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When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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Related Experiment Video

Updated: Feb 24, 2026

Determining 3D Flow Fields via Multi-camera Light Field Imaging
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A switchable 3D liquid-liquid biconvex lens with enhanced resolution using Dean flow.

L Liang1, X Q Zhu, H L Liu

  • 1School of Physics & Technology, Key Laboratory of Artificial Micro/Nano Structure of Ministry of Education, Wuhan University, Wuhan 430072, China. yangyiys@whu.edu.cn.

Lab on a Chip
|August 24, 2017
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Summary

Researchers developed novel three-dimensional (3D) liquid-liquid (L2) biconvex microlenses for enhanced cell imaging. These 3D L2 lenses offer improved resolution and tunable focal lengths for lab-on-a-chip applications.

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Area of Science:

  • Microfluidics and Optics
  • Biomedical Engineering
  • Materials Science

Background:

  • Traditional liquid-liquid (L2) microlenses are limited to two-dimensional (2D) profiles, hindering applications in cell imaging and analysis.
  • Existing 2D microlenses face challenges in effectively imaging and analyzing flowing cells due to their planar nature.

Purpose of the Study:

  • To demonstrate a feasible design for three-dimensional (3D) L2 biconvex microlenses capable of detecting flowing cells.
  • To overcome the limitations of 2D microlenses in cell imaging and analysis systems.

Main Methods:

  • Formation of a 3D L2 biconvex lens using Dean flow within auxiliary curved microchannels.
  • Modulation of lens shape and focal length by adjusting liquid flow rates.
  • Experimental measurement of focal length modulation (435 μm range) and numerical aperture (0.175-0.198).

Main Results:

  • Successful achievement of 3D light focusing with tunable focal lengths.
  • Demonstrated a 1.79-fold improvement in resolution compared to traditional 4×/0.1 objective lenses.
  • Successfully imaged mouse myeloma cells (sp2/0) and acute promyelocytic leukemia cells (NB4) with a rapid time response of approximately 2.7 ms.

Conclusions:

  • The developed 3D L2 biconvex microlenses offer significant advantages for high-resolution cell imaging and analysis.
  • These microlenses show great potential for integration into lab-on-a-chip systems for advanced biological applications.
  • The tunable nature and improved resolution make them a promising tool for future microfluidic imaging systems.