The essence of the sedimentation method of analysis is to measure the rate at which particles settle (mainly from a liquid medium). And using the values of the settling rate, the sizes of these particles and their specific surface area are calculated. This method determines the parameters of particles of many types of disperse systems, such as suspensions, aerosols, emulsions, that is, those that are widespread and important for various industries.
The concept of dispersion
One of the main technological parameters characterizing substances and materials in various production processes is their fineness. It is necessarily taken into account during the selection of apparatus for chemical technology, in the production of various food products, etc. This is due not only to the fact that with a decrease in the particles of substances, the surface area of the phases increases and the rate of their interaction increases, but also to the fact that some properties of the system change in this case. In particular, the solubility increases, the reactivity increasessubstances, the temperatures of phase transitions decrease. Therefore, it became necessary to find quantitative characteristics of the dispersion of various systems and in sedimentation analysis.
Depending on how the particle sizes in the dispersed phase are related, systems are divided into monodisperse and polydisperse. The former consist exclusively of particles of the same size. Such disperse systems are quite rare and in reality are very close to true monodisperse ones. On the other hand, the vast majority of existing disperse systems are polydisperse. This means that they consist of particles differing in size, and their content is not the same. In the course of sedimentation analysis of disperse systems, the sizes of the particles that form them are determined, followed by the construction of their size distribution curves.
Theoretical foundations
Sedimentation is the process of precipitation of particles that make up the dispersed phase in gaseous or liquid media under the action of gravity. Sedimentation can be reversed if particles (droplets) float in various emulsions.
Gravity Fg acting on spherical particles can be calculated using the hydrostatic correction formula:
Fg=4/3 π r3 (ρ-ρ0) g, where ρ is the density of matter; r is the particle radius; ρ0 – fluid density; g - accelerationfree fall.
The force of friction Fη, described by the Stokes law, counteracts the settling of particles:
Fη=6 π η r ᴠsed, where ᴠsed is the particle velocity and η is the fluid viscosity.
At some point in time, the particles begin to settle at a constant speed, which is explained by the equality of the opposing forces Fg=Fη, which means that the equality is also true:
4/3 π r3 (ρ-ρ0) g=6 π η r ·ᴠsed. By transforming it, you can get a formula that reflects the relationship between the particle radius and its settling rate:
r=√(9η/(2 (ρ-ρ0) g)) ᴠsed=K √ᴠsed.
If we take into account that the speed of particles can be defined as the ratio of its path H to the time of movement τ, then we can write the Stokes equation:
ᴠsat=N/t.
Then the radius of the particle can be related to the time of its settling by the equation:
r=K √N/t.
However, it is worth noting that such a theoretical justification of sedimentation analysis will be valid under a number of conditions:
- Solid particle size should be between 10–5 to 10–2 see
- Particles must be spherical.
- Particles must move at a constant speed and independent of neighboring particles.
- Friction must be an internal phenomenon of a dispersion medium.
Due to the fact that real suspensions often containparticles that significantly differ in shape from spherical ones introduce the concept of equivalent radius for the purposes of sedimentation analysis. To do this, the radius of hypothetical spherical particles made of the same material as the real ones in the studied suspension and settling at the same speed is substituted into the calculation equations.
In practice, particles in dispersed systems are heterogeneous in size, and the main task of sedimentation analysis can be called the analysis of particle size distribution in them. In other words, during the study of polydisperse systems, the relative content of various fractions is found (a set of particles whose sizes lie in a certain interval).
Features of sedimentation analysis
There are several approaches to performing analysis of dispersed systems by sedimentation:
- monitoring in a gravitational field the speed at which particles settle in a calm liquid;
- suspension agitation for its subsequent separation into fractions of particles of given sizes in a liquid jet;
- separation of powdered substances into fractions with certain particle sizes, performed by air separation;
- monitoring in a centrifugal field the parameters of subsidence of highly dispersed systems.
One of the most widely used is the first version of the analysis. For its implementation, the sedimentation rate is determined by any of the following methods:
- watching through a microscope;
- weighing the accumulated sediment;
- determining the concentration of the dispersed phase in a certain period of the settling process;
- measuring hydrostatic pressure during subsidence;
- determining the density of the suspension during the settling period.
Suspension Concept
Suspensions are understood as coarse systems formed by a solid dispersed phase, the particle size of which exceeds 10-5 cm, and a liquid dispersion medium. Suspensions are often characterized as suspensions of powdered substances in liquids. In fact, this is not entirely true, since slurries are dilute suspensions. The particles of the solid phase are kinetically independent and can move freely in the liquid.
In real (concentrated) suspensions, which are often called pastes, solid particles interact with each other. This leads to the formation of a certain spatial structure.
There is another type of dispersed systems formed by solid dispersed phases and liquid dispersion media. They are called lyosols. However, the particle size is much smaller (from 10-7 to 10-5 cm). In this regard, sedimentation in them is insignificant, but lyosols are characterized by such phenomena as Brownian motion, osmosis and diffusion. The sedimentation analysis of suspensions is based on their kinetic instability. This means that suspensions are characterized by time variability of such parameters as fineness and equilibrium distribution of particles in a dispersion medium.
Methodology
Sedimentation analysis is performed using a torsion balance with a foil cup(diameter 1-2 cm) and a tall glass. Before starting the analysis, the cup is weighed in the dispersion medium, immersing it in a filled beaker and balancing the balance. Along with this, the depth of its immersion is measured. After that, the cup is removed and quickly placed in a glass with the test suspension, while it must be hung on the hook of the balance beam. At the same time, the stopwatch will start. Data on the mass of precipitated precipitation at arbitrary points in time are entered into the table.
| Time from start of study, s | Mass of the cup with sediment, g | Mass of sediment, g | 1/t, c-1 | Sedimentation limit, g |
Using the data in the table, draw a sedimentation curve on graph paper. The mass of settled particles is plotted along the ordinate axis, and time is plotted along the abscissa axis. In this case, an adequate scale is selected so that it is convenient to perform further graphical calculations.
Curve analysis
In a monodisperse medium, the settling rate of particles will be the same, which means that settling will be characterized by uniformity. The sedimentation curve in this case will be linear.
During the settling of a polydisperse suspension (which happens in practice), particles of different sizes also differ in settling speed. This is expressed on the graph in the blurring of the boundary of the settling layer.
The subsidence curve is processed by dividing it into several segments and drawing tangents. Each tangent will characterize the subsidence of a separatemonodisperse part of the suspension.
General idea of particle size distribution
The quantitative content of particles of a certain size in the rock is usually called the granulometric composition. Some properties of porous media depend on it, for example, permeability, specific surface area, porosity, etc. Based on these properties, in turn, conclusions can be drawn about the geological conditions for the formation of rock deposits. That is why one of the first stages in the study of sedimentary rocks is granulometric analysis.
Thus, according to the results of the analysis of the granulometric composition of sands in contact with oil, they choose equipment and work procedures in oilfield practice. It helps to select filters to prevent sand from entering the well. The amount of clay and colloidal-dispersed minerals in the composition determines the processes of absorption of ions, as well as the degree of swelling of rocks in water.
Sedimentary analysis of granulometric composition of rocks
Due to the fact that the analysis of dispersed systems based on the principles of sedimentation has a number of limitations, its use in its pure form for the granulometric study of rock composition does not provide due reliability and accuracy. Today it is performed using modern equipment using computer programs.
They allow the study of rock particles from the starting layer, allow you to continuously record the accumulationsediment, excluding approximation by equations, measure the sedimentation rate directly. And, no less important, they allow the study of the sedimentation of irregularly shaped particles. The percentage of fraction of one size or another is determined by the computer, based on the total mass of the sample, which means that it does not need to be weighed before analysis.
