6. (Maestro) A Dp = 10 µm-diameter particle of density = 1 g cm^-3 is being carried by an airs

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Question

6. (Maestro) A $D_p = 10 \text{ µm}$-diameter particle of density $\rho_p = 1 \text{ g cm}^{-3}$ is being carried by an airstream with velocity of $u = 100 \text{ cm s}^{-1}$ and dynamic viscosity of $\mu = 1.8 \times 10^{-5} \text{ kg m}^{-1} \text{s}^{-1}$ in the $x$ direction. The stream enters a device where the particle immediately acquires a charge of 100 electrons (the charge of a single electron is $e = 1.602 \times 10^{-19} \text{ C}$) and in which there exists an electric field of constant potential gradient $E_y = 10^4 \text{ V m}^{-1}$. Assume $C_c \approx 1$ and neglect gravitational and buoyancy forces. Assume the particle's Reynolds number satisfies $Re < 0.1$ so that the Stokes law can be used. Determine (a) the characteristic time of the particle and (b) the x and y coordinate location of the particle at any downstream location in the device as a function of time.

          6. (Maestro) A $D_p = 10 \text{ µm}$-diameter particle of density $\rho_p = 1 \text{ g cm}^{-3}$ is being carried by an
airstream with velocity of $u = 100 \text{ cm s}^{-1}$ and dynamic viscosity of $\mu = 1.8 \times 10^{-5} \text{ kg m}^{-1} \text{s}^{-1}$
in the $x$ direction. The stream enters a device where the particle immediately acquires a charge
of 100 electrons (the charge of a single electron is $e = 1.602 \times 10^{-19} \text{ C}$) and in which there exists
an electric field of constant potential gradient $E_y = 10^4 \text{ V m}^{-1}$. Assume $C_c \approx 1$ and neglect
gravitational and buoyancy forces. Assume the particle's Reynolds number satisfies $Re < 0.1$ so
that the Stokes law can be used. Determine (a) the characteristic time of the particle and (b) the
x and y coordinate location of the particle at any downstream location in the device as a function
of time.

6. (Maestro) A Dp = 10 µm-diameter particle of density = 1 g cm^-3 is being carried by an
airstream with velocity of u = 100 cm s^-1 and dynamic viscosity of μ = 1.8 × 10^-5 kg m^-1s^-1
in the x direction. The stream enters a device where the particle immediately acquires a charge
of 100 electrons (the charge of a single electron is e = 1.602 × 10^-19 C) and in which there exists
an electric field of constant potential gradient Ey = 10^4 V m^-1. Assume Cc ≈ 1 and neglect
gravitational and buoyancy forces. Assume the particle's Reynolds number satisfies Re < 0.1 so
that the Stokes law can be used. Determine (a) the characteristic time of the particle and (b) the
x and y coordinate location of the particle at any downstream location in the device as a function
of time.

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