A MATHEMATICAL MODEL ON THE USE OF VIBRATION TO REDUCE MACRO-FOULING IN A SPHERICAL MEMBRANE WITH TENSION
SHEILA J. KIPROTICH *
Department of Mathematics, Kisii University, Kenya.
*Author to whom correspondence should be addressed.
Fouling is the accumulation of unwanted materials on the solid surfaces to the detriment of function .The use of filters and sieves is applicable in domestic and industrial sectors and the efficiency of filtration membranes is hindered by fouling. Fouling is caused by high solute deposited on the contact surface of the membrane. This can be reduced through bubbling, aeration, and most effectively by induced vibrations which generates 3-D wave equations in spherical co-ordinates with respect to the transverse motion and oscillation of the vibrating membrane. This study will develop a mathematical model of vibration in reducing macro fouling in a circular membrane with tension. The model equation will be solved using separation of variables. The expected results will be determined analytical solution for the 3-D wave equation, giving determined effects of oscillation on the rate of fouling. These results will indicate threshold values that are necessary to eliminate fouling.
Keywords: Mathematical model, vibration, reduce macro-fouling, membrane with tension.