Range of effectiveness of hydraulic diameter model as an analytical solution for rectangular microchannels

Area of Science:

• Fluid dynamics
• Microfluidics
• Engineering

Background:

• Spontaneous capillary flow in rectangular microfluidic channels is crucial for many microfluidic applications.
• Exact solutions for flow in rectangular channels involve complex infinite sum terms and depend on the channel's depth-width ratio (ε).
• Previous approximations were limited to ε values below 1 or 2.

Purpose of the Study:

• To propose a novel conversion equation relating the hydraulic diameter (HD) model to the rectangular-channel (RC) model.
• To provide a more accurate analytical tool for capillary flow in microfluidic devices with rectangular cross-sections.
• To quantify the deviation between HD and RC models based on the depth-width ratio.

Main Methods:

• Development of a conversion equation ($$) linking the HD and RC models.
• Conducting experimental studies using ethanol solutions in rectangular microfluidic channels.
• Comparing flow analyses derived from both the RC and HD models.

Main Results:

• The conversion equation ($$) is dependent on the depth-width ratio ($$).
• The HD and RC models show agreement at $$.
• Significant deviations ($$) between the models occur for $$.

Conclusions:

• The proposed conversion equation offers a more accurate method for analyzing capillary flow in rectangular microfluidic channels.
• The study highlights the limitations of the hydraulic diameter model for non-circular microchannels, especially at higher depth-width ratios.
• Accurate modeling of microfluidic flow is essential for optimizing device performance in various scientific and engineering fields.