Sedimentation: Tangent and Concentration Essay

Custom Student Mr. Teacher ENG 1001-04 2 August 2016

Sedimentation: Tangent and Concentration

Sedimentation is the process of separating a liquid mixture of suspended particles into clear supernatant liquid and denser slurry having a higher concentration of solids. This is usually accomplished by allowing the particles to settle through the force of gravity, mechanically using centrifugal force, or electrostatically using an electric current. Continuous sedimentation tanks are usually used in wastewater treatment facilities to separate suspended particles from wastewater.

This experiment aims to determine the effect of initial concentration and initial height of the slurry on its settling characteristics. Using a set of data obtained from the experiment, a continuous thickener or clarifier must then be designed. The batch sedimentation experiment was accomplished by measuring the height of the clear liquid interface at two-minute intervals using initial concentrations of 25, 50, and 75 grams per liter and initial volumes (convertible to height) of 1000, 900, and 800 milliliters. Two trials were conducted for each matrix.

From the data, it was observed that as the initial concentration of slurry is increased, the initial settling velocities decrease. The initial height has no effect on the initial settling velocity but can affect the rate at which solids compact. However, it was found that how the height affects compaction can be unpredictable. For the design of a thickener using batch sedimentation data, the required area was calculated using the Coe and Clevenger, and the Talmadge and Fitch methods. The results were 1.3112 m2 and 2.2714 m2, respectively.

During the course of the experiment, various problems were encountered that may have lead to slight errors. These problems were usually problems of measurement. Using masking tape can cause slight errors if not applied to the cylinder properly. There were slight difficulties during the initial stirring of the slurry because of the lack of long stirring rods. Furthermore, results from the data gathered were slightly erroneous as the aforementioned methods rely heavily on graphical approaches of computation.


Sedimentation is the separation of a suspension into a supernatant clear fluid and dense slurry which contains a higher concentration of solid. This process describes the motion of particles in suspensions or molecules in solutions in response to external forces such as gravity, centrifugal force, or electric force. This also pertains to objects of various sizes, ranging from suspensions of dust and pollen particles to cellular suspensions to solutions of single molecules such as proteins and peptides.

Sedimentation may be divided into the functional operations of thickening and clarification. The main purpose of thickening is to increase the concentration of suspended solids in a feed stream, while that of clarification is to remove a relatively small quantity of suspended particles and produce a clear effluent. These two functions are similar and occur simultaneously, and the terminology merely makes a distinction between the primary process results desired. In general, thickener mechanisms are designed for the heavier-duty requirements imposed by a large quantity of relatively concentrated pulp, while clarifiers usually will include features that ensure essentially complete suspended – solids removal, such as greater depth, special provision for coagulation or flocculation of the feed suspension, and greater overflow-weir length.

Commercial sedimentation of water suspensions is conducted as a continuous process in thickeners or large tanks which receive the suspension or dilute slurry at the center or side, permit the overflow of supernatant liquid, and produce sludge from the bottom of the tank.

Sedimentation essentially proceeds according to the scheme shown below.

At the beginning of the operation, the suspended solids fall through the liquid under hindered settling conditions. Eventually, various zones form. Zone A is the supernatant liquid. The interface between A and B is distinct only when the particles in B are closely sized with respect to the smallest particles. Otherwise, a milky interface is formed. B is a suspended mixture of solids and liquid and has uniform concentration. Between B and C is a distinct transition zone. This zone is due to the rising liquid as the highly concentrated sludge D compacts. Zone c, unlike B, is a region of variable concentration. Note that regions A and D grow larger at the expense of B and C until such a point where maximum compaction of D is obtained. This point is called the critical settling point. At his point, only a single, distinct interface is formed between the concentrated sludge and the clear liquid.

To determine the effect of concentration or height on the settling characteristics of a suspension, batch sedimentation experiments are conducted. The data from these experiments can be used to design a continuous thickener.

Continuous thickeners consist of zones similar to a batch sedimentation process except that these zones are of constant height when steady state is achieved. The design of these thickeners s based on the identification of the concentration of the rate limiting layer.

First, batch settling data is obtained by plotting the height of the interface (between the clear liquid and slurry), z versus time. Please refer to the figure below. This uses the Talmadge and Fitch method.

A tangent line is drawn at the beginning (line B) and at the end (line D). The portions from which these tangent lines are drawn represent portions during the test where settling velocities are nearly constant. An angle bisector line is then drawn. The intersection between this line and the curve represents Cc from which one can estimate the tc and Zc. These are the critical condition, time, and height respectively. By specifying the initial height, Zo, initial concentration, Co, and underflow concentration, Cu, on can determine the ultimate height Zu, using the following equation:

Zu = ZoCo


A tangent line (line E) is then drawn. Using the value for Zu, tu is then estimated.

The design engineer usually specifies the feed flow rate, Lo. By using the following equation, the area of the unit can then be calculated:

A= Lo tu


Another method used to determine the thickener area is a method devised by Coe and Clevenger. Their working equation is

coZo = cLZi

where co = initial slurry concentration

Zo= initial height

cL= concentration of solids when the slurry is of height Zi.

Using batch-settling test data, a plot of interface height as a function of time is made. Because initial concentration and height is easily known or measured, one can determine CL at height Zi corresponding to a particular instant of time, t.

The working equation is thus rearranged as follows:

cL = coZo


To determine Zi at a particular time t1, a tangent line is first drawn at a point of the curve there t=t1. Please see the figure below.

The height Zi is the y-intercept of the tangent line.

The settling velocity at a particular time, t1, is the slope of the curve at that instant. Therefore, v = dz/dt. Simply put, the velocity is equal to the slope of the tangent line.

To determine the thickener area, one must first compute for the total flux of the settling properties. This is the sum of the batch flux and the flux related to the removal of solids due to the removal of solids due to the underflow. Mathematically,

F = Fb + Fu

where Fb= cLV and Fu= cLVu. Note that Vu is the underflow velocity and is usually arbitrarily chosen by the design engineer based on a number of conditions. The values for Fb, Fu and F at different instances of time are usually listed on a table which typically arranged like so

t. hrs or mins

CL, g/L

V, cm/hr or cm/mins

Fb, g/cm2hr

,Fu, g/cm2hr







Fb1 + Fu1






Fb2+ Fu2

A plot of F as a function of concentration is then made. The lowest point of the plot of F is taken as FL. This value is then used in the equation,

A= Lo Co


to determine the area, A. Lo in this case is the feed rate and is specified by the design engineer.



Six (6) 1000 mL graduated cylinders

Calcium carbonate (CaCO3)

top loading balance

tap water as the solvent


stirring rods



Effect of Initial Concentration

Samples of calcium carbonate weighing 25, 50, and 75 grams were weighed using a top loading balance. Each sample was then placed in a 1000 mL graduated cylinder and was filled using tap water up to the 1000 mL mark. The solutions were mixed thoroughly using a stirring rod until uniform distribution of the solids was observed. The initial heights of the mixtures were immediately recorded after stirring. Clear liquid interface heights were measured at every two minute interval following the first measurement. Measurement continued until no significant change in height was observed. Two trials were conducted.

Effect of Initial Height

Samples weighing 20, 22.5, and 25 grams were weighed using a top loading balance. Each sample was then placed in a 1000 mL graduated cylinder and was filled using tap water up to the 800, 900, and 1000 mL marks so that the mixtures have uniform concentrations of 25 g/L. The solutions were thoroughly mixed using a stirring rod until uniform distribution of the solids was observed. The initial heights were recorded immediately after stirring. At two minute intervals thereafter, the heights of the clear liquid interface were measured. Readings continued until no significant changes in the height were observed. Two trials were made.


The first objective of this exercise was to determine the effect of the initial concentration (co) of a slurry on its settling characteristics. This was accomplished by measuring the height of the clear liquid interface (at two-minute intervals) of slurries having various concentrations of 25, 50, and 75 g/L. The data collected (height as a function of time) shall hereafter be referred to as _batch sedimentation data_. To describe the settling characteristics of the slurry, the data obtained were treated using the method proposed by Coe and Clevenger (Foust, 1980) in which tangent lines are drawn at arbitrary points along the plot. The slope of a tangent line is equal to the settling velocity of the solids at that particular arbitrary point.

The data obtained were thusly processed and a careful scrutiny of which revealed that a higher concentration generally causes a decrease in the overall settling velocity of the solids. This trend is illustrated in a plot of velocity versus time in the following figure. Please refer to this figure in the discussion to follow.


It is evident in the graph that slurries with lower concentrations have higher settling velocities. It was discussed in the introductory section that as batch sedimentation begins, the particles fall at their terminal (or maximum) velocities at hindered-settling conditions. At higher concentrations, more solid particles are present per arbitrary layer of a particular volume. It therefore follows that at these conditions, the rate at which particle A settles is lower because of the closer distance between it and particle B, C, D, and so on. This is because the other particles hinder particle A from falling. This can be likened to a traffic jam. The greater the number of cars per strip of road, the slower they run.

Notice the sudden incline in the plot. This sudden decrease in settling velocity is more prominent at lower concentrations. According to Brown (1973), this is due to the decreasing suspended-solids zone (or zone B in the _Principles_ section). It is at this point where the clear liquid interface approaches the solid-liquid interface. As they approach, zone B increases in fluid viscosity and density. This causes a sharp decrease in settling velocity for lower concentrations and a more shallow decrease for higher concentrations.

The lower part of the plot represents the phase at which the solids enter compaction. This is characterized by a very slow process of solid buildup which may be analogous to a fluid flowing through a bed of decreasing porosity (Brown, 1973). As the solids compact, the particles occupy voids within the interstices of the compacting layer. This causes an equal volume of liquid to flow upwards and into the variable concentration zone. This causes a steady decrease in the settling velocity. Note that at higher concentrations, compaction occurs at a faster rate. Although the literature is inadequate concerning this phenomenon, it is generally believed that the increased settling rate is due to the heavier compacting layer present at higher concentrations.

Note also that the aforementioned observations were the key assumptions used by Coe and Clevenger. They assumed that sedimentation rates are a function of local concentration. It is found that the data conforms to their assumptions and clearly supports them. Below are plots of the clear liquid interface height as functions of time. Notice that at higher concentrations, the slope during the initial settling period is lower. Because the slope is equal to the settling velocity, a lower slope indicates a lower rate of settling. These graphs clearly show the velocity’s dependence on slurry concentration.

To explain the effect of initial height on the settling characteristics of a slurry, please refer to the following plots.

Results of the effect of varying initial height with constant concentration can be generated from these figures. Brown et al. (1973) stated that the constant rate of sedimentation at the beginning is the same and independent of the height. Apparently, results from trial 1 and trial 2 clearly support this statement. At the start of sedimentation, all particles begin to settle and are assumed to rapidly approach their terminal velocities under hindered-settling conditions (Foust et al.) Particle settling can be categorized into two types: free-settling and hindered settling. The former pertains to the particles at low concentration that are sufficiently far apart to settle freely while the latter refers to the particles that are close together that they continuously collide such that their motion is impeded by other particles.

For trial 1 and trial 2 of the experiment, the height of the clear liquid interface can be described as constantly decreasing until approximately five minutes of settling time. From the beginning up to the estimated five minute-settling time, the graphs generated seem to be a straight line for both trials. The slopes of these graphs, having time as the independent variable and height as the dependent variable, are almost equal with respect to the given concentrations. Thus, the particles are experiencing a constant settling rate. It has also been observed that during these times in the experiment, settling rate is independent of the height. That is, the initial settling velocities of the particles are unaffected by the initial height of the slurry.

However, after the estimated five minute-settling time, the graphs seem to change their direction independent to each other. The graduated cylinder with a 20g/800mL sample reached hindered-settling first for both trials while the sample that has a 25g/L reached last. During the hindered-settling period, particles are being affected by other particles more than it has experienced during the free-settling period. Eventually, the graph approaches an almost straight horizontal line. This horizontal line, according to literature, is the ultimate height.

Ultimate height is just the final height of the solids when settling stops. Thus, settling rate after free-settling is now dependent on the initial height. The lower the initial height, the faster it can reach the hindered-settling regime and the ultimate height. This phenomenon can be attributed to the fact that solids at a lower slurry depth have a shorter distance of travel or settling compared to the solids at a higher slurry depth given they have equal free settling velocities.

The figure above shows that samples with equal concentration (in this case, 25 g/L) have a constant or almost equal settling-rate. This data can support some of the statements prior to this part of the discussion. As stated earlier, velocities of the sample before hindered-settling are constant regardless of the height. Thus, samples with the same concentration have a constant settling rate regardless of the height prior to the hindered-settling regime.

A comparison between the velocities corresponding to the given initial heights can be generated from the figure above. From the graph, the samples seem to have different initial settling rates. According to literature, the initial settling rate is dependent only on concentration. But due to slight experimental errors, the constructed graph above does not clearly illustrate this trend. Furthermore, it is also unclear how the initial height affects the rate at which solids compact. All that is known is that the initial height of a slurry does not affect the initial settling velocity of the particles (McCabe, 1993).

A fundamental difference between batch and continuous sedimentation is that, at steady state, the heights of the various zones in a continuous sedimentation tank are constant. To keep the tank running at steady state, the influx of solids in every zone must approximately equal the out flux. Otherwise, there will be a continuous buildup of solids until sludge appears in the overflow (Foust, 1980). The design of a continuous thickener involves the estimation of the capacity of the rate-limiting layer or the layer with the least solids capacity. Batch sedimentation data is used for this purpose and is usually treated using the Coe and Clevenger approach or the Talmadge and Fitch method of determining the thickener area.

As an illustration, the 75 g/L (trial 1) slurry concentration data was used to determine the required thickener area if the slurry were to be subjected to a continuous thickening operation. This particular concentration was chosen solely by virtue of its “near-perfect” curve. It is desired that the thicker underflow contain a concentration of 1050 g/L, attained using a feed rate of 50,000 L/day, and an underflow velocity of 3.472 mm/min. Using the Coe and Clevenger method, the area was calculated to be approximately 1.3112m2. This was accomplished by calculating the total flux, F using the given parameters and the 75 g/L batch sedimentation data. Please refer to the following table.

Free Sedimentation: Tangent and Concentration Essay Sample


  • Subject:

  • University/College: University of Arkansas System

  • Type of paper: Thesis/Dissertation Chapter

  • Date: 2 August 2016

  • Words:

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