# Energy-Efficient AC Electothermal Microfluidic Pumping via Localized External Heating
## 1 Introduction  
AC Electroosmotic (ACEO) flow is a microfluidic technique that utilizes a time-varying electric field between electrodes to induce fluid movement [1, 2, 3, 4, 5]. By applying an alternating-current (AC) field between two electrodes, ACEO generates both normal and tangential forces within the channel. ACEO forms an electrical double layer (EDL) along the electrodes, where alternating polarization creates ionic movement and fluid flow. A benefit of this process is that lower voltages than direct-current (DC) electroosmosis are required, offering a more efficient means to manipulate fluid dynamics by adjusting the waveform, voltage, and frequency of the applied electric field [1, 6]. As a result, ACEO has proven effective in various microfluidic applications such as particle manipulation, cell sorting, and fluid mixing and has played a critical role in developing advanced lab-on-a-chip devices [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. ACEO can significantly enhance thermal management in semiconductor applications by regulating cooling fluid flow across densely packed chips. What may follow implementationfor high-power devices such as GPUs and CPUs is more efficient heat dissipation from critical areas, preventing both overheating and the cessation of valuable work due to such [14; 15; 16]. ACEO's low voltage and precise control make it an ideal solution for integrating compact, efficient thermal management systems into modern semiconductor packaging. AC Electrothermal Flow (ACET) can further extend the capabilities of microfluidic devices by introducing temperature gradients created through Joule heating, which interact with the electric field to drive fluid flow [17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28]. These gradients cause fluid properties such as conductivity and permittivity variations, resulting in fluid motion even in electrically diverse environments. ACET offers significant value for microfluidic tasks such as mixing, pumping, and concentrating chemical samples especially in lab-on-a-chip systems where mechanical pumps are impractical. Unlike ACEO, ACET has been shown to be effective in a wide range of frequencies, whereas ACEO is more common at low frequencies and relatively low salt concentrations [22; 29]. The precision of ACET in manipulating fluids at the micro-scale makes it indispensable for various biomedical and industrial applications. [PERSON] et al. showed the ACET phenomenon works well for pumping non-Newtonian fluid, like blood, in ring electrode-equipped 3D microfluidic devices [30]. Their devices pump non-Newtonian fluid more efficiently than Newtonian fluid. [PERSON] et al. used microfluidics devices for mixing non-Newtonian fluid using ACET phenomenon [31], demonstrating that the shear-dependent viscosity of the non-Newtonian fluid influences both mixing and flow rate. ACET research has importance for improving fluid dynamics and thermal management system design within chip design, processes, and applications. Examples of processes that can be positively illuminated are in performance optimization, particularly in semiconductor cooling, by modeling the interactions between electric fields, temperature gradients, and fluid properties [1; 6; 17; 19; 23]. Computational tools also help researchers explore scaling effects and predict the challenges of integrating ACET into new applications. Through the ability to enable improved versatility in fluid control, ACET offers significant potential for enhancing microfluidic systems in the semiconductor industry, which is crucial for managing heat dissipation in densely packed chips and ensuring the consistent performance of MEMS [1; 2; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 6  
where \(\rho_{r}\) is the density of fluid at \(T_{0}=273.15\) K, \(\rho\) is the temperature-dependent fluid density, and \(g\) is gravitational acceleration.