Send over 2000 e-mails with PHP mail function - php

Question

I am trying to create a system that sends an e-mail to everyone of the users of my webpage.
It seems though that there are too many emails - about 2400 emails, to send for it to work.
Is there a smarter way, or a way to send 10 at a time or something like that?
Here is my code:
<?php
include('../../includingThis.php');
$fra = "ME <me#me.com>";
$emne = "";
$sql = "SELECT * FROM sendThese WHERE id=1";
if ($result = mysqli_query($con, $sql)) {
while($row = mysqli_fetch_assoc($result)) {
$emne = $row["subject"];
$message = $row["message"];
$mailsHere = $row["mailsHere"];
$til = explode(",", $mailsHere);
}
}
$besked = file_get_contents('sendThese.html');
$besked = str_replace("%%message%%", $message, $besked);
// HEADERS
$headers = "MIME-Version:1.0\r\n";
$headers .= "Content-type: text/html; charset=UFT-8\r\n";
$headers .= "From: ".$fra."\r\n";
// Mail til ejeren af siden
$mailsSend = 0;
foreach ($til as $value) {
mail($value,$emne,$besked,$headers);
$mailsSend++;
echo $value . "<br>";
sleep(2);
}
// Sender vi brugeren videre til en side
//header("Location: index.php");
echo "Done - " . $mailsSend . " e-mails sendt.";
die();
?>