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Tribology Letters

, 66:66 | Cite as

Correction to: A Model for Lubricant Transfer from Media to Head During Heat-Assisted Magnetic Recording (HAMR) Writing

  • Siddhesh V. Sakhalkar
  • David B. Bogy
Correction
  • 285 Downloads

1 Correction to: Tribol Lett (2017) 65:166  https://doi.org/10.1007/s11249-017-0952-3

The original version of this article unfortunately contained an error in the following equations. The corrected equation (1) is given below:
$$ \begin{aligned} & \frac{{\partial h_{\rm d} }}{\partial t} + u_{\rm d} \frac{{\partial h_{\rm d} }}{\partial x} + \frac{\partial }{\partial x}\left[ { - \frac{{h_{\rm d}^{3} }}{{3\mu_{\rm d} }}\frac{{\partial p_{\rm d} }}{\partial x} + \frac{{h_{\rm d}^{2} }}{{2\mu_{\rm d} }}\tau_{x,{\rm d}} } \right] \\ & \quad + \frac{\partial }{\partial y}\left[ { - \frac{{h_{\rm d}^{3} }}{{3\mu_{\rm d} }}\frac{{\partial p_{\rm d} }}{\partial y} + \frac{{h_{\rm d}^{2} }}{{2\mu_{\rm d} }}\tau_{y,{\rm d}} } \right] + \frac{{\dot{m}_{\rm d} }}{\rho } = 0 \\ \end{aligned} $$
(1)
The corrected equations from Section 2.1 are:
$$ \begin{aligned} p_{\rm lap}{\varvec{n}} & = ( - \gamma \nabla \cdot \varvec{n})\varvec{n} = (\gamma \nabla^{2} h)\varvec{n} \\\varvec{\tau}& \varvec{ = }\nabla \gamma - (\nabla \gamma \cdot \varvec{n})\varvec{n} \\ \end{aligned} $$
The corrected terms in equations (9), (10) and the corrected equations (11), (12) are given below:
$$ \mu_{\rm d}^{*} = \mu_{0} \mu_{\rm d} $$
(9)
$$ S \equiv \frac{{2\mu_{0} L^{2} \dot{m}_{\rm d} }}{{h_{0,{\rm d}}^{2} c\varDelta T_{\rm d} \rho }} $$
(10)
$$ \begin{aligned} & \frac{{\partial h_{\rm d} }}{\partial t} + C_{u} \frac{{\partial h_{\rm d} }}{\partial x} + \frac{\partial }{\partial x}\left[ {\frac{{h_{\rm d}^{3} }}{{\mu_{\rm d} }}\frac{{\partial \pi_{\rm d} }}{\partial x} - \frac{{h_{\rm d}^{2} }}{{\mu_{\rm d} }}\frac{{\partial T_{\rm d} }}{\partial x}} \right] \\ & \quad + \frac{\partial }{\partial y}\left[ {\frac{{h_{\rm d}^{3} }}{{\mu_{\rm d} }}\frac{{\partial \pi_{\rm d} }}{\partial y} - \frac{{h_{\rm d}^{2} }}{{\mu_{\rm d} }}\frac{{\partial T_{\rm d} }}{\partial y}} \right] + S_{\rm d} = 0 \\ \end{aligned} $$
(11)
$$ \begin{aligned} & \frac{{\partial h_{\rm s} }}{\partial t} + \frac{\partial }{\partial x}\left[ {\frac{{h_{\rm s}^{3} }}{{\mu_{\rm s} }}\frac{{\partial \pi_{\rm s} }}{\partial x} - \frac{{h_{\rm s}^{2} }}{{\mu_{\rm s} }}\frac{{\partial T_{\rm s} }}{\partial x}} \right] \\ & \quad + \frac{\partial }{\partial y}\left[ {\frac{{h_{\rm s}^{3} }}{{\mu_{\rm s} }}\frac{{\partial \pi_{\rm s} }}{\partial y} - \frac{{h_{\rm s}^{2} }}{{\mu_{\rm s} }}\frac{{\partial T_{\rm s} }}{\partial y}} \right] + S_{\rm s} = 0 \\ \end{aligned} $$
(12)

These correct equations were used in all calculations in the original paper, so none of the numerical simulations or conclusions based on them need to be changed.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Computer Mechanics Laboratory, Department of Mechanical EngineeringUniversity of California at BerkeleyBerkeleyUSA

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