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A solid particle or liquid droplet moving by gravity through a viscous fluid eventually acquires a constant velocity. This is called the settling rate. If the density of the particle is lower than the density of the liquid, it will move upward at the ascent rate. These speeds are designated by the letters vg (g is gravity). The rate of settling / ascent is determined by the following physical parameters:

particle diameter d, m

particle density ρp, kg / m3

density of the continuous phase, ρl, kg / m3

continuous phase viscosity η, kg / m, s

acceleration of gravity g = 9.81 m / s2.

If the values ​​of all of the above parameters are known, then the rate of sedimentation / ascent of a particle or drop can be calculated using the following formula derived from Stokes' law (formula 1):

Substituting these values ​​into the formula, we get:

As you can see from the result obtained, the fat globules rise very slowly. In practice, fat globules form large clumps and float much faster.

Periodic separation by gravity

Picture 1

In vessel A shown in Fig. 1, contains a liquid in which solid particles are suspended the same size and more dense than liquid. It takes quite a long time for the particles on the surface of the liquid to sink to the bottom.

The settling time can be reduced by reducing this distance. The height of the vessel (B) was reduced and the area increased so that the volume remained unchanged. The settling distance (h2) decreased to 1/5 of the first option (h), and the time required for complete separation of fractions was also reduced to 1/5 (Figure 2).

Picture 2

Continuous separation by gravity

The simplest vessel in which particles of different diameters can be continuously separated from the liquid is shown in Fig. 3. A liquid containing particles in the form of sludge enters the vessel from one end of it and moves towards the outlet at the other end under a certain pressure. When moving, the particles settle at different speeds depending on their diameters.

Figure 3

With the continuous separation of suspended matter from the liquid in a vessel with horizontal screens, the settling channels will be constantly clogged with particles collecting in them. Eventually the process will stop. In a vessel with inclined screens shown in Fig. 4, particles deposited on the screens slide off the screens under the action of gravity and accumulate at the bottom of the vessel.

Figure 4

Why are the particles settling on the screens not being captured by the liquid flowing up between the screens? An explanation is given in Fig. 5, on which

shows a section of a part of the sedimentation channel. When the fluid flows between the screens, its boundary layer closest to the screens is decelerated by friction, and therefore its velocity drops to zero. A stationary boundary layer has a braking effect on the adjacent layer, and so on towards the center of the channel, where the velocity is maximum.

Figure 5

The resulting velocity profile is as shown in Figure 5 - laminar flow in the channel. The particles deposited in the stationary boundary zone are thus only influenced by the force of gravity.

The deposition surface used when passing through the vessel with sloped maximum flow inserts must be pre-calculated. To fully utilize the capacity of the separation vessel, it is necessary to provide the settling particles with as large a surface as possible. The distance within which sedimentation occurs does not directly affect the throughput of the vessel, but some minimum channel width must be maintained in order to prevent clogging of the channels by settling particles.

Abstract on the topic:

Particle sedimentation

Particle sedimentation rate

By the word "particle" we will agree to mean (if we talk about it) and large macromolecules of proteins or nucleic acids.

1. At the same densities, larger particles settle much faster than smaller ones.

2. The sedimentation rate ("sedimentation") increases with increasing particle density. This is especially pronounced under conditions when the density of the medium is close to the density of the particle. A situation is possible when small, but denser particles will settle faster than large ones.

3. The sedimentation rate of the particles is proportional to the square of the rotor speed per minute.

4. The higher the viscosity of the medium, the slower the settling of the particles.

5. The sedimentation rate is proportional to the distance of the particle from the rotor axis of rotation. This distance increases as the particle moves along the axis of the test tube; therefore, with the constancy of other conditions, the sedimentation rate should increase continuously (albeit slowly). If this is undesirable, then the density or viscosity of the medium should be increased in the radial direction so that they compensate for the increase in the radius of rotation.

It makes sense to introduce the concept of "floating density" of particles. The fact is that the density of a particle that manifests itself during ultracentrifugation is due not only to its chemical composition and spatial structure. For example, it strongly depends on the degree of particle "hydration" - the amount of water firmly bound to it. This water moves with the particle, significantly reducing its effective density. The amount of this water decreases noticeably in the presence of high concentrations of ions or other hydrophilic molecules that also bind water (there is not enough free water!). On the other hand, some ions or molecules can themselves firmly bind to particles, increasing their effective density.

Therefore, for a given type of particles settling in a given medium, the concept of "buoyant density" is introduced. It can be determined experimentally by measuring the density of the medium at the point where the motion of the particle stops due to the equality of the brackets in formula 1 to zero (see below - "equilibrium ultracentrifugation").

Finally, the deviation of the particle shape from the spherical one also affects (not very strongly) the rate of their settling. In this regard, it is worth recalling that both protein macromolecules and molecules of fairly high polymer nucleic acids in solution roll up into chaotic coils, the shape of which is close to spherical.

Separate sedimentation of particles

Suppose that ribosomes, inner membranes, and even smaller particles are required to be isolated from a homogenate of cells, already freed from the nucleus, mitochondria, and fragments of the outer membrane by low-speed centrifugation. It is possible to select a moderate rotation speed of the angular rotor (with a significant volume of test tubes) so that only the largest particles will get into the sediment, even those that were initially near the meniscus. In this case, smaller particles will almost completely remain in the supernatant (supernatant), with the exception of those that were already at the bottom of the tube from the very beginning - they will become part of the sediment. For good purification of large particles, the supernatant is carefully discarded, the pellet is resuspended (in buffer) in the entire volume of the tube and centrifuged again under the same conditions. This operation can be repeated 2-3 times, after which the precipitate will be practically homogeneous. There is one subtle point here related to the suspension of sediments. The formation of lumps suspended in the liquid is highly undesirable. They may not disperse for a long time, keeping smaller particles inside themselves. To avoid this, it is necessary each time with a minimum amount of buffer, or without it at all, for a long time with a glass rod to rub the sediment along the surrounding walls of the test tube. The stick should not be too thin - only 3-4 times smaller in diameter than the test tube - and end in an even sphere without a drop-like thickening. (The art of the experimenter to a large extent consists in prudence in relation to such "trifles".) Precipitation may be invisible, but it still needs to be rubbed. For orientation, you can pre-mark the tubes at the upper edge with paint and install them into the rotor with this mark outward.

The first drained supernatant can be centrifuged again at a higher speed and the medium sized particles can be purified in the same way. Then, if necessary, collect the smallest ones.

Zone-speed ultracentrifugation

The peculiarities of this type of centrifugation are reflected in its very name: "high-speed" - because the particles are separated according to the speed of their settling, and their density is much higher than the density of the medium; "Zonal" - as particles of various sizes settle in more or less thin layers - "zones". No precipitation is formed. Centrifugation is carried out in bucket rotors. After the zones have reached an optimal distribution along the length of the tube, the centrifugation is stopped, and the zones of particles are removed one after the other in the manner described below.

Here, in contrast to the previous case, particles of different sizes are not cleaned separately, but simultaneously - with one centrifugation.

An initial mixture of particles of different sizes (at least the same half-purified cell homogenate) is applied in a thin layer onto a denser (than homogenate buffer) medium filling the bucket rotor tube. During centrifugation, the heaviest particles move rapidly towards the bottom of the tube, to some extent retaining the outline of the original layer where they were distributed. Behind them, with a lag, but also in the form of a separate layer, smaller particles move, then even smaller ones, etc. This is how discrete zones of particles of different sizes are formed.

In order for the zones to remain narrow, it is necessary to counteract the convection of the liquid in which the particles move. An effective way to suppress convection is to increase the density of this liquid along the radius of rotation in the direction from the meniscus to the bottom of the test tube. For example, you can fill a bucket rotor tube with an aqueous solution of sucrose, the concentration of which increases towards the bottom of the tube. And then on this "sucrose gradient" (as it is called for brevity) layering the drug - a mixture of particles to be separated.

In addition, with zonal-speed centrifugation, it is desirable to get rid of the previously mentioned increase in the speed of movement of particles as they move along the tube. Otherwise, a situation may arise when the heaviest particles reach the bottom of the test tube before the two zones of light particles have time to separate from each other. As can be seen from formula 1, an increase in the density of the medium already partially neutralizes the effect of the removal of the zone from the meniscus. But it is not very effective, especially if the particle density is much higher than the density of the medium. An increase in viscosity can be much more effective. Therefore, to create a "inhibitory gradient", it is advisable to use a concentration gradient of a substance that would have both desirable qualities (+ chemical neutrality). Perhaps, sucrose solutions meet this requirement best of all, as can be seen from the following table, where p is expressed in g / cm 3, and g - in centipoises. Everything at a temperature of + 5 ° C - the usual temperature for processing biological products.

In practice, depending on the task, sucrose gradients of 5-20% and 15-30% are most often used. The device for creating a linear gradient of sucrose concentration is similar to that for creating a porosity gradient in PAGE. The difference is that, due to the high viscosity of sucrose solutions, instead of a magnetic stirrer, a screw-shaped strip rotating in the mixer glass is used, made of heated plexiglass, which drives the liquid upward (Fig.).

The material of polyalmer and polycarbonate tubes is poorly wetted with water. Therefore, it is inconvenient to feed liquid into a test tube along the wall - it will roll down in drops, disrupting the smoothness of the gradient. It is better, as shown in the figure, to feed the sucrose solution through a long needle to the bottom of the test tube. In this case, a sucrose solution of the minimum concentration is poured into the mixer, and the maximum concentration is poured into the tank. A denser sucrose solution will smoothly push the less dense layers upward.

In some cases, for example, when it is desirable that large particles, approaching the bottom of the test tube, would not only not increase the speed of their movement, but, on the contrary, decrease it, it makes sense to select a nonlinear sucrose concentration gradient steeply increasing to the bottom of the test tube. So that the combined effect of increasing the density and especially the viscosity of the centrifugation medium is stronger than the effect of increasing the radius of rotation. This can be achieved if the diameter of the mixer is made larger than the diameter of the tank. When filling a tube, the sum of the volumes of liquid in both beakers must be used up completely. At first, small additions of dense sucrose from the reservoir, diluted in a large volume of liquid in the mixer, will only slightly increase the initial density of the solution. Nevertheless, at the end of the filling of the test tube, the density of the solution in it will still reach its maximum value - the gradient will be slowly increasing in the upper part of the test tube and steep at its bottom.

The extraction and identification of the separated zones after the end of centrifugation (since they are not colored) have to be done "by touch." The easiest way, as it was done at first, is to fix the open test tube vertically in the clamp, pierce its bottom with a syringe needle and collect fractions by a certain number of drops into a sequential row of test tubes installed in a rack, which the experimenter himself should move in a timely manner. The method is not good not only because of its stupid laboriousness, but also because of the change in the volume of the drops as the tube is emptied. It is better to attach a thin polyethylene tube to the needle, and to a peristaltic pump (to be described in the next chapter) with a given pumping rate. From the pump feed the selected number of drops into the test tubes installed in the "fraction collector". The latter is a mechanical device, where about 100-150 tubes are alternately, automatically, at specified time intervals or after counting a specified number of drops, are fed under a dropper, which ends with a tube coming from the pump.

You can not pierce the test tube, but carefully lower the needle from the top to the bottom of the test tube and thus suck out its contents fractionally. In any case, the detection of separated zones is carried out by sequentially checking all tubes for ultraviolet absorption: at a wavelength of 280 tc for proteins and 260 tc for nucleic acids. The fractions that find the content you are looking for are combined.

As an interesting example for us of the use of sucrose density gradient centrifugation, I chose the historical experiments of Okazaki (1971), which laid the foundation for modern concepts of the mechanism of DNA reduplication. In these experiments, bacteria growing in a liquid nutrient medium received through this medium a pulse label with radioactive thymidine lasting from 2 seconds to 2 minutes (in different experiments). At the end of the pulse, the bacteria were quickly cooled, the total DNA was isolated and centrifuged in an alkaline (for complete DNA denaturation) gradient of 5-20% sucrose in a bucket rotor at a speed of 25 thousand rpm for 16 hours. After digging out the gradient, the content of newly synthesized DNA in each fraction was estimated by radioactivity (in a liquid scintillator - see Chapter 15).

Further, a redistribution of the label occurs between the "free" (separated during DNA extraction) fragments of Okazaki and large fragments of mature DNA lying in the range of 20-60 S. A part of the radioactivity in the fragments of Okazaki also passes into these latter after their inclusion in the complementary composition. DNA strands. So, for curves 5 and 6, the relative proportion of the inclusion of the label in the Okazaki fragments and mature DNA changes significantly.

Equilibrium ultracentrifugation

The idea of ​​the method is to create such a gradient along the length of the tube (in a bucket rotor) so that the density of the centrifugation medium at the bottom is higher than that of the most dense particles, and at the meniscus it is less than that of the least dense particles. With a sufficiently long centrifugation, the particles will move along the gradient until they reach a position in which the density of the medium is equal to their buoyant density. The movement stops, particles of different density are located in different parts of the gradient. Thus, the particles are fractionated according to their density.

This division has the following features:

1. Particle size and mass will not affect the final distribution. The position on the gradient will be determined only by the density of the particles.

2. The movement of particles to the equilibrium position will occur both from the region of a lower density of the gradient than their buoyant density, and from the region of higher density. Thus, along with sedimentation, flotation will also occur. This means that there is no need to apply a thin initial layer of formulation to the liquid filling the tube. It is even possible to mix the entire preparation with the entire volume of the gradient medium.

3. The centrifugation process should be very long, since when approaching the equilibrium position, the particles will move very slowly.

4. The viscosity of the medium is therefore an undesirable factor.

5. With equilibrium ultracentrifugation, a noticeably higher loading of the drug is possible than with zonal-speed centrifugation.

6. In the equilibrium region, the particles will be located in the form of a strip, the width of which is determined by the ratio of the two processes:

concentration due to sedimentation - flotation and thermal diffusion of particles. This width will be the smaller, the steeper the gradient of the density of the medium and the greater the mass of the particles - an increase in mass reduces the tendency to diffusion. The distribution of the concentration of a substance in the band is described by a symmetric (Gaussian) curve. From its width, knowing the coordinate of the center of the strip (Gd), the angular velocity of rotation and the steepness of the density gradient of the medium in the center of the strip (dp / dr), one can calculate the mass of the (solvated) particle.

Sucrose is not suitable for creating a gradient in equilibrium centrifugation. As can be seen from the table given in the previous paragraph, the density of even a 30% sucrose solution is much lower than that of the main biological objects, while the viscosity is already increasing "catastrophically".

A concentrated solution of a heavy metal salt can be expected to be a suitable medium for equilibrium centrifugation. The density of such a solution can be quite significant, while the viscosity of the saline solution is weakly dependent on its concentration. Experience has shown that the most convenient media for equilibrium ultracentrifugation were concentrated solutions of cesium chloride or sulphate (CsCI). The following table shows the density values ​​of CsCI solutions of various weight concentrations:

Considering this table, it is useful to recall the dependence of the floating density of biological molecules on the addition of water and ions. It indicated the value of the floating density of DNA in a concentrated solution of CsCI - 1.7 g / cm 3. thus, DNA molecules of different density can obviously be fractionated by equilibrium ultracentrifugation in a CsCl gradient. The same cannot be said about RNA, the buoyant density of which under these conditions reaches a value of> 1.9 g / cm 3. Proteins, on the other hand, can be successfully separated under the described conditions. For them, the buoyant density in concentrated solutions of CsCI ranges from 1.3 to 1.33 g / cm 3.

Particles

Acceleration and transfer particles sprayed material to the coated surface (base); sedimentation particles on the surface of the base ... electrocrystallization, temperature and duration of heating, nature besieged metals, as well as other structural factors ...

Ministry of Education and Science of the Russian Federation

Federal Agency for Education

Saratov State Technical University

sedimentation

solid particles

by gravity

Methodical instructions

on the courses "Processes and Apparatuses food production»

and "Processes and devices of chemical production"

for students of specialties

full-time and part-time forms of study

Approved

editorial board

Saratov State

technical university

Saratov 2006

Objective: Get acquainted with the methods of calculating the sedimentation rate under the influence of gravity and experimentally verify the results of the calculation.

BASIC CONCEPTS

A number of chemical technology processes are associated with movement solids in dripping liquids and gases. These processes include the deposition of particles from suspensions and dusts under the action of inertial or centrifugal forces, mechanical mixing in liquid media, and others. The study of the laws of these processes is an external problem of hydrodynamics.

The following forces act on a solid particle deposited under the action of gravity: the force of gravity, the buoyancy force of the Archimedean force, and the force of resistance of the medium. The main difficulty in calculating the deposition rate lies in the fact that the resistance force of the medium depends on the mode of motion of the particle, and, consequently, on the deposition rate:

where F is the projection area of ​​the body onto a plane perpendicular to the direction

his movement, m2;

ρ is the density of the medium, kg / m3;

ω - sedimentation rate, m / s;

φ is the coefficient of resistance of the medium, depending on the mode of movement -

In laminar motion, which is observed at low speeds and small sizes of bodies or at high viscosity of the medium, the body is surrounded by a boundary layer of liquid and is smoothly flowed around by the flow. The resistance of the medium in such conditions is due to overcoming only the forces of internal friction and is described by Stokes' law:

With the development of flow turbulence (for example, with an increase in the speed of motion of a body and its dimensions), inertial forces begin to play an increasingly important role. Under the action of these forces, the boundary layer is detached from the surface of the body, which leads to the formation of a zone of random vortices behind the moving body and a decrease in pressure in this zone. In this case, the pressure difference in the frontal and cortical parts of the streamlined body increases sharply. At Re> 500, the role of the frontal resistance becomes dominant, and the frictional resistance can be practically neglected. The deposition mode becomes self-similar in relation to the Reynolds criterion, i.e., the medium resistance coefficient φ does not depend on the Re criterion. At 500< Re < 2·105 сопротивлений среды описывается квадратичным законом сопротивление Ньютона:

φ = 0.44 = const. (3)

In the transient mode of deposition, when 2 ≤ Re ≤ 500, the forces of friction and forces of inertia are comparable and none of them can be neglected. In this area, the resistance of the medium is described by an intermediate law:

When a body moves in a fluid, its speed will increase until the resistance force of the medium balances the body minus the buoyancy force. Further, the particle moves by inertia at a constant speed, which is called the settling speed.

1 ... From the equation for the balance of forces acting on the deposited particle, we obtain an expression for calculating the deposition rate:

, (5)

where ρh is the density of a solid particle, kg / m3;

g - acceleration of gravity, m / s2.

Study the derivation of equation (5) in detail by.

When calculating the sedimentation rate according to equation (5), the method of successive approximations is used, and the calculations are performed in the following sequence:

1) are set by an arbitrary value of the criterion Re;

2) according to one of the equations (3) - (4), the coefficient is calculated

resistance of the environment φ;

3) according to equation (5), the deposition rate is determined;

4) determine the value of the criterion Re:

;

5) determine the error:

Δ = (Re back - Re subtracted) / Re back;

6) if Δ> 0.03, then the new value of the criterion is specified

Re back = Re back · (1-Δ) and the whole calculation is repeated anew;

7) calculations are carried out until Δ ≤ 0.03.

Equation (5) is the most accurate, but inconvenient for practical use.

2. Due to the laboriousness of the method of successive approximations, it is more convenient to use the method proposed for determining the deposition rate. This method is based on transforming equation (5) to criterion form: Re = f (Ar). The derivation of criterion equations of the form Re = f (Ar) can be studied in detail by.

As a result of transformation of equation (5), the following calculated dependences were obtained:

for laminar deposition at Ar ≤ 36:

for transient deposition at 36< Ar ≤ 83000:

; (7)

for turbulent deposition at Ar> 83000:

; (8)

where Аr is Archimedes' criterion .

Calculations are performed in the following sequence:

1) the value of the Archimedes criterion is determined;

2) the deposition mode is determined by the found value of the Archimedes criterion;

3) one of the equations (6) - (8) determines the value of the Reynolds criterion;

4) the deposition rate is calculated:

https://pandia.ru/text/79/041/images/image010_11.gif "width =" 168 "height =" 49 ">. (9)

4 ... To calculate the deposition rate, a generalized graphic-analytical method is used, suitable for any deposition mode. In this case, a criterion dependence of the form is used: Ly = f (Ar),

where Ly is the Lyashchenko criterion . (10)

Determination of the sedimentation rate is carried out as follows:

1) determine the Archimedes criterion;

2) according to the found value of the criterion Ar, according to Fig. 1 determine the value of the criterion Lu;

3) calculate the sedimentation rate:

. (11)

Fig. 1 Dependence of Lyashchenko and Reynolds criteria on Archimedes criterion

for the deposition of a single particle in a stationary environment:

1-spherical particles; 2-rounded;

3- angular; 4-oblong; 5- lamellar.

EXPERIMENTAL PROCEDURE

The experimental setup consists of three vertical cylinders 1 (Fig. 2), which contain liquids with different physical properties.

The cylinders are fixed between the bottom 9 and top 10 bases. The upper base has a groove in which the movable plate 3 moves. The movable plate is covered with a fixed plate 2. The movable plate reciprocates under the action of the retractor relay 4, which turns on when the button 7 is pressed and returns to its original position when it is released. Button 7 simultaneously serves to control the electrosecondometer 5. When the button is pressed, the stopwatch starts, and when it is released, it stops. The stopwatch is reset by knob 6.

The test particle 8 is placed in one of the holes in the fixed plate 2.

The path traveled by the particle is measured with a ruler 11 with an accuracy of ± 0.5 mm, the settling time is measured with a stopwatch 5 with an accuracy of up to ± 0.5 s. The sedimentation rate is calculated by the formula:

To exclude a systematic measurement error when measuring the settling time, the observer's eyes should be at the level of the lower base.

The equivalent diameter of irregularly shaped particles is determined

according to the formula:

where M is the mass of the particle, kg.

Particle mass is determined by weighing five times

10-20 g on an analytical balance.

Fig. 2. Experimental setup diagram:

1- cylinder with liquid, 2 - fixed plate,

3 - movable plate, 4 - retractor relay,

5 - electric stopwatch, 6 - reset handle,

7 - button, 8 - test particle,

9 - bottom base, 10 - top base,

11 - ruler, 12 - thermometer

ORDER OF PERFORMANCE OF WORK

1. Prepare the installation for the experiment. If necessary, fill the cylinders with the appropriate fluids so that their level reaches the upper base.

2. Obtain test particles from a teacher or laboratory assistant and determine their equivalent diameter.

3. The test particle is placed in one of the holes in the upper fixed plate.

4. Press button 7 (Fig. 2). In this case, the retractor relay turns on, the movable plate moves, the holes in the fixed and movable plates and the upper base coincide, and the test particle falls into the cylinder with liquid and begins to settle. At the same time, the stopwatch is activated 5.

5. Button 7 is kept pressed until the particle reaches the bottom of the vessel. At the moment the particle touches the bottom, the button is released. In this case, the stopwatch stops.

6. The settling time and the distance traveled by the particle are recorded in an observation log.

7. Each experiment is repeated 5-6 times.

8. The measurement results are entered in table. one.

Table 1

9. Calculate the rate of sedimentation:

a) according to equation (5);

b) according to the method, according to the equations (;

c) according to the interpolation equation (9);

d) graphic-analytical method.

10. Compare the calculation results with the experimental data and draw conclusions about the accuracy and complexity of each calculation method.

11. The calculation results are summarized in table. 2.

table 2

EXPERIMENTAL PROCESSING

To increase the reliability of the experimental data and estimate the measurement error, the experimental determination of the deposition rate must be repeated 5-7 times with the same particle.

Preliminary experiments have shown that for a sufficiently large number of measurements, the experimental value of the deposition rate obeys the normal distribution law. Therefore, the accuracy will be assessed by determining estimates and confidence limits for the parameters of the normative distribution in accordance with GOST 11.004-94.

Unbiased for general average normal distribution is the sample mean (arithmetic mean), determined by the formula:

https://pandia.ru/text/79/041/images/image018_8.gif "width =" 100 "height =" 53 ">, (12)

where Xi is a set of observed values random variable(sko

deposition rate);

n - sample size (number of measurements).

RMS error of measurement:

https://pandia.ru/text/79/041/images/image021_7.gif "width =" 87 "height =" 25 ">. (14)

The value of the Mk coefficient is determined according to table. 3 depending on the number of measurements K = n-1.

Table 3

Unbiased estimate for the variance of the normal distribution:

The upper confidence limit for the general average:

where tγ is the quantile of the Student distribution for the confidence

sti (determined by Table 4).

The report on the work is drawn up in a notebook. It should contain:

1) the name of the laboratory work;

2) the formulation of the purpose of the work;

3) basic concepts, definitions and calculation formulas;

4) installation diagram;

5) the results of observations, tabulated;

6) all intermediate calculations;

7) a block diagram for calculating the deposition rate;

8) a printout of the calculation of the deposition rate on a computer;

9) a table comparing the calculated and experimental data;

10) analysis of the results obtained and conclusions.

Self-test questions

1. What is called the settling rate?

2. Give a qualitative and quantitative description of the deposition modes?

3. What forces determine the resistance of the medium during laminar deposition?

4. What forces determine the resistance of the medium in a turbulent deposition regime?

5. Describe the kinetics of particle sedimentation under the action of gravity. Make a balance equation for the forces acting on the particle.

Literature

1., Popov and food production apparatus. - M: Agropromizdat, 1985.-503s.

2. With and others. Processes and apparatus of food production:
Textbook for universities. - M .: Kolos, 1999 504s

3., Korolev and food apparatuses
productions: Textbook for universities .- M .: Agropromizdat, 1991.-
432 p.

4. "The main processes and apparatuses of chemical
technologies". Ed. 6th Moscow: Goskhimizdat, 1975.-756 p.

5. Laboratory workshop on the course "Processes and devices
food production "/ Ed. .- Edition 2, add.-
M .: Food. pr-th, 1976.-270s.

6.Laboratory workshop on the processes and apparatuses of food
productions / Ed. CM. Grebenyuk.- M.: Light and food
industry, 1981.-152 s

7 Guide to laboratory practice
processes and devices of chemical technology. / Under

Edited, from-e 4th., L .; 1975.-255s.

sedimentation of solid particles

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