LECTURE NOTES 05/07 STKM3212: FOOD PROCESSING

TECHNOLOGY FLUIDS MECHANIC: VISCOSITY OF FLUIDS

(MEKANIK BENDALIR: KELIKATAN BENDALIR)

SAIFUL IRWAN ZUBAIRI PMIFT, Grad B.E.M. B. Eng. (Chemical-Bioprocess) (Hons.), UTM

M. Eng. (Bioprocess), UTM

ROOM NO.: 2166, CHEMISTRY BUILDING,TEL. (OFF.): 03-89215828,

FOOD SCIENCE PROGRAMME,CENTRE OF CHEMICAL SCIENCES AND FOOD TECHNOLOGY,

UKM BANGI, SELANGOR

1.1 OUTLINES

1.2 NEWTON’S LAW AND VISCOSITY.1.3 VISCOSITIES OF NEWTONIAN

FLUIDS.1.4 VISCOSITIES OF NON-

NEWTONIAN FLUIDS.1.5 IDENTIFICATION OF FLUIDS

RHEOLOGY USING VISCOMETER.1.6 LAMINAR AND TURBULENT FLOW.1.8 REYNOLDS NUMBER (Re).

1.2 NEWTON’S LAW AND VISCOSITY Some of the food substances are in the form of LIQUID. One of the PHYSICAL PROPERTIES FOR LIQUID FOOD VISCOSITY

(Kelikatan). REASON FOR APPLYING THE SCIENCE OF VISCOSITY:

(1)Will influence the perception of consumer:

(a) e.g.: ‘KAYA’ Cannot be too dilute, viscose is the best.

(b) e.g.: SAUCE Must be in certain value of viscosity.

(c) e.g.: JUICES Need to be diluted, not viscose.

(2)Easy to transport:

(a) e.g.: For transporting the liquid food to the other location in the factory.

(3)Easy for gripping (adhesion) :

(a) e.g.: Adhesion of coated flour to the chicken meat.

(b) e.g.: Adhesion to the container or wrapper.

CONTINUE: Movement of FLUID will occur if the STRESS (TEGASAN) is given. STRESS/PRESSURE = Force (N)/Area (m2) If the FORCE (N) is perpendicular (at 90o angle) with surface It is

called NORMAL STRESS (Tegasan Normal). Normally, it is called = PRESSURE (P)

If the FORCE is HORIZONTAL/PARALLEL (1800) with the surface It is called SHEAR STRESS (Tegasan Ricihan).

Different materials will give different effect of the SHEAR STRESS.

P3P2P1

(Force) F1 = N (V 0 to A)

V 0 = m/s

Fluid

r (distance of the fluid movement), m

Viscosity () = Pa.s OR kg/m.s

V A = m/s

CONTINUE:

VISCOSITY, (Kelikatan) = “resistance (rintangan) of GASSES OR FLUIDS towards the flow of the SHEAR STRESS”.

When STRESS is applied Fluids will move. SO, STRESS (F/A); VELOCITY (m/s). Fluids is assumed to be combination of FLUID LAYERS. When the lower layer is given the STRESS, it will effect the upper

layer. USUALLY, viscosity of lower layer > upper layer. Each layer will move at different velocity (m/s). The far the layer from the source of STRESS, the velocity (m/s)

of that layer. Upper layer has < velocity (m/s). The subsequent layer has > velocity (m/s).

CONTINUE:

The English unit for VISCOSITY are called “Poise” or “centipoise” (cp) = g/cm.s

The SI UNIT for VISCOSITY Pa.s ( N.s/m2 OR kg/m.s)

1 cp = 1 × 10-3 kg/m.s =

1 × 10-3 Pa.s = 1 × 10-3 N.s/m2 (SI Unit)

1 cp = 0.01 poise = 0.01 g/cm.s (English Unit)

CONTINUE:

THEREFORE: ------- NEWTON’S LAW SHEAR STRESS () (shear stress) is shear force (N) per area (m2)

(tau) = F/A = - .dv/dr -------- (N/m2) SHEAR RATE () is defined as velocity gradient (m/s) at the r

distances (m) :

(gamma) = dv/dr = (v1-v2)/(r2-r1) -------- (s-1)Where: r = distance at velocity zero, v = velocity at distance r

RELATIONSHIP BETWEEN: VISCOSITY () VS VS are :

= / -------- (N.s/m2)

CONTINUE:

(1)For ELASTIC SOLID when the shear stress is applied, it will change accordingly to the flow of the stress.

The material will RETURN BACK to its normal size when the stress is removed. e.g.: rubber materials.

(2) For SOLID that have a plastic properties when the SHEAR STRESS is applied, it will change accordingly to the flow of the stress.

BUT = it will not come back to its original shape right after the stress is removed. e.g.: jelly (agar-agar).

(3) For FLUIDS when the SHEAR STRESS is applied, it will change accordingly to the flow of the stress.

This material will not come back to its original shape & will moving towards the flow of the stress.

1.3 VISCOSITIES OF NEWTONIAN FLUIDS FLUIDS show LINEAR relationship between SHEAR STRESS

() & SHEAR RATE () = “NEWTONIAN FLUIDS”

SLOPE = Viscosity (). Viscosity () for the NEWTONIAN FLUIDS are not influenced by

the SHEAR RATE (). The “VISCOSITY” TERMS is ONLY SUITABLE “NEWTONIAN

FLUIDS”.

() = slope()

()

CONTINUE:

Examples of NEWTONIAN FLUIDS AND GASESS: (1 atm = 101.32 Kpa)

COMMON SENSE: T (OC); viscosity () ---- WHY? = when the temperature is increases, the molecules of substance will evaporate thus resulted in decreases of mass (mg). So, less shear force () is needed to measure its viscosity. REFER TO THE EQUATION ----- = /

1.4 VISCOSITIES OF NON-NEWTONIAN FLUIDS For “NON-NEWTONIAN FLUIDS” = The term of APPARENT

VISCOSITY (kelikatan tampak) is usually used. 

Examples of NON-NEWTONIAN FLUIDS: “pastes (perekat), slurries (lumpur lembik), high polymers, emulsions, etc”.

NON-NEWTONIAN FLUIDS = it has:

(1) ‘SHEAR-THINNING’ (ricihan-kekurangan) Pseudoplastic

(2) ‘SHEAR-THICKENING’ (ricihan-tambahan) Dilatant

(3) ‘YIELD STRESS’ (Tegasan berian) Bingham plastic

REMEMBER “Most of the non-newtonian fluids are TIME INDEPENDENT & EXHIBIT (pamerkan) elastic (rubberlike) behavior” ---- it is called “VISCOELASTICS FLUIDS”

CONTINUE:(1) ‘SHEAR-THINNING’ (ricihan-kekurangan) it has dispersed phase (fasa

terserak) which tends to COMBINE with the flow that has the minimum resistances. Its particle will form a position at the minimum resistances flow. e.g.: mayonnaise/biological fluids/paints/greases/detergent slurries.

(2) ‘SHEAR-THICKENING’ (ricihan-tambahan) it has dispersed phase (fasa terserak) which tends to EXPAND OR its molecule will make a cross bonding with each others.

e.g.: wet beach sand/starch in water/high conc. of powder in water.

(3) ‘YIELD STRESS’ (Tegasan berian) These are the simplest because they differ from newtonian only in that the linear relationship does not go through origin (Figure 3.5-1) A SET YEILD STRESS (shear) in N/m2 is needed to INITIATE FLOW.

e.g.: drilling muds/peat slurries/margarine/chocalate mix/soap/sewage sludge/toothpaste.

 

CONTINUE:

There are 2 equation that represent the “NON-NEWTONIAN FLUIDS”:

= K()n ------------ (1)

Where:

n = flow behavior index (dimensionless) - (n < 1.0: Pseudoplastic) OR (n > 1.0: Dilatant).

n = will shows whether it is “shear-thinning(pseudoplastic)” OR “shear-thickening (dilatant).

K = consistency index (N.sn/m2).

[Generally, the more viscose of fluids, the higher K values].

CONTINUE:

(A)

(B)

(C)

SLOPE: (A) > (B) > (C) = APPARENT VISCOSITY (app) ---- app with SHEAR RATE ()

(n > 1.0)

(n < 1.0)

(n = 1.0)

CONTINUE:

APPARENT VISCOSITY (Kelikatan tampak):

app = / = K()n-1 ------- (2)

Calculation of APPARENT VISCOSITY is done by assuming that the NON-NEWTONIAN FLUIDS is behave like NEWTONIAN FLUIDS.

Referring to Figure 3.5-1:

(1) app with SHEAR RATE () ----- PSEUDOPLASTIC

(2) app with SHEAR RATE () ----- DILATANT

“Disebabkan kelikatan tampak (apparent viscosity) berubah dengan kadar ricihan (shear rate), maka perlu apabila melaporkan kelikatan tampak untuk melaporkan juga kadar ricihan yang digunakan

1.5 IDENTIFICATION OF FLUIDS RHEOLOGY USING VISCOMETER RHEOLOGY “The science of the flow and deformation (pembentukan)

of fluids”. 2 types of measurement equipment :

(1) Rotational Type Viscometer (Viskometer Jenis Putaran):

Concentric cylinder (silinder konsentrik/berpusat sama). UKM: known as ---- “Wide-gap rotational viscometer with

spindle cylinder”

Parallel plate (plat selari).

Cone & plate (kon & plat).

Mixer (pengacau).

(2) Tube Type Viscometer (Viskometer Jenis Tiub):

Glass capillary (kapillari kaca).

Pipe (paip).

High pressure capillary (kapilari tekanan tinggi).

CONTINUE:

Tube Type Viscometer: High pressure capillary (kapilari tekanan tinggi)

NON-NEWTONIAN SUBTANCES:•Lubricating oil •Polymer solutions •Fuel oil •Emulsions •Fat melts •Suspensions •Printing inks •Liquid detergents •Latex •Adhesives •Lacquers •Glues

CONTINUE:

Rotational Type Viscometer Concentric cylinder (silinder konsentrik)

NON-NEWTONIAN SUBSTANCES:•suspensions •diary products •lacquers or varnishes •printing inks •emulsion paints •lubricants •latex •polymer solutions •coal suspensions •glues or adhesives •resins •coating slips •chocolate suspensions •sealing compounds •fruit mash or preparations •vegetable mash •coating colours •cosmetics •solutions •emulsions •mud

CONTINUE:

CONTINUE:

Rotational Type Viscometer: Mixer (pengacau)

CONTINUE:

The most common type of equipment concentric cylinder viscometer (viskometer silinder konsentrik).

Consisted with 2 concentric cylinder (silinder berpusat sama). Fluid substances is put between 2 cylinders (INTERNAL &

EXTERNAL CYLINDER) . INTERNAL CYLINDER (spindle) will spin & gives SHEAR FORCE

to the fluid substances. There are particular sizes of SPINDLE can be found depending on

the viscosity of the fluid substances (make a visual interpretation before selecting the sizes of spindle).

Resistance towards the flow will be experienced by SPINDLE & it will measured the resistance.

The measured values will be multiply with CERTAIN CONVERSION FACTOR for obtaining the “ACTUAL VISCOSITY”.

CONTINUE:

The CONVERSION FACTOR is different according to the SIZE of the SPINDLE & SPIN SPEED.

The example of viscometer brand: “Brookefield Viscometer” CALCULATION EXAMPLES:

Spindle = No. 2

Spindle speed (N) = 60 rpm

CF = 5

Reading from the device = 64

Viscosity (app:Non-newtonian OR Newtonian) : 64 x 5 = 320 cp

Spindle : No. 3; Spindle speed (N) = 6 rpm; CF = 200

Reading from the device = 64.4

(app:Non-newtonian OR Newtonian) : 64.4 x 200

= 12,880 cp

NEWTONIAN FLUIDS: ROTATIONAL VISCOMETER For NEWTONIAN FLUID it will give actual value of viscosity ().

n (flow behavior index) for NEWTONIAN = 1.0 and Plot graph Log vs. Log .

PLOT FROM ORIGIN (0,0) ------ SLOPE = Actual viscosity ()

SHEAR STRESS; (N.m2) torque (N.m) ------- (1)

SHEAR RATE; (s-1) N (spindle speed, rpm) ------------- (2)

() = slope()

()

CONTINUE: The SHEAR RATE () at the surface of the spindle for NEWTONIAN

FLUIDS is as follows with n = 1:

4N/1 - (Rb/Rc)2

Where: (a) Rb - radius of the spindle, m(b) Rc - radius of the outer cylinder or container, m(c) - angular velocity of the spindle, rad/s

= 2N/60 ,when N is the RPM

The SHEAR STRESS () at the wall of the spindle:

= A/2LRb2

=

Where:A = Torque (N.m)L = Height of the spindle, mRb = radius of the spindle, m

=

EXAMPLE 1 (NEWTONIAN):

Rotational Type Viscometer Concentric cylinder (Wide-gap rotational viscometer with spindle):

A wide-gap rotational viscometer with a spring constant of 7,187 dynes.cm are used to measure a viscosity (cps; %) of RO-H2O. The outer radius (Rc), spindle radius (Rb), and height (L) of the cylindrical spindle are 2.75 cm, 1.50 cm and 5.0 cm respectively. Determine the viscosity () in N.s/m2 of RO-H2O. Measurement values are given below:

Spindle speed (N) Device reading; cps (% scale)

20 rpm 16

50 rpm 22

100 rpm 45

CONTINUE:

Spindle cylinder

Test fluid - RO-H2O

Beaker

“Wide-gap rotational viscometer with spindle cylinder”

L

Rc Rb

CONTINUE:

ANS:

(1)RO-H2O = NEWTONIAN FLUIDS

(2)Firstly, we ONLY construct a graph of ---- vs. (3)The SLOPE = viscosity () in N.s/m2

(3)Convert: Device reading; cps (%) Torque (dynes.cm)

Torque (dynes.cm) = Device reading; cps (%) × spring constant

(7,187 dynes.cm)

e.g.: Torque (dynes.cm) = 16/100 × 7187 = 1,149.92

(4)Convert: {dynes.cm} {N.m} by using the conversion factor:

CONVERSION FACTOR: (1 dynes = 10-5 Newton)

e.g.: 1149.92 dynes.cm 10-5 N 1 m = 0.000115 N.m

1 dynes 100 cm

CONTINUE:

(5) Convert: Torque (N.m) (N/m2) by using the formula:

= A/2LRb2; A = Torque (N.m)

e.g.: = 0.000115/[2 × 3.14 × 5.0/100 × (1.5/100)2] = 1.62 N/m2

(6) Convert: N (rpm) (s-1) by using the formula:

= 4N/1 - (Rb/Rc)2

e.g.: = [4 × 3.14 × (20 rpm/60 s)]/1 - (0.015/0.0275)2 = 5.98 s-1

N (rpm) (s-1) Torque (dynes.cm) Torque (N.m) (N/m2)

20 rpm 5.98 1149.92 0.000115 1.62

50 rpm 14.95 1581.14 0.000158 2.24

100 rpm 29.90 3234.15 0.000323 4.57

CONTINUE:

You should get a LINEAR EQUATION WITH ‘0’ INTERCEPT

The equation: y = 0.16x ----- so; the SLOPE = viscosity () in N.s/m2

Viscosity () of RO-H2O = 0.16 N.s/m2

NON-NEWTONIAN FLUIDS: ROTATIONAL VISCOMETER For NON-NEWTONIAN FLUID it will give apparent viscosity

(app).

Besides viscosity value, n (flow behavior index) and K [consistency index (N.sn/m2)] can also be calculated using the graph of (Log torque vs. Log N) & (Log vs. Log ).

(1)Log torque vs. Log N ------ To get the n value: SLOPE: n

(2)Log vs. Log --------- To get the K value: INTERCEPT: y-axis = log K

SHEAR STRESS (); N.m2 torque (N.m) ------- (1)

SHEAR RATE (); s-1 N (spindle speed, rpm) ------------- (2)

CONTINUE: The SHEAR RATE () at the surface of the spindle for NON-

NEWTONIAN FLUIDS is as follows for 0.5 < Rb/Rc < 0.99:

--------------- (1)

Where: (a) Rb - radius of the spindle, m(b) Rc - radius of the outer cylinder or container, m(c) n - flow behavior index (dimensionless)(d) - angular velocity of the spindle, rad/s

= 2N/60 ,when N is the RPM

The SHEAR STRESS () at the wall of the spindle:

= A/2LRb2

=

Where:A = Torque (N.m)L = Height of the spindle, mRb = radius of the spindle, m

CONTINUE:VARIOUS SPECIAL CASES CAN BE DERIVED FROM EQUATION (1):

(1) VERY LARGE GAP (Rb/Rc < 0.1) = This is the case of a spindle immersed in a large beaker of test fluid. [ = 2N/60 ,when N is the RPM]

Test fluid

Rb Rc

Spindle

Container or cylinder

= = 4N/n

CONTINUE:VARIOUS SPECIAL CASES CAN BE DERIVED FROM EQUATION (1):

(1) VERY NARROW GAP (Rb/Rc > 0.99) = This is similar to flow parallel plates. Taking the shear rate at radius (Rb + Rc)/2.

[ = 2N/60 ,when N is the RPM]

Test fluid

Rb

RcSpindle

Container or cylinder

=

EXAMPLE 2 (NON-NEWTONIAN):Rotational Type Viscometer Concentric cylinder (Wide-gap rotational viscometer with spindle):

A wide-gap rotational viscometer with a spring constant of 7,187 dynes.cm are used to measure a viscosity (cps; %) of a tomato sauce. The outer radius (Rc), spindle radius (Rb) and height (L) of cylindrical spindle are 2.70 cm, 0.15 cm and 5.0 cm respectively. Determine the K and n? Calculate also the apparent viscosity (app) of tomato sauce in N.s/m2 at spindle speed of 35 rpm. Measurement values are given below:

Spindle speed (N) Device reading; cps (% scale)

20 rpm 29

50 rpm 44

100 rpm 60

CONTINUE:

Spindle cylinder

Test fluid - Tomato sauce

Beaker

“Wide-gap rotational viscometer with spindle cylinder”

L

Rc Rb

CONTINUE:

ANS: Rb/Rc = 0.15 cm/2.7 cm = 0.055 < 0.1 --- So, equation very large gap is used

n value determination:

(1)Sauce tomato = NON-NEWTONIAN FLUIDS

(2)Firstly, we have to construct a graph of ---- Log torque vs. Log N

(3)Convert: Device reading; cps (%) Torque (dynes.cm)

Torque (dynes.cm) = Device reading; cps (%) × spring constant

(7,187 dynes.cm)

e.g.: Torque (dynes.cm) = 29/100 × 7187 = 2,084.23

(4)Convert: {dynes.cm} {N.m} by using the conversion factor:

CONVERSION FACTOR: (1 dynes = 10-5 Newton)

e.g.: 2084.23 dynes.cm 10-5 N 1 m = 0.000208 N.m

1 dynes 100 cm

(5)Log (N) rpm ---- “see table”

CONTINUE:(6) Plot the graph:

N (rpm) Log N Cps (%) Torque (dynes.cm) Torque (N.m) Log Torque

20 rpm 1.30 29 2084.23 0.000208 -3.68

50 rpm 1.70 44 3162.28 0.000316 -3.50

100 rpm 2.00 60 4312.20 0.000431 -3.37

CONTINUE:

(7) So, we have the LINEAR equation:

y = 0.451x - 4.268 -------- n value is the SLOPE

n = 0.451 (n < 1.0 = PSEUDOPLASTICS FLUIDS)

K value determination:

(1) Convert: Torque (N.m) (N/m2) by using the formula:

= A/2LRb2; A = Torque (N.m)

e.g.: = 0.000208/[2 × 3.14 × 5.0/100 × (0.15/100)2] = 294.62 N/m2

(2) Log ------- ‘see table’

(3) Convert: N (rpm) (s-1) by using the formula:

= 4N/n

e.g.: = [4 × 3.14 × (20 rpm/60 s)]/0.451 = 9.26 s-1

CONTINUE:

(3) Plot the graph:

N (rpm) (s-1) Log Torque (N.m) (N/m2) Log

20 rpm 9.26 0.97 0.000208 294.62 2.47

50 rpm 23.16 1.36 0.000316 447.60 2.65

100 rpm 46.32 1.67 0.000431 610.36 2.79

CONTINUE:

(4) So, we have the LINEAR equation:

y = 0.451x + 2.033 ---------- intercept (c) = K

c = Log ---- Antilog (c): Antilog [2.033] = K = 107.89 N.s0.451/m2

Apparent viscosity (app) in N.s/m2 at spindle speed of 35 rpm:

Convert: N (rpm) (s-1) by using the formula:

= 4N/n

= [4 × 3.14 × (35 rpm/60 s)]/0.451 = 16.25 s-1

Log [16.25] = 1.21

Based on the equation: y = 0.451x +2.033;

y = 0.451( 1.21) + 2.033 = 2.58

Antilog (y) = = 380.19 N/m2 ---- SO;

(app) = / = 380.19/16.25 = 23.40 N.s/m2

OR ALTERNATIVELY using equation: app = / = K()n-1 = 107.89[(16.25)0.451-1]app = 107.89 16.25-0.549 = 23.40 N.s/m2

1.6 LAMINAR AND TURBULENT FLOW These 2 types of flow can commonly seen in a open stream or

RIVER. When velocity (m/s) of flow is SLOW the FLOW PATTERNS are

SMOOTH. When velocity (m/s) of flow is HIGH unstable PATTERN IS

OBSERVED in which EDDIES (small packets of fluids particles) are present moving in all directions and at all angles to the normal line of flow.

(1)“LAMINAR FLOW” = flow at low velocities where layers of fluids seem to slide by one another without eddies/swirls (pusaran) being present.

(2)“TURBULENT FLOW” = flow at higher velocities where eddies are present giving the fluid a fluctuating nature.

CONTINUE:

“The was no mixing in any parts of the tube and the fluid flowed in straight parallel lines” LAMINAR/VISCOUS FLOW

“As the velocity increased, it was found that a definite velocity the thread of dye became dispersed and the pattern was very erratic/inconsistent” TURBULENT/CRITICAL VELOCITY

1.7REYNOLDS NUMBER (Re)

FLUID FLOWS can be as LAMINAR or TURBULENT. (Re) is important to identify whether the flow is LAMINAR or TURBULENT. Studies has shown that the transition from LAMINAR to TURBULENT flow

in the tubes is not only a function of velocity (m/s), but also density, viscosity & tube diameter.

 

Re = Dv/ ----------- (1) [DIMENSIONLESS] D = tube diameter (m)

v = average velocity (m/s) - volumetric flow rate (m3/s)/cross sectional area of the pipe (m2)

= density of the fluid (kg/m3)

= viscosity of the fluid (Pa.s) IF, Re 2100 ------------- LAMINAR FLOW IF, Re > 4000 ------------- TURBULENT FLOW

In between the 2100 & 4000 = the flow will be TURBULENT or VISCOUS, depending upon the apparatus details, which can not be predicted. It is called “TRANSITION REGION”

EXAMPLE 1:

CONTINUE: