Acoustic force spectroscopy (AFS) is a technique used to apply and measure forces on small particles, like microspheres, by utilizing sound waves. Here's a basic understanding of how forces are exerted on microspheres during AFS:

Mechanism of Acoustic Forces

1. Acoustic Waves: In AFS, an acoustic field, often an ultrasonic wave, is used. These waves can exert forces on small particles suspended in a fluid.

2. Standing Wave Formation: When an acoustic wave reflects back and forth in a confined space, it can form a standing wave. This wave has alternating nodes and antinodes of pressure.

3. Radiation Pressure: Microspheres placed in the path of these standing waves experience a force known as acoustic radiation force. This is due to the pressure gradient inherent in the standing wave pattern.

4. Primary Acoustic Radiation Force: This force is the result of the interaction between the incident wave and the scattered wave. It acts on the microspheres to move them towards the nodes or antinodes, depending on factors like particle size and density relative to the surrounding medium.

5. Secondary Acoustic Forces: Apart from the primary forces, particles can also experience secondary forces due to particle-particle interactions, generally leading to aggregation if they are close enough.

Factors Affecting the Forces

• Particle Size and Material: The magnitude and direction of the force depend on the size and acoustic properties (e.g., density and compressibility) of the microspheres.

• Frequency and Amplitude of the Acoustic Wave: Higher frequencies and amplitudes usually result in stronger forces.

• Medium Properties: The viscosity and density of the medium surrounding the microspheres also have significant effects on the resulting forces.

Applications

• Cell Manipulation: Acoustic forces are non-invasive and can handle biological samples gently, making them excellent for applications like cell sorting or manipulation.

• Material Science: AFS is useful for studying the mechanical properties of various materials at the microscale.

For a deeper dive, including mathematical formulations and experimental setups, references from specialized journals or textbooks on acoustic force spectroscopy would be beneficial. A good starting point can be found through specialized publications on acoustic technologies or biophysics.

For more detailed resources or applications, you might want to refer to academic articles or reviews available through platforms like PubMed or Google Scholar.