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

Definitions and Keywords Gravity Flux (N B ° ) - Flux of solids moving downwards due to hindered settling N B ° = C i × V s, where C i is the concentration of solids and V s is the settling velocity Underflow Flux (N u ° ) - Flux of solids due to the bulk flow of recyclable sludge N u ° = C i × u, where u is the underflow velocity Total flux (N s ° ) = Gravity flux + Underflow flux Solid handling Capacity (N L ° ) - Flux of solids at which all the solid particles reach the bottom of clarifier

Definitions and Keywords C f - Solid concentration of clarifier feed C u - Solid concentration of the clarifier underflow Underflow rate is the rate at which sludge is recycled - Q r Overflow rate is the feed rate to the clarifier- Q f

Concept details At C i =0, gravity flux N B °= 0, As concentration increases, N B ° increases to a peak and then decreases as V s 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 2 At C i =0, underflow flux N u °= 0, As concentration increases, N u ° increases proportionately The curve will start moving from zero as a straight line. During the entire animation the concentration should increase simultaneously 3 Total flux N s ° is the sum of gravity flux and underflow flux 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

Concept details 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 Dotted line will move from the lowest point of the sagged portion of total flux line and will meet Y axis at N L °. 5 Tangent drawn to the gravity flux curve from the point on X axis corresponding to Cu if extended to Y axis will meet at N L °. This tangent is the underflow rate line Locate C u 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 N L ° 6 The point on the underflow rate line corresponding to C f is the state point. The flux corresponding to state point should be the applied flux N° app Move a vertical line from C f to intercept the underflow rate line. Locate the point of interception as the state point. Locate N° app on Y axis.

Concept details 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 When underflow rate or concentration changes state point shifts and accordingly N L ° and overflow rate changes. For lower C u, flux is lower and overflow rate is higher Move the underflow rate line downwards and locate another state point for a different C u. Join the new state point to 0 to get another overflow rate line. Also locate corresponding flux at Y axis as the new N L ° 8 9 When underflow rate changes, the slope of underflow line changes and thus C u also changes. This also leads to change in flux and overflow rate

Interactivity and Boundary limits 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

INSTRUCTIONS SLIDE Questionnaire to test the user 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

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

Thank you