and approaching to the critical value the differences between liquid and her saturated steam disappear.  Near critical temperature σ→0. At the removal from a critical temperature the value σ linearly decreases with growth of temperature.

If the surface of liquid is limited by the perimeter of moistening, surface tension in equals to the force operating on unit of the moistening perimeter length and directed perpendicular to her.

The minimum of free surface energy is the condition of stable equilibrium of liquids. In the absence of external forces a liquid has the minimum area of surface (spherical form) at the set volume. 

On the boundary of touch of three phases (1- liquid, 2 - gas, 3 - solid) there is the phenomenon of moistening. The free surface of liquid near the surface of solid is distorted and forms a meniscus. A line, on which a meniscus intersects with a solid, is named the perimeter of moistening. The phenomenon of moistening is characterized by the regional corner of moistening between the moistened surface of solid and meniscus in the points of their crossing. The measure of moistening

                               cosθ = (σ₂₃ – σ₁₃)/ σ₁₂,                                           (4)

where σ₂₃, σ₁₃, σ₁₂ – surface tensions on three surfaces of section. At  σ₂₃ > σ₁₃ just expression of θ < π/2. In this case a liquid has a concave meniscus and moistens a solid; the surface of him is hydrofilo.

When σ₂₃ < σ₁₃,  θ > π/2, and a liquid has a protuberant meniscus, and the surface of solid is hydrophobic.

 In the narrow cylinder vessels (capillaries) of radius the r level of moistening (unmoistening) liquid is higher (below), than in the large vessel connected with them on a value   

                              h = 2σ cosθ/(rρg),                                                   (5)

where ρ – density of liquid, g – acceleration of gravity. If a capillary has the form of slit with the permanent thickness of δ, the meniscus of liquid represents by itself the cylinder surface of radius of δ/2, and the height of lifting (lowering) up of moistening (unmoistening) liquid in a capillary is evened

                                h = 2σ cosθ/(δρg),                                                 (6)

 The nature conforms the use effectiveness of internal energy of molecules of water, force of surface tension and effect of moistening of matter for creation of the hydrodynamic systems. These physical phenomena are involved in such important atmospheric phenomenon as a rotation of water in nature. Enormous masses of water in the earth's crust move under action of these phenomena, forming whole underground lakes and even seas, periodically rising on capillaries to the terrene or going down into underground lakes. The work which is done by molecular forces is measured by significant numbers.

Calculations and conducted researches show the possibility of creation of the artificial molecular hydropower systems with the use of energy of surface tension.

The chart of the molecular hydrodynamic system for hydroaccumulation and electric power production is shown on fig. 7. She consists of capillary volume structure (capillary matrix), water stock devise, located above capillary matrix and providing water stock and flow to the upper reservoir, lower reservoir and power equipment «hydro-turbine – electrogenerator». A capillary volume structure is submerged by it base in a lower reservoir with water.

The water from a lower reservoir under action of intermolecular forces of water and capillary matter rises up, where it is going by means of water stock, located above the surface of capillary structure in an overhead reservoir. The potential energy accumulated by water at falling on a hydro-turbine from a height H is transformed into kinetic energy of stream of water, and then into kinetic energy of hydro-turbine rotor and electrogenerator rotor, mechanically connected with him. Thus on the output of electrogenerator an electric current is formed which after certain transformation can be set to users. The «worked» water goes back into a lower reservoir.

The main feature of the given device is his work in the closed cycle when it does not need the presence of external streams of water to product electric current. The stream of water is created in the closed system due to intermolecular forces action.

With the purpose power increase of hydropower device the capillary structures (capillary matrices) can be set in great numbers into a lower reservoir, multiplying thus the stream of water from the lower reservoir into upper reservoir. For the increase of height lifting of water the capillary structures can be placed one above the anther, creating on each level intermediate water storage reservoirs which execute the same role, as the lower reservoir, differing by a capacity only. The closed cycle multy-levels self-lifting capillary water system for hydroaccumulation and e-energy production concludes N columns and M height levels of water lifting. Water stock device is general for all columns. He gets all lifted water and directs it into upper reservoir. The lower and upper reservoirs, intermediate storage reservoirs (on the number of height levels of water lifting) and power equipment «hydro-turbine – electrogenerator». In all another the closed cycle multy-levels self-lifting capillary water system for hydroaccumulation and e-energy production works after the same algorithm, as the device showed upper.

By Vasil Sidorov E-mail: sidorovvasil@gmail.com

on March 4, 2009 after MIT Tech Talk