Instability of nanofluid film flow under external electric field: Linear and weakly nonlinear analysis

doi:10.1088/1674-1056/addcc0

Abstract This study investigates the instability of nanofluid thin films flowing down an inclined plane under the influence of a normal electric field. Based on the long-wave approximation and a systematic asymptotic expansion, a nonlinear evolution equation is derived to capture the coupled effects of the electric field and nanoparticle properties. Linear stability analysis reveals that the electric field enhances interfacial disturbances and promotes instability, whereas the presence of nanoparticles suppresses this effect by attenuating disturbance amplitudes. A weakly nonlinear analysis further clarifies the interplay among electric field strength, nanoparticle volume fraction, and density difference, enabling a classification of nonlinear stability regimes. Numerical simulations support the analytical predictions, showing that in unstable regimes, perturbations grow over time and eventually destabilize the film. These findings offer theoretical insights into the control of nanofluid film stability via electric field regulation and nanoparticle tuning.

Keywords: thin film instability nonlinear evolution equation nanofluid

Received: 29 March 2025
Revised: 04 May 2025
Accepted manuscript online: 23 May 2025

PACS:	47.20.Dr	(Surface-tension-driven instability)
	47.11.St	(Multi-scale methods)
	47.10.A-	(Mathematical formulations)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11902165, 12272188, 12102205, and 12262025), the National Science Foundation for Distinguished Young Scholars of the Inner Mongolia Autonomous Region of China (Grant No. 2023JQ16), the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Grant No. NJYT23098), and the Scientific Startin and the Innovative Research Team in Universities of Inner Mongolia Autonomous Region of China (Grant No. NMGIRT2208).

Corresponding Authors: Zhaodong Ding
E-mail: dingzhd@imu.edu.cn

Cite this article:

Xinshan Li(李欣珊), Danting Xue(薛丹婷), Ruigang Zhang(张瑞岗), Quansheng Liu(刘全生), and Zhaodong Ding(丁兆东) Instability of nanofluid film flow under external electric field: Linear and weakly nonlinear analysis 2025 Chin. Phys. B 34 124701

[1] Benjamin T B 1957 J. Fluid Mech. 2 554
[2] Yih C S 1955 Q. Appl. Math. 12 434
[3] Yih C S 1969 Fluid Mechanics: A Concise Introduction to the Theory (McGraw-HilleBooks)
[4] Oron A, Davis S H and Bankoff S G 1997 Rev. Mod. Phys. 69 931
[5] Kalliadasis S, Kiyashko A and Demekhin E A 2003 J. Fluid Mech. 475 377
[6] Tseluiko D and Papageorgiou D T 2006 J. Fluid Mech. 556 361
[7] Thiele U, Goyeau B and Velarde M G 2009 Phys. Fluids 21 014103
[8] Hu K X, He M and Chen Q S 2016 Phys. Fluids 28 033105
[9] Hu K X, He M, Chen Q S and Liu R 2017 Phys. Fluids 29 073101
[10] Morad A M, M A S and I E G 2020 Phys. Scr. 95 025205
[11] Hu K X, Zhang S N and Chen Q S 2023 J. Fluid Mech. 958 A22
[12] Tian K, Xue C, Cui J, Qin K and Ding Z 2024 J. Non-Newtonian Fluid Mech. 333 105324
[13] Hu K X, Du K and Chen Q S 2024 J. Fluid Mech. 999 A14
[14] Liu R and Ding Z 2020 J. Fluid Mech. 899 A14
[15] Ding Z and Wong T 2017 Phys. Fluids 29 011701
[16] Chattopadhyay S 2021 Phys. Fluids 33 082102
[17] Samanta A 2020 Phys. Fluids 32 064105
[18] Chen C I, Chen C K and Yang Y T 2003 Int. J. Eng. Sci. 41 1313
[19] Closa F, Ziebert F and Raphael E 2012 Math. Model. Nat. Phenom. 7 6
[20] Wasa K 2012 Handbook of sputter deposition technology: fundamentals and applications for functional thin films, nano-materials and MEMS (William Andrew)
[21] Zargar R A 2023 Metal Oxide Nanocomposite Thin Films for Optoelectronic Device Applications (John Wiley & Sons)
[22] Kumar A, Verma C and Thakur A 2023 Corrosion Mitigation Coatings: Functionalized Thin Film Fundamentals and Applications (Walter de Gruyter GmbH & Co KG)
[23] Benney D J 1966 J. Math. Phys. 45 150
[24] Lin S P 1974 J. Fluid Mech. 63 417
[25] Gjevik B 1970 Phys. Fluids 13 1918
[26] Nakaya C 1975 Phys. Fluids 15 1407
[27] Chang H C 1989 Phys. Fluids 1 1314
[28] Kondic L 2003 SIAM Rev. 45 95
[29] Banerjee D, Souslov A and Abanov A 2017 Nat. Commun. 8 1573
[30] Bauer R J and Kerczek C V 1991 J. Appl. Mech. 58 278
[31] Zhang Y and Ding Z 2023 Phys. Rev. Fluids 8 064001
[32] Sheremet M A, Trimbitas R, Grosan T and Pop I 2018 Appl. Math. Mech. -Engl. Ed. 39 1425
[33] Lin J Z, Xia Y and Ku X K 2016 Int. J. Heat Mass Transfer 93 57
[34] Xiong X P, Chen S and Yang B 2017 Appl. Math. Mech. Engl. Ed. 38 585
[35] Nayak A K, Gartia M R and Vijayan P K 2008 Exp. Therm. Fluid Sci. 33 184
[36] Nayak A K, Gartia M R and Vijayan P K 2009 Nuc. Eng. Des. 239 526
[37] Lin J Z, Xia Y and Bao F B 2014 Fluid Dyn. Res. 46 055512
[38] Dero S, Rohni A M, Saaban A and Khan I 2019 Energies 12 4529
[39] Lin J and Yang H 2019 Appl. Math. Mech. Engl. Ed. 40 1227
[40] Bankoff S G, Griffing E M and Schluter R A 2002 Ann. N. Y. Acad. Sci. 974 1
[41] Griffing E M, Bankoff S G and Miksis M J 2006 J. Fluids Eng. 128 276
[42] Gonzalez A and Castellanos A 1996 Phys. Rev. E 53 3573
[43] Tseluiko D, Blyth M G and Papageorgiou D T 2008 J. Fluid Mech. 597 449
[44] Samanta A 2019 Phys. Fluids 31 034109
[45] Uma B and Usha R 2010 Phys. Rev. E 82 016305
[46] Hatami M and Jing D 2020 Nanofluids: mathematical, numerical, and experimental analysis (Academic Press)
[47] Cheng Z and Peng J 2020 Int. J. Heat Mass Transfer 146 118895
[48] Cao Z, Zhao J, Wang Z, Liu F and Zheng L 2016 J. Mol. Liq. 222 1121
[49] Dandapat B S and Mukhopadhyay A 2003 Int. J. Appl. Mech. Eng. 8 379
[50] Mukhopadhyay A and Dandapat B S 2004 J. Phys. D Appl. Phys. 38 138
[51] Mukhopadhyay A, Dandapat B S and Mukhopadhyay A 2008 Int. J. Non-Linear Mech. 43 632
[52] Chattopadhyay S, Subedar G Y, Gaonkar A K, Barua A K and Mukhopadhyay A 2022 Int. J. Non-Linear Mech. 140 103905
[53] Porgar S, Oztop H F and Salehfekr S 2023 J. Mol. Liq. 386 122213
[54] Jia B and Jian Y 2022 Phys. Fluids 34 044104
[55] Wang J, Jia B and Jian Y 2024 Phys. Fluids 36 094101
[56] Verma R, Sharma A, Kargupta K and Bhaumik J 2005 Langmuir 21 3710

[1]	Thermal investigation of water-based radiative magnetized micropolar hybrid nanofluid flow subject to impacts of the Cattaneo-Christov flux model on a variable porous stretching sheet with a machine learning approach Showkat Ahmad Lone, Zehba Raizah, Rawan Bossly, Fuad S. Alduais, Afrah Al-Bossly, and Arshad Khan. Chin. Phys. B, 2025, 34(6): 064401.
[2]	Neural network analysis for prediction of heat transfer of aqueous hybrid nanofluid flow in a variable porous space with varying film thickness over a stretched surface Abeer S Alnahdi and Taza Gul. Chin. Phys. B, 2025, 34(2): 024701.
[3]	Finite element analysis of copper nanoparticles in Boger fluid: Effects of dynamic inter-particle spacing, nanolayer thermal conductivity, nanoparticles diameter, and thermal radiation over a stretching sheet Qadeer Raza, Xiaodong Wang(王晓东), Tahir Mushtaq, Bagh Ali, and Nehad Ali Shah. Chin. Phys. B, 2025, 34(11): 114402.
[4]	Blood-based magnetohydrodynamic Casson hybrid nanofluid flow on convectively heated bi-directional porous stretching sheet with variable porosity and slip constraints Showkat Ahmad Lone, Rawan Bossly, Fuad S. Alduais, Afrah Al-Bossly, Arshad Khan, and Anwar Saeed. Chin. Phys. B, 2025, 34(1): 014101.
[5]	Mixed convectional and chemical reactive flow of nanofluid with slanted MHD on moving permeable stretching/shrinking sheet through nonlinear radiation, energy omission Saleem Nasir, Sekson Sirisubtawee, Pongpol Juntharee, and Taza Gul. Chin. Phys. B, 2024, 33(5): 050204.
[6]	Exact solutions for magnetohydrodynamic nanofluids flow and heat transfer over a permeable axisymmetric radially stretching/shrinking sheet U. S. Mahabaleshwar, G. P. Vanitha, L. M. Pérez, Emad H. Aly, and I. Pop. Chin. Phys. B, 2024, 33(2): 020204.
[7]	Couple stress and Darcy Forchheimer hybrid nanofluid flow on a vertical plate by means of double diffusion Cattaneo-Christov analysis Hamdi Ayed. Chin. Phys. B, 2023, 32(4): 040205.
[8]	Coupled flow and heat transfer of power-law nanofluids on non-isothermal rough rotary disk subjected to magnetic field Yun-Xian Pei(裴云仙), Xue-Lan Zhang(张雪岚), Lian-Cun Zheng(郑连存), and Xin-Zi Wang(王鑫子). Chin. Phys. B, 2022, 31(6): 064402.
[9]	Influences of Marangoni convection and variable magnetic field on hybrid nanofluid thin-film flow past a stretching surface Noor Wali Khan, Arshad Khan, Muhammad Usman, Taza Gul, Abir Mouldi, and Ameni Brahmia. Chin. Phys. B, 2022, 31(6): 064403.
[10]	Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium: A stability analysis Astick Banerjee, Krishnendu Bhattacharyya, Sanat Kumar Mahato, and Ali J. Chamkha. Chin. Phys. B, 2022, 31(4): 044701.
[11]	Reconstruction model for temperature and concentration profiles of soot and metal-oxide nanoparticles in a nanofluid fuel flame by using a CCD camera Guannan Liu(刘冠楠), Dong Liu(刘冬). Chin. Phys. B, 2018, 27(5): 054401.
[12]	An extension of integrable equations related to AKNS and WKI spectral problems and their reductions Xian-Guo Geng(耿献国), Yun-Yun Zhai(翟云云). Chin. Phys. B, 2018, 27(4): 040201.
[13]	Theoretical studies and molecular dynamics simulations on ion transport properties in nanochannels and nanopores Ke Xiao(肖克), Dian-Jie Li(李典杰), Chen-Xu Wu(吴晨旭). Chin. Phys. B, 2018, 27(2): 024702.
[14]	A more general form of lump solution, lumpoff, and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation Panfeng Zheng(郑攀峰), Man Jia(贾曼). Chin. Phys. B, 2018, 27(12): 120201.
[15]	Multiple exp-function method for soliton solutions ofnonlinear evolution equations Yakup Yıldırım, Emrullah Yašar. Chin. Phys. B, 2017, 26(7): 070201.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Instability of nanofluid film flow under external electric field: Linear and weakly nonlinear analysis

Cite this article:

Online attention