Clarification Dynamics and Limiting Flux

1. Name of the Course Instructor: Professor Suparna Mukherjee Clarification Dynamics and Limiting Flux

2. Definitions and Keywords 1 • Gravity Flux (NB°) - Flux of solids moving downwards due to hindered settling NB° = Ci × Vs , where Ci is the concentration of solids and Vs is the settling velocity • Underflow Flux (Nu°) - Flux of solids due to the bulk flow of recyclable sludge Nu° = Ci × u , where u is the underflow velocity • Total flux (Ns°) = Gravity flux + Underflow flux • Solid handling Capacity (NL°)- Flux of solids at which all the solid particles reach the bottom of clarifier 2 3 4 5

3. Definitions and Keywords 1 • Cf - Solid concentration of clarifier feed • Cu - Solid concentration of the clarifier underflow • Underflow rate is the rate at which sludge is recycled - Qr • Overflow rate is the feed rate to the clarifier- Qf 2 3 4 5

4. Concept details 1 2 At Ci =0, gravity flux NB°= 0, As concentration increases, NB° increases to a peak and then decreases as Vs approaches 0 The curve will start moving from zero towards its peak and then move down. During the entire animation the concentration should increase simultaneously At Ci =0, gravity flux NB°= 0, As concentration increases, NB° increases to a peak and then decreases as Vs approaches 0 1 3 At Ci =0, underflow flux Nu°= 0, As concentration increases, Nu° increases proportionately At Ci =0, underflow flux Nu°= 0, As concentration increases, Nu° increases proportionately The curve will start moving from zero as a straight line. During the entire animation the concentration should increase simultaneously 2 4 In this step, the total flux line will move from 0 simultaneously with the gravity flux line (step-1), underflow flux line (step-2) so that at any point of time the sum of gravity flux and underflow flux will represent as total flux Total flux Ns° is the sum of gravity flux and underflow flux Total flux Ns° is the sum of gravity flux and underflow flux 3 5

5. Concept details 1 2 Dotted line will move from the lowest point of the sagged portion of total flux line and will meet Y axis at NL° . The lowest point in the sagged portion of total flux line is the limiting flux. The lowest point in the sagged portion of total flux line is the limiting flux 4 3 Tangent drawn to the gravity flux curve from the point on X axis corresponding to Cu if extended to Y axis will meet at NL° . This tangent is the underflow rate line Tangent drawn to the gravity flux curve from the point on X axis corresponding to Cu if extended to Y axis will meet at NL°. This tangent is the underflow rate line Locate Cu on X axis. Move a tangent from Cu to the gravity flux curve and extend to Y axis. See that at meets Y axis at NL° 5 4 The point on the underflow rate line corresponding to Cf is the state point. The flux corresponding to state point should be the applied flux N°app The point on the underflow rate line corresponding to Cf is the state point. The flux corresponding to state point should be the applied flux N°app Move a vertical line from Cf to intercept the underflow rate line. Locate the point of interception as the state point. Locate N°app on Y axis. 6 5

6. Concept details 1 2 The line connecting 0 to the state point is the overflow rate line The line connecting 0 to the state point is the overflow rate line Start moving a line from 0 to the state point and extend it 7 3 When underflow rate or concentration changes state point shifts and accordingly NL° and overflow rate changes. For lower Cu, flux is lower and overflow rate is higher Move the underflow rate line downwards and locate another state point for a different Cu. Join the new state point to 0 to get another overflow rate line. Also locate corresponding flux at Y axis as the new NL° When underflow rate or concentration changes state point shifts and accordingly NL° and overflow rate changes. For lower Cu, flux is lower and overflow rate is higher 8 4 When underflow rate changes, the slope of underflow line changes and thus Cu also changes. This also leads to change in flux and overflow rate 9 5

7. Interactivityand Boundary limits 1 2 While changing or shifting the state point or underflow rate line the original one should remain blinking so that it would be easy to correlate the new one with the old one 3 4 5

8. INSTRUCTIONS SLIDE Questionnaire to test the user 1 • A small, (5 questions) questionnaire can be created in the next slide, to test the user's comprehension. • This can be an objective type questionnaire. • It can also be an exercise, based on the concept taught in this animation. 2 3 4 5

9. Questionnaire 1 1. Which flux has a larger value? Answers: a) Gravity flux b) Underflow flux c) Total flux d)‏ None of the above 2. From which curve’s slope you determine underflow rate? Answers: a) Total flux curve b) Underflow curve c) Gravity flux curve d)‏ Limiting flux line 3. State point is the interception point of underflow rate line and which line? Answers: a) Overflow rate line b) Limiting flux line c) Gravity flux curve d)‏ total flux line 4. What happens overflow rate when underflow concentration decreases? Answers: a) Increases b) Decreases c) Does not change d)‏ None of the above 5. Applied flux should be lower than Answers: a) Gravity flux b) Underflow flux c) Limiting flux d)‏ Underflow concentration 2 3 4 5

10. Thank you