wseas-edit-11641-20260916093837-7e6221 20260916093837718 wseas/wseas wseas.group@gmail.com WSEAS WSEAS TRANSACTIONS ON FLUID MECHANICS 1790-5087 2224-347X 01 09 2026 01 09 2026 21 Meirim Amantay Institute of Automation and Information Technologies Auezov University of South Kazakhstan Tauke Khan av., 5, Shymkent KAZAKHSTAN Arnold Brener Institute of Automation and Information Technologies Auezov University of South Kazakhstan Tauke Khan av., 5, Shymkent KAZAKHSTAN Akhmetbek Mussabekov Institute of Automation and Information Technologies Auezov University of South Kazakhstan Tauke Khan av., 5, Shymkent KAZAKHSTAN Aliya Yegenova Institute of Automation and Information Technologies Auezov University of South Kazakhstan Tauke Khan av., 5, Shymkent KAZAKHSTAN Ablakim Muratov Institute of Automation and Information Technologies Auezov University of South Kazakhstan Tauke Khan av., 5, Shymkent KAZAKHSTAN The paper deals with a problem of deriving reliable and convenient models for the viscous suspension films of variable rate flows. The contribution and novelty of this work lies in the fact that a general concept is presented for the mathematical model of the formation of nonlinear waves in the film flows containing a dispersed solid phase, an asymptotic analysis is given, and a set of the main control parameters has been established. Unlike the previous works, this paper focuses specifically on clearly identifying the control parameters and deriving the general control equation. The decisive role of the special control parameter depending on the viscosity of the suspension near the support wall has been established. 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