Тұбырлардағы екі сұйықтың арасындағы капиллярлық қысым

Pressure between two fluids from forces between the fluids and tube walls
In fluid statics, capillary pressure is the pressure between two immiscible fluids in a thin tube (see capillary action), resulting from the interactions of forces between the fluids and solid walls of the tube. Capillary pressure can serve as both an opposing or driving force for fluid transport and is a significant property for research and industrial purposes (namely microfluidic design and oil extraction from porous rock). It is also observed in natural phenomena.

Capillary pressure formulas are derived from the pressure relationship between two fluid phases in a capillary tube in equilibrium, which is that force up = force down. These forces are described as:

Methods for taking physical measurements of capillary pressure in a microchannel have not been thoroughly studied, despite the need for accurate pressure measurements in microfluidics. The primary issue with measuring the pressure in microfluidic devices is that the volume of fluid is too small to be used in standard pressure measurement tools. Some studies have presented the use of microballoons, which are size changing pressure sensors. Servo nulling, which is historically used for measuring blood pressure, has also been demonstrated to provide pressure information in microfluidic channels with the assistance of a LabVIEW control system. Essentially, a micropipette is immersed in the microchannel fluid and is programmed to respond to changes in the fluid meniscus. A displacement in the meniscus of the fluid in the micropipette induces a voltage drop, which triggers a pump to restore the original position of the meniscus. The pressure exerted by the pump is interpreted as the pressure within the microchannel.

Current research in microfluidics is focused on developing point of care diagnostics and cell sorting techniques (see lab on a chip), and understanding cell behavior (e. g. cell growth, cell aging). In the field of diagnostics, the lateral flow test is a common microfluidic device platform that utilizes capillary forces to drive fluid transport through a porous membrane. The most famous lateral flow test is the take home pregnancy test, in which bodily fluid initially wets and then flows through the porous membrane, often cellulose or glass fiber, upon reaching a capture line to indicate a positive or negative signal. An advantage to this design, and several other microfluidic devices, is its simplicity (for example, its lack of human intervention during operation) and low cost. However, a disadvantage to these tests is that capillary action cannot be controlled after it has started, so the test time cannot be sped up or slowed down (which could pose an issue if certain time dependent processes are to take place during the fluid flow). Another example of point of care work involving a capillary pressure related design component is the separation of plasma from whole blood by filtration through porous membrane. Efficient and high volume separation of plasma from whole blood is often necessary for infectious disease diagnostics, like the HIV viral load test. However, this task is often performed through centrifugation, which is limited to clinical laboratory settings. An example of this point of care filtration device is a packed bed filter, which has demonstrated the ability to separate plasma and whole blood by utilizing asymmetric capillary forces within the membrane pores.

Capillary pressure plays a vital role in extracting sub surface hydrocarbons (such as petroleum or natural gas) from underneath porous reservoir rocks. Its measurements are utilized to predict reservoir fluid saturations and cap rock seal capacity, and for assessing relative permeability (the ability of a fluid to be transported in the presence of a second immiscible fluid) data. It is crucial to understand these geological properties of the reservoir for its development, production, and management (e. g. how easy it is to extract the hydrocarbons). The Deepwater Horizon oil spill is an example of why capillary pressure is significant to the petrochemical industry. It is believed that upon the Deepwater Horizon oil rig’s explosion in the Gulf of Mexico in 2010, methane gas had broken through a recently implemented seal, and expanded up and out of the rig. Although capillary pressure studies (or potentially a lack thereof) do not necessarily sit at the root of this particular oil spill, capillary pressure measurements yield crucial information for understanding reservoir properties that could have influenced the engineering decisions made in the Deepwater Horizon event. Capillary pressure, as seen in petroleum engineering, is often modeled in a laboratory where it is recorded as the pressure required to displace some wetting phase by a non wetting phase to establish equilibrium. For reference, capillary pressures between air and brine (which is a significant system in the petrochemical industry) have been shown to range between 0.67 and 9.5 MPa. There are various ways to predict, measure, or calculate capillary pressure relationships in the oil and gas industry. These include the following:

The Leverett J function serves to provide a relationship between the capillary pressure and the pore structure (see Leverett J function).

This method is well suited to irregular rock samples (e. g. those found in drill cuttings) and is typically used to understand the relationship between capillary pressure and the porous structure of the sample. In this method, the pores of the sample rock are evacuated, followed by mercury filling the pores with increasing pressure. Meanwhile, the volume of mercury at each given pressure is recorded and given as a pore size distribution, or converted to relevant oil/gas data. One pitfall to this method is that it does not account for fluid surface interactions. However, the entire process of injecting mercury and collecting data occurs rapidly in comparison to other methods. Other methods include the Vapor Pressure Method, Gravity Equilibrium Method, Dynamic Method, Semi dynamic Method, and the Transient Method.

It has been shown that as reservoir simulators use the primary drainage capillary pressure data for saturation height modeling calculations, primary drainage capillary pressure data should be averaged in the same manner that water saturations are averaged. Also, as reservoir simulators use the imbibition and secondary drainage capillary pressure data for fluids displacement calculations, these capillary pressures should not be averaged like primary drainage capillary pressure data. These can be averaged by Leverett J function. The averaging equations are as follows

in which is the number of core samples, is the effective porosity, is the bulk volume of sample, and is the primary drainage capillary pressure data vs. normalized water saturation.

in which is the number of core samples, is the effective porosity, is the absolute permeability, is the interfacial tension or IFT, and is the imbibition or secondary drainage capillary pressure data vs. normalized water saturation.

Capillaries in the circulatory system are vital to providing nutrients and excreting waste throughout the body. There exist pressure gradients (due to hydrostatic and oncotic pressures) in the capillaries that control blood flow at the capillary level, and ultimately influence the capillary exchange processes (e. g. fluid flux). Due to limitations in technology and bodily structure, most studies of capillary activity are done in the retina, lip and skin, historically through cannulation or a servo nulling system. Capillaroscopy has been used to visualize capillaries in the skin in 2D, and has been reported to observe an average range of capillary pressure of 10.5 to 22.5 mmHg in humans, and an increase in pressure among people with type 1 diabetes and hypertension. Relative to other components of the circulatory system, capillary pressure is low, as to avoid rupturing, but sufficient for facilitating capillary functions.