The essence of the sedimentation analysis method is to measure the speed at which particles settle (mainly from a liquid medium). And using the values of the sedimentation rate, calculate the size of these particles and their specific surface area. Using this method, the particle parameters of many types of dispersed systems are determined, for example, 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 dispersion. It is necessarily taken into account during the selection of devices for chemical technology, in the production of a variety of food products, etc. This is due not only to the fact that with decreasing particles of substances, the surface area of the phases increases and the rate of their interaction increases, but also due to the fact that some properties of the system change. In particular, solubility increases, the reactivity of a substance increases, and the temperatures of phase transitions decrease. Therefore, the need arose 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, the systems are divided into monodisperse and polydisperse. The former consist solely of particles of the same size. Such disperse systems are quite rare and in reality are very close to true monodisperse systems. But the vast majority of existing disperse systems are polydisperse. This means that they consist of particles of different sizes, and their content is not the same. In the course of sedimentation analysis of dispersed systems, the sizes of the particles forming them are determined, followed by the construction of their size distribution curves.
Theoretical basis
Sedimentation is the process of precipitation of particles that make up the dispersed phase in a gaseous or liquid medium under the action of gravity. Sedimentation may be reversed if particles (droplets) float in various emulsions.
The value of gravity F g acting on particles of a spherical shape can be calculated by the formula, taking into account the hydrostatic correction:
F g = 4/3 · π · r 3 · (ρ-ρ 0 ) · g,
where ρ is the density of the substance; r is the particle radius; ρ 0 is the density of the liquid; g is the acceleration of gravity.
Friction force F η , described by the Stokes law, counteracts the subsidence of particles:
F η = 6 · π · η · r · ᴠ sed ,
where ᴠ sed is the particle velocity, and η is the fluid viscosity.
At some point in time, the particles begin to settle at a constant speed, due to the equality of the opposing forces F g = F η , which means that the equality is also true:
4/3 · π · r 3 · (ρ-ρ 0 ) · g = 6 · π · η · r · ᴠ gray Transforming it, you can get a formula that reflects the relationship of the particle radius with its sedimentation rate:
r = √ (9η / (2 · (ρ-ρ 0 ) · g)) · ᴠ sed = K · √ᴠ sed .
If we take into account that the particle velocity can be defined as the ratio of its path H to the motion time τ, then we can write the Stokes equation:
ᴠ sed = N / t.
Then the particle radius can be associated with the time of its sedimentation by the equation:
r = K · √ N / t.
However, it is worth noting that such a theoretical justification of sedimentation analysis will be true if a number of conditions are met:
- The size of solid particles should correspond to values from 10 –5 to 10 –2 cm.
- Particles must have a spherical shape.
- Particles must move at a constant speed and independently of neighboring particles.
- Friction should be an internal phenomenon of a dispersion medium.
Due to the fact that real suspensions often contain particles that differ significantly in shape from spherical, for the purposes of sedimentation analysis, the concept of an equivalent radius is introduced. For this, the radius of hypothetical spherical particles made of the same material as the real ones in the suspension under study and that settle 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 the distribution of particle size in them. In other words, in the study of polydisperse systems, the relative contents of various fractions are found (a set of particles whose sizes lie in a certain range).
Features of sedimentation analysis
There are several approaches to the analysis of dispersed systems by sedimentation:
- observation in the gravitational field of the speed at which particles settle in a calm liquid;
- stirring up the suspension for its subsequent separation into fractions of particles of a given size in a liquid stream;
- separation of powdered substances into fractions with specific particle sizes, performed by air separation;
- observation in a centrifugal field of the settling parameters of finely 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:
- observing 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 in the process of subsidence;
- determining the density of the suspension during the settling period.
Suspension concept
Suspensions are understood as coarse-dispersed systems formed by a solid dispersed phase, particle sizes of which exceed 10 -5 cm, and a liquid dispersion medium. Often suspensions are characterized as suspensions of powdered substances in liquids. In fact, this is not entirely true, since suspensions are diluted suspensions. Particles of a solid phase are kinetically independent and can freely move in a 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 size of the solid particles in them is much smaller (from 10 -7 to 10 -5 cm). In this regard, the 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 dispersion 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, weigh the cup in a dispersion medium, immersing it in a filled glass and balancing the balance. Along with this, the depth of its immersion is measured. After this, the cup is removed and quickly placed in a glass with the test suspension, while it should be hung on the hook of the balance beam. At the same moment, the stopwatch will start. The table contains data on the mass of precipitated sediment at arbitrary points in time.
| Time from the start of the study, s | The mass of the cup with sediment, g | The mass of sediment, g | 1 / t, s -1 | Sedimentation limit, g |
Using the data in the table, draw a sedimentation curve on graph paper. The mass of the settled particles is plotted along the ordinate axis, and the time is plotted along the abscissa axis. At the same time, an adequate scale is chosen so that it is convenient to carry out further graphical calculations.
Curve analysis
In a monodisperse medium, the sedimentation rate of particles will be the same, which means that sedimentation will be characterized by uniformity. The sedimentation curve in this case will be linear.
During the sedimentation of a polydisperse suspension (which is what happens in practice), particles of different sizes differ in sedimentation rate. This on the graph is expressed in the blurring of the boundary of the settling layer.
The subsidence curve is processed by breaking it into several segments and drawing tangents. Each tangent will characterize the subsidence of a single monodisperse 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 particle size distribution. Some properties of porous media depend on it, for example, permeability, specific surface, porosity, etc. According to 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 of the study of sedimentary rocks is particle size analysis.
So, according to the results of the analysis of the particle size distribution of sands in contact with oil, equipment and the order of work in oilfield practice are chosen. It helps to select filters to prevent sand from entering the well. The processes of ion absorption, as well as the degree of swelling of rocks in water, depend on the amount of clay and colloidal dispersed minerals in the composition.
Sedimentation analysis of grain size distribution of rocks
Due to the fact that the analysis of disperse systems based on the principles of sedimentation has a number of limitations, its use in its pure form for granulometric studies of the composition of rocks does not provide adequate reliability and accuracy. Today it is carried out using modern equipment using computer programs.
They allow the study of rock particles from the starting layer, they can continuously record sediment accumulation, excluding approximation by equations, and measure the deposition rate directly. And just as importantly, the study of sedimentation of irregularly shaped particles is allowed. The percentage of a 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.