VISCOSITY

Viscosity is a characteristic property of all fluids. The internal resistance to flow of a liquid is called viscosity. Viscosity of a liquid is defined as its property by virtue of which it tends to oppose the relative motion between its different layers. In other words, it may be regarded as an internal friction between the different layers of a liquid. Resistance to flow is largely due to the intermolecular attractive forces-Van der Waal's forces in liquids.

A liquid that flows with ease is said to be mobile, whereas a liquid that does not flow easily is said to be viscous. To some extent, we can picture a mobile liquid as one whose molecules flow smoothly over each other, with few tangles between the layers. In a viscous liquid, tangles between molecules in different layers interfere with the smooth flow. The greater the viscosity, the less mobile will be the liquid. Molten polymeric materials and glass are highly viscous because their large molecules become greatly entangled. In order to make viscosity mare understandable, consider a liquid flowing through a tube consisting of concentric Inyers. The layers in contact with the walls of the tube remain stationary, whereas the layer in the centre has the maximum velocity and intermediate layers move with a gradation of velocities. Each layer exerts a drag on the next layer due to internal friction. When a steady flow is reached, the velocity difference between any two layers will become constant.

 

The flow of liquid through a tube is said to be stream-lined (laminar, non-turbulant or Newtonian), if the path of every moving particle of the liquid coincides with the line motion of liquid as a whole Fig. The flow is termed turbulent, if the motion of liquid particles is a disordered one, and an actual mass transport from layer to another takes place.

Consider two adjacent moving layers of a liquid, which are separated by a distance dr and have a velocity difference dv. The force of friction (F) resisting the relative motion of two layers is directly proportional to the area A and the velocity difference dv and is inversely proportional to the distance, dx, between the two layers, i.e.,

 F A dv/dx  or F = nA dv/ dx

where dv/dz is the velocity gradient and n is called the coefficient of viscosity, and is defined as, the force per unit area required to maintain a unit difference of velocity between two parallel layers of a liquid, unit distance apart at a given temperature.

 Dimensions and Units of ໗. From Eq.

  ໗= force/area×distance/velocity =newton×m/ m2×ms-1=kgms-2×m/m2×ms-1=kgm-1s-1

 

, The SI unit of coefficient of viscosity ໗ is kg m-1 s-1. the CGS system, the dimensi of n are delta' are generally cm-1 s-1 and is called a poise. Since this unit is rather large, viscosities usually given in centipoise ( 10 ^ - 2 poise). The relation of poise to SI units is, eta= force area * distance velocity = newton* m m ^ 2 * m * s ^ - 1 = (kgm * s ^ - 2 * m)/(m ^ 2 * m * s ^ - 1) = kg * m ^ - 1 * pi ^ - 1

 

          1 poise 10-1 kg m -18-1

 

The reciprocal of coefficient of viscosity is called fluidity.

         Fluidity =1/໗

 

MEASUREMENT AND VISCOSITY

Most methods, used for the measurementPoiseuille's equation. The Poiseuille's Equation for the coefficient of viscosity of liquids is

       ໗=pi ptr4/8VL

where is the volume of a liquid having viscosity n flowing through a capillary tube of radius and length L in time t (seconds) under an applied pressure  

It is found empirically that Poiseuille equation governs the flow of liquids only when the diameter of the tube is small and the flow rate is slow and steady. When the flow rate becomes higher or the diameter of the tube is enlarged, the type of flow changes from stream-lined to turbulent or non-Newtonian. Eq. (16) is applicable only to stream-lined or laminar flow of liquids.

In order to decide the type of flow, we use the Reynold's number (a dimensionles quantity) empirically defined by the equation:

Reynold's number =2rvd/n

 where is the radius of the tube, v coefficient of viscosity. (17)

 average velocity of liquid, d density, and

Empirically, it has been seen, if the Reynold's number is equal or less than 2000. the flow is Newtonian, and if the value is greater than 4000, it is turbulent (Non-Newtonian), and for the intermedinte values the type of flow cannot easily be anticipated eta =

The direct experimental measurement of absolute viscosity of a liquid using Poiseuille's equation offers considerable difficulty, since measurement of P. r. and V involves considerable difficulty. Therefore, the viscosities of liquids are expressed in relative terms, that is in terms of ratio of the viscosity of the sample of a liquid to the viscosity of water taken as the reference standard. This is called relative viscosity. If we measure the time of flow of the same volume of two different liquids through the same capillary, then the expression for relative viscosity (eta_{1} / eta_{2}) can be derived from the Poiseuille equation as:

 

eta_{1}/eta_{2} = (pi*P_{1}*t_{2} * r ^ 4)/(8VL) * (8VL)/(pi*P_{2}*t_{2} * r ^ 4) = (P_{1}*t_{1})/(P_{2}*t_{2})

 

 Since the P_{1} and P_{2} are directly proportional to the densities of the two liquids d_{1} and d_{2r} we may write:

 

or (18) eta_{1}/eta_{2} = (P_{1}*t_{1})/(P_{2}*t_{2}) = (d_{1}*t_{1})/(d_{2}*t_{2}) eta_{1} = (d_{1}*t_{7})/(d_{2}*t_{2}) * eta_{2}

d_{1} d_{2} and eta_{2} are known, determination of t_{1} and t_{2} permits the calculation of the viscosity coefficient of the liquid under examinationThe quantities t_{1} and t_{2} are conveniently determined with the help of a discoverer.

REFRACTIVE INDEX

 "Refractive index in) of a transparent substance is defined as the ratio of the lity of light in warm to the elocity of light in the given medium" The refractive indes of any suletanee depends upon, the nature of substance, temperature and the wave length of light used. Whenever a beam of manschromatic light passes from one medium into the other, it suffers a change in the direction of propagation. This change of direction is called refraction. depends on the nature (refractive index) of the twe media, and the direction which the light travels When a ray of light passes from a rarer (air) to a denser medium liquid or glass), it bends towarde the normal at the point of incidence, as shown in Fig 3.12. According to Snells law, the ratio of the sine of angle of incidence and that of refraction in onstant and characteristic for that medium.

                          n=Sin i / Sin r         (Snell's law)

Arding to the way theory of light, the ratio of the sines of the angles of incidence and refracton is identical with the ratio of the velocities of light in the two media. Thus

          

                 n = (sin i)/(sin r) = velocity in air / velocity ia liquid

According to the law of refraction,

             

                     (sin i)/sin r. = n2/ n1

 

where the refractive index of the rarer and the refractive indes of the denser of refraction also increases. ronches maximum value and is known as the critical angle. Since sin 90 = 1 Eq (27) becomes

                    Sinr  =n1/n2

If the angle of incidener is grunter than 90, the ray is totally reflected. Most of the refractometers work on the principle of critical angle for measuring refractive index di mediam.

MEASUREMENT OF REFRACTIVE INDEX :

The refractive indices of liquids can be measured directly with calibrated mutrument called refractometer In practice, Abbe and Pulfrich refractometere are unly used

 Abbe Refratometer

A general sketch of the Ahe refractometer is shown in Fig. 3.13 the ptical system of the Abbe refractometer consists of three parts (1) a mirror M. (2) two prisms A and B had in a box hinged at H and (3) a fixed telescope Tand an eye-piece O The two prism faces can be held in contact with knob C. To the box carrying the prisme, is attached an arm R which moves along a graduated scale S, a direct reading on the scale given the refractive index.

Procedure

 The priam box is opened, a drop of the eliqund is placed between the two priams and then the box is closed. The cross-wires of the telescope are focused by rotating the eye-piece and the mirror is bus is slowly moved backwards and forwarda by means of the knoh C until the field of view becomes partly dark and partly bright. When the white light is used the moured fring alserved are removed by rotating the compensatori consisting of twe prime sctached st the use of the telescope and a sharp line will divide the bright and dark portions The priame bax is then rotated until the end of the bright portion coincides with pint ef intersection of the cross-wires of the telescope, and the refractive indes is directly anted on the scale through the eye piece 0.

Since refractive indes is affected by the temperature and wavelength of light. In order to maintain consistency of temperature and wavelength, prisms A and Bar mclused in a water jacket J and sodium or mercury light is preferably used.

 

 

PULFRICH REFRACTOMETERE:

 Pulfrich refractometer is very accurate and simple is principle for measuring the refractive andises of liquids The basic  design of the strument is shown in Fig (3:14) The essential part of the instrument is a right angled glass prism with a small glass cell cemented to its top.

The liquid to be examined is placed is the glass coll and beam of Лалабивних light is made to enter at grading taxideas along the surface beiteteny che big and the prim. It follows the path ABCD and is observed by a telescope at D If be the angle of refraction when the angle af incidence is 90 degree

                                sin r = n1/n2

 where n1 the refractive index of the liquid and n2 that of the glass prism. It is clear fem Fig. 14) that

        Sin I/ sin (90-r)  = n2

        But sin(90-r)=cos r , thus we have

        Sin i/ Sin r = n2.  Or. Cos r = sin I/n2

But. Sin r   = 1-Sin2i/n2 2 = n2 2 - sin2 I/n2 2

Or n2 sin r = n2 2-sin2i

          n1 = n2 2 - sin 2 i ( since n1=n2 sin r from (eq28)

 If the refractive index n2 of the prism is known and the angle is measured, the refractive index of the liquid, can be calculated. In practice, tables of sqrt n2 2-sin2i putting the refractive indices from the values of the measured angle i.

 

 

 

LIQUID:

The liquid state may be regarded as the intermediate state between the gaseous and the solid states of matter. Liquide and gases are both fluids and flow rendity under applied stress, but like solids, liquids are dena krelatively incompressible and have properties that are largely determined by the nature and strength of intermolecular forces.

STRUCTURAL DIFFERENCE BETWEEN GASES, LIQUIDS AND SOLIDS:

 In gases, the molecules are widely separated from one another, moving freely in space and are in completely random arrangement. But in liquids, the molecules are close to each other and there is very little space between the molecules. However the random movement of the molecules may often leave holes at places in the bulk of the liquid. In solids, the malecules are closely packed in the form of a crystal lattice, are not free to move, and possess vibratory motion only. The major difference in the microscopic structure of gases, liquids and solid involves randomness and order. A gas has essentially no order. A liquid has short-range order and long-range disorder. The molecules in a small region of the liquid may have an orderly arrangement, but this arrangement is not repeated throughout the liquid. Solids have both long-range as well as short-range order. A solid has its constituent particles arranged in a regularly ordered internal array

In a gas any particular molecule is not surrounded by a definite number of molecules, while in a liquid any particular molecule is surrounded by a definite number of molecules, arranged in a regular manner in a small region. In a solid, the number of atoms or molecules at any distance from the individual atom is fixed. A gas has no definite surface while a liquid as well as solid has a definite surface as the molecules cannot easily escape from the surface. The X-ray diffraction studies of liquids show the presence of short-range order. long-range disorder and holes in the packing of molecules. The structure of a liquid depends somewhat on the geometry and intermolecular forces of the molecules.

 

SURFACE TENSION AND CHEMICAL CONSTITUTION PARACHOR

Surface tension to due to an inward force acting on the molecules at the surface of a liquid and is, therefore, considered to be dependent on the structure of molecules

The Parachor

In 1923, D.B. Macleod suggested an empirical relationship between the surface tension and density of a liquid, which may be stated as

                   

γgamm+a

𝛾

D-d=C

 where D and d are the densities and its vapour, respectively, y is the surface tension at the same temperature and C is a characteristic constant of the liquid                                               

S. Sugden (1924) obtained a relationship by multiplying Macleod equation with the molecular mam. M. of the liquid, and called the new constant as Parachor [P] 

 SURFACE TENSION AND CHEMICAL CONSTITUTION PARACHOR

Surface tension to due to an inward force acting on the molecules at the surface of a liquid and is, therefore, considered to be dependent on the structure of molecules

The Parachor

In 1923, D.B. Macleod suggested an empirical relationship between the surface tension and density of a liquid, which may be stated as                   

γgamm+a

𝛾

D-d=C

 where D and d are the densities and its vapour, respectively, y is the surface tension at the same temperature and C is a characteristic constant of the liquid

 . Sugden (1924) obtained a relationship by multiplying Macleod equation with the molecular mam. M. of the liquid, and called the new constant as Parachor [P] 

                 MY1-4/D-d=MC=[p]

At ordinary temperature, the density of vapour, d, is negligible as compared with D for the liquid, the equation (8) redues to

                 MY1-4/D=[p]

Or.            VmY1-4=[P]      (since M/D=Vm)

where Vm is the molar volume of the liquid. If surface tension y is unity (ie., gamma = 1 ) then equation (10) may be written as

                Vm=[p]

Thus, the Parachor [P] may be defined as the molar volume of a liquid at a temperature at which its surface tension is unity. It is approximately independent of temperature. It was shown by Sugden that Parachor is both additive and constitutive property and its value for any compound can be expressed as the sum of two sets of constants, one depending on the atoms present and the other upon the structural factor. The former is called atomic structural parachor and the latter is called structural parachor. 

For two liquids 1 and 2

             M1Y1 ¼ /D1.   = [p1]             (11)

             M2Y2  ¼ D2.  =[p2]               ( 12)

Divided equation(12)by Eq.(11),ifY1=Y2,we get

        [P1]/[P2]=M1Y1 ¼/D1÷M2Y2 ¼ /D2=M1/D1÷M2/D2=( Vm)1÷(Vm)2.                                      (13)

Thus, a comparison of parachor means, the comparison of molar veiumes under such conditions that the liquids have the same surface tensions.

Parachor and Chemical Constitution-Uses of Parachor in Elucidating Structures 

The comparison of experimental parachor values with the theoretically calculated calues of a compound helps us to decide about its chemical constitution as illustrated by the Following examples

Deciding constitution-Structure of Benzene If the Kekule formula for benzene be aneepted, the value of ita parachor can be calculated using Vogel's data

 

 6 carbon atoms.  6×8.6 = 51.6

 

 6 hydrogen atom.   6x15.7 = 94 2

 

 3 double bonds.   3x19.9 =59.7

 

 6 membered ring.              =1.4

 

Calculated parachor value for benzene =  206.9

 

 The experimental parachor value for benzene is 206.2. which is, therefore, in agreement with Kekule's formula.

 

Kekule formula:

           

        

Deciding the Nature of Valency Bonds.

 The parachor has also been found useful in providing information regarding the nature of bonds in certain groups. The nitre group (NO₂) for example, may be represented

      O                 O               0

_N \\            _N//             _N\

      \\                 \ O              \O

       O

1.                  II                  III

[P]= 98.9         [P]=74.1      [49.3]

The experimental value of parachor for - N * O_{2} group has been found to be 73.0. which is obviously in favour of the structure II.

 Existence of singlet linkage

Sugden suggested the existence of singlet linkage in compounds like PCI, and S*F_{0} A singlet linkage is a coordinate linkage formed by the donation of one electron onlythus in such a case we have the sharing of a single electron instead of the usual lone pair.

 

    (5 covalent linkage)        3 covalent and 2 single linkage

     [P]=316.9                      [P]=284

 

The experimental value for the parachor of PCls is 282.5, which is in agreement with the proposed structure (II) involving two singlet linkage and confirms the existence of two single-electron linkages in PCl, molecule. This prediction is supported by the observation that two of the chlorine atoms are easily eliminated on heating. 1

 

                    PCI→PCl3+ Cl₂

 

The Position of Substituent in an Aromatic Ring does not change the parachor value of the compound. The observed value of o-chlorotoluene is 280.8 and for p-chlorotoluene is 283.6. The theoretically calculated value for both the isomers is the same and is 283.3. Hence, the positional isomerism does not affect the parachor value.

 

 

 

                 MY1-4/D-d=MC=[p]

At ordinary temperature, the density of vapour, d, is negligible as compared with D for the liquid, the equation (8) redues to

                 MY1-4/D=[p]

 

Or.            VmY1-4=[P]      (since M/D=Vm)

 

where Vm is the molar volume of the liquid. If surface tension y is unity (ie., gamma = 1 ) then equation (10) may be written as

                Vm=[p]

 

Thus, the Parachor [P] may be defined as the molar volume of a liquid at a temperature at which its surface tension is unity. It is approximately independent of temperature. It was shown by Sugden that Parachor is both additive and constitutive property and its value for any compound can be expressed as the sum of two sets of constants, one depending on the atoms present and the other upon the structural factor. The former is called atomic structural parachor and the latter is called structural parachor.

 

For two liquids 1 and 2

             M1Y1 ¼ /D1.   = [p1]             (11)

             M2Y2  ¼ D2.  =[p2]               ( 12)

Divided equation(12)by Eq.(11),ifY1=Y2,we get

        [P1]/[P2]=M1Y1 ¼/D1÷M2Y2 ¼ /D2=M1/D1÷M2/D2=( Vm)1÷(Vm)2.                                      (13)

 

Thus, a comparison of parachor means, the comparison of molar veiumes under such conditions that the liquids have the same surface tensions.

 

 

 

 

 

Parachor and Chemical Constitution-Uses of Parachor in Elucidating Structures

 

The comparison of experimental parachor values with the theoretically calculated calues of a compound helps us to decide about its chemical constitution as illustrated by the Following examples

 

Deciding constitution-Structure of Benzene If the Kekule formula for benzene be aneepted, the value of ita parachor can be calculated using Vogel's data

 

 6 carbon atoms.  6×8.6 = 51.6

 

 6 hydrogen atom.   6x15.7 = 94 2

 

 3 double bonds.   3x19.9 =59.7

 

 6 membered ring.              =1.4

 

Calculated parachor value for benzene =  206.9

 

 The experimental parachor value for benzene is 206.2. which is, therefore, in agreement with Kekule's formula.

 

Kekule formula:

           

                 

 

Deciding the Nature of Valency Bonds.

 

 The parachor has also been found useful in providing information regarding the nature of bonds in certain groups. The nitre group (NO₂) for example, may be represented

      O                 O               0

_N \\            _N//             _N\

      \\                 \ O              \O

       O

1.                  II                  III

 

[P]= 98.9         [P]=74.1      [49.3]

 

The experimental value of parachor for - N * O_{2} group has been found to be 73.0. which is obviously in favour of the structure II.

 

Existence of singlet linkage

Sugden suggested the existence of singlet linkage in compounds like PCI, and S*F_{0} A singlet linkage is a coordinate linkage formed by the donation of one electron onlythus in such a case we have the sharing of a single electron instead of the usual lone pair.

 

    (5 covalent linkage)        3 covalent and 2 single linkage

     [P]=316.9                      [P]=284

 

s

 

The experimental value for the parachor of PCls is 282.5, which is in agreement with the proposed structure (II) involving two singlet linkage and confirms the existence of two single-electron linkages in PCl, molecule. This prediction is supported by the observation that two of the chlorine atoms are easily eliminated on heating. 1

 

                    PCI→PCl3+ Cl₂

 

The Position of Substituent in an Aromatic Ring does not change the parachor value of the compound. The observed value of o-chlorotoluene is 280.8 and for p-chlorotoluene is 283.6. The theoretically calculated value for both the isomers is the same and is 283.3. Hence, the positional isomerism does not affect the parachor value.

 

 

SURFACE TENSION

Molecules in the interior of a liquid are attracted equally in all directions by the Fig 3.2 O molecules around it, and are thus subjected to a balanced set of forces, whereas molecules at the surface are attracted only towards the interior as shown in Fig. The attractions pull the surface layer toward the centre, because of the difference in the strength of interactions of the surface molecule with the molecule in the vapour phase and one that is in the bulk below it. As a result of the inward attraction the surface of the liquid experiences an attractive force known as surface tension and surface behaves like a stretched membrane. That is why the surface of any liquid tends to minimize its surface area. A droplet assumes a spherical shape because a sphere has the minimum surface area for a given volume.

The Surface Tension is defined as the force in netwtons acting at right angle on a unit length (Im) along the surface of a liquid. It is denoted by (gamma). The SI unit of surface tension is newton per meter (Nm). Note that the units of Nim, are equivalent to joules per square meter,jm-2.

Surface tension is related to the attractive forces between molecules Liquids with large attractive forces have relatively large surface tensions. The large surface tension of Surface tension is related to the attractive forces between molecules Liquids with Effect of Temperature. The surface tension of a liquid decreases with increasing water is mainly due to more extensive hydrogen bonding in the water structure temperature and becomes zero near the critical temperature.

Capillary Action. The rise or fall of a liquid in a capillary tube is related to the surface depressed, like mercury, depends on the relative magnitude of the forces of cohesion tension of the liquid. Whether a liquid rises in a glass capillary, like water, or is depressed, like mercury, depends on the relative magnitude of the forces of cohesion tension of the liquid. Whether a liquid rises in a glass capillary, like water, or is between the liquid molecules themselves, and the forces of adhesion between the liquid and the walls of the tube These forces determine the contact angle 0, which the liquid makes with the walls of the tube. If a contact angle is less than 90, the liquid is said to wet the surface and a concave meniscus is formed. If the contact angle is greater that 90. the liquid does not wet the surface and a convex meniscus is formed.

The formation of a concave meniscus by a liquid that gets the glass leads to a capillary rise,the formation of a concave meniscus leads to the depression of the liquid (which does not wet the glass) in a capillary tube.

MEASUREMENT OF SURFACE TENSION

 The methods commonly employed for the measurement of surface tension are A fine capillary tube of radius is vertically

The Capillary Rise Method.

A fine capillary tube of radius r is vertically immersed in a test liquid that wets glass. The liquid rises to a certain height 'a' until the force of surface tension pulling the liquid upward is counterbalanced by the downward hydrostatic force.

The force of surface tension (i.e.. upward force) acting along the total circumference of the tube is 2tr y cos 0. The hydrostatic force fie., downward force) is equal to the product of pressure and area of cross-section of the tube (=ghdpir2)

 

But Upward force   = downward force

          2pirYcos0.   =   ghdpi r2

 

           Y = ghdr/2cos0

 

where y is the surface tension, d is the density of the liquid, g is the acceleration due to gravity and o is the contact angle. For most liquids, 0 is essentially zero, and ens 01 Therefore, Eq (1) reduces to

             Y ghdr/ 2

 In order to calculate the value of y, one needs to know the values of g.h.d and r.

DROP FORMATION METHOD

The size and hence the weight of a drop of a liquid falling from the end of a capillary tube depends upon the surface tension of the liquid and the sou the outer circumference of the tube. The weight of drop pulls it. When the two forces are of the capillary end. The drop is supported by the upward force of surface tension acting balanced, the drop breaks. Thus at the point of breaking

 γ. 2pir    =  W  = mg  =  Vdg

where,r  is the radius of the capillary tube. V is the volume of the drop and d is its  density.This equations being a basis of the drop Method is used for the comparison of the surface tensions of different liquids  

Drop Weight Method:

 In this method, the mass of a single drop of liquid, and that of reference liquid (say water) is determined. Then from Eq.(5), and

W1= m1g= 2pirY1

 W₂mg = 2pi r Y2

Therefore Y1/Y2 = m1/m2

 

Knowing the surface tension of reference liquid, that of the experimental liquid can be determined.

 

DROP-NUMBER METHOD:

Drop-Number Method Instead of finding the weights of single drops, it is easier to count the number of drops formed from an equal volume of two liquids If n. and nare the number of drops produced from the same volume V of the two liquids, then

 

.The volume of a single drop of liquid 1 = V/n1

.The mass of a single drop of liquid 1 V/n1 d1 .Similarly, the mass of a single drop of liquid 2 V/n2 d2

Y1/Y2= (V/n1)d1/(V/n2)d2 =n2d1/n1d2 or Y1 = n2d1/n1d2 Y2

The instrument used for determining surface tension is called stalagmometer, which consists of a bulb fused with a capillary tube as shown in Fig.3.7. The stalagmometer is thoroughly cleaned and water is sucked up to the upper mark A. The water is allowed to flow and the number of drops is counted until the lower mark B is reached. Next the experiment is repeated with the other (experimental) liquid and surface tension of the liquid can be determined by using the Eq.(7). For reference liquid water, Eq.(7) can be written as:

Y1= d1 /dw×nw/n1×Yw